Products ranking through two-stage online customer reviews information

Abstract

In the process of product ranking considering online reviews, they often are based on initial reviews and do not consider additional consumer reviews, but additional review information can sometimes directly affect consumers’ final decisions. To fully characterize the rich emotional preferences of consumers embedded in two-stage online customer reviews information, considering consumers’ individual preferences and product objective evaluation information, we construct a combination weighting method to calculate comprehensive weights of product attributes, and then exploit the sentiment analysis technique, interval-valued probabilistic linguistic term set (IVPLTS) and preference ranking organization method for enrichment evaluations (PROMETHEE) to establish a products ranking method based on compound reviews, and then we use it to identify the sentiment orientation of reviews and the results. Finally, a real-life case illustrates a real-world application of the proposed method.

Keywords

Product ranking additional review information sentiment analysis interval-valued probabilistic linguistic term set customer reviews information

1. Introduction

With the rapid development of e-commerce, online sales channels have become the main channel for business sales [3]. When consumers purchase products, they usually browse review information about alternative products, which can finally influence their purchasing decision [10]. In 2014, a survey of 2,458 consumers of automobiles, beauty products, and smartphones by Google and Ogilvy showed that product word of mouth had the greatest influence on purchasing decisions, accounting for 74%. Consumers post a large amount of review information about products and services on shopping platforms. Most of these reviews are in the form of structured or unstructured text which is rich in valuable information, including consumers’ emotions, attitudes, and preferences. For platform merchants, focusing on points where consumers often complain about bad reviews can help them promptly identify consumer demands and weaknesses in their products and services. In addition, analysis of online customer reviews can also help companies with product owner identification and competitive analysis [24]. In particular, for service companies, mining customer demand contained in online customer reviews can help them optimize the configuration of their service elements [32]. For potential consumers, the information contained in online customer reviews from consumers who have already purchased can help them gain a more comprehensive and objective understanding of the products. Research on online customer reviews has rich theoretical value and practical significance. Mining information within online customer reviews has promoted the advancement of text analysis technology and driven the development of online customer reviews sentiment analysis technology, product feature extraction, product recommendation algorithms, and other technologies. Research on online customer reviews can help merchants manage reviews more appropriately, and research on product recommendation methods through online customer reviews can help consumers avoid browsing a lot of reviews but make faster, more rational purchasing decisions. The research on online customer reviews, especially the research on product recommendation methods through online customer reviews, has become a hot research topic for many scholars.

Thanks to the rapid development of communication technology, online customer reviews are published in a timely and convenient manner but this also causes redundancy of review information which will lead to information overload for the viewers of online customer reviews. Therefore, it is necessary for shopping platform companies, as management of online customer reviews, to effectively deal with review information and reduce the burden of potential consumers browsing too much review information during the shopping process. Shopping platform companies need to deeply analyze online customer reviews, explore consumers’ emotions and preference information contained within, and develop more reasonable, convenient, and effective product recommendation methods to help potential consumers make purchasing decisions that can reduce the cognitive dissonance caused by browsing too much review information. Therefore, how to rank products through online customer reviews has become a topic worthy of discussion.

At present, scholars’ research on product ranking methods based on online customer reviews is still relatively few. Existing research mainly focuses on the following two aspects: information description and fusion model based on online customer reviews and product ranking method through online customer reviews. The weighted averaging (WA) operator [9] and the ordered weighted averaging (OWA) operator [31] are the two most commonly used operators for information fusion in the early days. In later research, scholars have proposed many other operators based on these two operators, such as the intuitionistic fuzzy weighted averaging (IFWA) operator and an intuitionistic fuzzy ordered weighted averaging (IFOWA) operator [30], which overcome the information distortion caused by the first two operators in the operation process. Besides, the problem of ranking methods based on online customer reviews can be modeled as a multi-attribute decision making (MADM) problem. After online customer reviews are fused, this problem can be solved with many classical MCDM theories.

Currently, the information description and fusion model under online customer reviews for product ranking mainly include fusion model based on the construction of weighted directed graph and fusion model based on fuzzy set theory. In the aspect of online customer reviews information fusion based on fuzzy set theory, Liu et al. [18, 19] proposed a method based on the sentiment analysis technique and the intuitionistic fuzzy set theory to rank the products through online reviews. In their method, the performance of an alternative product is represented by intuitionistic fuzzy number and aggregated by intuitionistic fuzzy weighted averaging (IFWA). Bi et al. [2] considered the accuracy rates of sentiment analysis results of online customer reviews and used interval type-2 fuzzy numbers to represent the results. Peng et al. [22] proposed a fuzzy PROMETHEE to rank alternative products based on online customer reviews in which triangular fuzzy numbers are used to represent linguistic variables. Fu et al. [7] used interval-valued Pythagorean fuzzy (IVPF) to represent the interval-valued sentiment and proposed an IVPF-weighted Heronian mean operator to aggregate the attribute information. These information descriptions and fusion models can represent uncertain information well, but inevitably cause some emotional information loss during information fusion. For example, the method [18, 19] will cause the loss of neutral sentiment orientations when converting sentiment analysis results into intuitionistic fuzzy numbers. In the aspect of online customer reviews information description and fusion based on the construction of weighted directed graph, scholars have conducted many meaningful studies and explorations. Guo et al. [8] proposed a method to mine and integrate textual reviews and numerical information. In their method, the directed graph model is used for information fusion and improved PageRank method is deployed to calculate the node value. Li et al. [14] used a hierarchical structure-based model to propagate and reassign the aspect-based comparative opinions and applied graph-based ordering algorithms to get comparison results. Kpiebaareh et al. [11] proposed a generic graph-based opinion mining and analysis method for product design improvement based on online customer reviews. Zhang et al. [34] propose an improved label propagation algorithm with a propagation intensity and an automatic filtering mechanism to find candidate spammer groups based on the constructed reviewer relationship graph. The advantage of information fusion methods based on the construction of weighted directed graph is the ability to integrate heterogeneous information and intuitively reflect the comparative advantages among alternative products. [6] can intuitively reflect the comparative network and comparative advantages However, this kind of online customer reviews information description and fusion method cannot describe the sentiment orientation under each attribute of the product in detail.

In the aspect of product ranking methods based on online customer reviews, scholars have carried out much valuable and meaningful research. Li and Lai [14] proposed a social appraisal framework to support a user’s online purchase decisions in the micro-blogosphere that integrates the methodologies and techniques of social network analysis (SNA), intuitionistic fuzzy sets (IFSs), and the technique for order preference by similarity to the ideal solution (TOPSIS). Mi et al. [20] established grey 2-tuple linguistic model to combine online reviews with ratings. However, in this method, experts are required to evaluate greyness for each review, which seems to be difficult and time-consuming when faced with a large number of reviews. To make the tourism product selection process quicker, Liang et al. [15] proposed a novel distribution linguistic VIKOR (DL-VIKOR) method to solve the problem of selecting tourism products with online reviews through data processing technology. Compared to the previous models, the model processed the text data into distribution linguistic evaluation which can avoid information loss or distortion. Liu et al. [18] proposed a method based on the sentiment analysis technique and the intuitionistic fuzzy set theory to rank the products through online reviews. Taking the neutral sentiment orientations and the number of reviews of different products into consideration, Liu et al. [19] proposed another method for ranking products through online customer reviews based on sentiment classification and the interval-valued intuitionistic fuzzy Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS). Wu et al. [27] proposed a novel group consensus-based travel destination evaluation method with online reviews to deal with the increasing tourism products and group tourists. The method used sentiment matrix with the percentage distribution to represent decision opinions and designed a minimum adjustment cost feedback mechanism to reach group consensus. Then, by aggregating the percentage distribution with the weight vector of attributes, the ranking of all alternatives can be obtained.

In general, previous studies either transformed the review information into fuzzy numbers or aggregated the review information with the help of graphs. Few studies have used probabilistic linguistic term sets (PLTS) to characterize review information. In addition, previous studies ignored the impact of additional review information on the final product ranking results and therefore did not consider additional reviews in the modeling process. However, this paper uses PLTS to characterize review information and consider the effect of additional reviews. Also, we propose a comprehensive weight determination method that considers both subjective weight information and objective weight information.

According to the above discussion and analysis, although they have proposed effective methods to solve relevant problems, there are still some limitations.

(1)
Most of the existing research on product ranking methods based on online customer reviews is based on initial reviews and does not take additional customer reviews into account which is not reasonable. This is because after using a product for a while, consumers have a deeper understanding of the product and give more comprehensive and objective information about the product, so it is very necessary to consider additional reviews for product recommendations.
(2)
Some of the sentiment information has been lost in the process of quantifying consumer reviews in previous studies, so there is a need to propose a new way to quantify and characterize consumers’ emotional orientation embedded in Online customer reviews.
(3)
In most of the existing studies, the weights of product feature either subjectively determined by consumers or determined by external evaluation information contained in Online customer reviews. But when a consumer wants to buy a product from several alternatives, the consumer may have personal preference for product features according to his/her subjective evaluation. And, because the consumer has limited knowledge of the product, he/she needs to browse and analyze the Online customer reviews of the product to help him/her determine the importance of each product feature. A single subjective or objective weight determination method cannot determine the optimal weight.

To address the problems of existing studies, we propose a novel IVPLTS-PROMETHEE method to solve the product ranking problem through online customer reviews. The main contribution of this paper can be concluded as follows:

(1)
This paper takes both initial and additional customer reviews into consideration and proposed a novel IVPLTS-PROMETHEE method to rank products.
(2)
An interval-valued probabilistic linguistic term set is proposed to characterize the rich emotional orientation of consumers, and further give some of its properties.
(3)
Considering consumers’ individual preferences and product objective evaluation information, a combination weighting method is proposed to calculate the comprehensive weights of product features that consider individual preferences and collective external evaluation simultaneously.

The remainder of this paper is organized as follows: Some concepts are introduced in Section 2. In Section 3, based on sentiment analysis of online customer reviews, IVPLTS is proposed to characterize two-stage online customer reviews, and then a combination weighting method is proposed. After that, a novel IVPLTS-PROMETHEE product selection method is proposed to determine the ranking of alternative products. A real-world case study is furnished in Section 4 to illustrate how the proposed method can be applied. The paper concludes with some remarks in Section 5.
2. Related concepts

2.1. Linguistic term sets (LTS)

To present the decision maker’s qualitative judgment about a decision event, Zadeh [33] first proposed the linguistic variable, after which two probabilistic linguistic sets (LTS). $S = {s_{α} | α = 0, 1, \dots, τ}$ , $S = {s_{α} | α = - τ, \dots, - 1, 0, 1, \dots, τ}$ have been most widely used, where $τ$ is a positive integer, $s_{α}$ represents the possible values of the linguistic variable. The set must satisfy the following two conditions.

(1)
The set is ordered: $s_{α} > s_{β}$ , if $α > β$
(2)
There is a negation operator: $n e g (s_{α}) = s_{β}$

Note: To prevent information loss in the operation process, Xu [29] extended the discrete LTS $S = {s_{α} | α = 0, 1, \dots, τ}$ to a continuous LTS $S = {s_{α} | α = 0, 1, \dots, τ}$ , where if $s_{α} \in S$ , $s_{α}$ is called an original linguistic term; otherwise, $s_{α}$ is called a virtual linguistic term. In practical application, the original linguistic term is provided for experts to make decisions and the virtual one is used for calculation.
2.2. Hesitant fuzzy linguistic term set (HFLTS)

Considering that humans may hesitate among several options in real decision-making situations, Rodrigue et al. [23] presented the concept of HFLTS.

Definition 1.
Let $S = {s_{α} | α = 0, 1, \dots, τ}$ be an LTs, then an HFLTS, $H_{S}$ is an ordered finite subset of consecutive lots of $S$ .
Example 1.
For an LTs, $S = {s_{0} = very bad, s_{1} = b a d, s_{2} = m e d i u m, s_{3} = g o o d, s_{4} = very good}$ , it is easy for us to get two different HFLTS, $H_{S}^{1} = {s_{0}, s_{1}}$ , $H_{S}^{2} = {s_{2}, s_{3}, s_{4}}$ .

However, HFLTS fails when people use a non-consecutive linguistic term set to describe the evaluation objects. To better handle this kind of uncertain situation, Wang [26] proposed the concept of EHFLTS.
2.3. Extended hesitant fuzzy linguistic term set (EHFLTS)

Definition 2.
Suppose that $S = {s_{α} | α = 0, 1, \dots, τ}$ is an LTs, then an EHFLTS, $H_{S}^{E}$ , is an ordered finite subset of linguistic terms of $S$ which can be represented by $H_{S}^{E} = {s_{i} | s_{i} \in S}$ . $H_{S}^{E}$ is called an extended hesitant fuzzy linguistic term set (EHFLTS) [26].
Remark 1.
It should be noted that HFLTS is a special case of EHFLTS and EHFLTS is a general form of the HFLTS. At the same time, EHFLTS can take all possible linguistic values into account during the process of information aggregation and model more complex decision-making problems.
2.4. Probabilistic linguistic term sets (PLTS)

In real-world decision-making situations, people may express their preferences in different linguistic terms and assign them to different degrees of importance. However, the HFLTS and EHFLTS models consider each linguistic term to be equally important and assign them with the same weight, which is not following reality. Therefore, for the above situation, Pang et al. [21] introduced the concept of PLTS.

Definition 3.
Let $S = {s_{α} | α = 0, 1, \dots, τ}$ be an LTS, a PLTS can be defined as:
$\begin{aligned} L (p) = {L^{(k)} (p^{(k)}) ∣ L^{(k)} \in S, p^{(k)} ⩾ 0, k = 1, 2, \dots, # L (p), \sum_{k = 1}^{# L (p)} p^{(k)} ⩽ 1} \end{aligned}$
(1)

Where, $L^{(k)} (p^{(k)})$ is the linguistic term $L^{(k)}$ associated with the probability $p^{(k)}$ , and $# L (p)$ represents the number of LTS in $L (p)$ . If $\sum_{k = 1}^{# L (p)} p^{(k)} = 1$ , the PLTS has the complete probability distribution about all LTS. If $\sum_{k = 1}^{# L (p)} p^{(k)} < 1$ , the probability distribution of LTS in the PLTS is incomplete which means that partial ignorance exists in the PLTS. If $\sum_{k = 1}^{# L (p)} p^{(k)} = 0$ , it means that the probability distribution of LTS is completely unknown.
Definition 4.
Let $L (p)$ be a PLTS with $\sum_{k = 1}^{# L (p)} p^{(k)} < 1$ , then a normalized PLTS is defined by $\bar{L} (p) = {L^{(k)} ({\bar{p}}^{(k)}) ∣ k = 1, 2, \dots, # L (p)}$ , where:
$\begin{aligned} {\bar{p}}^{(k)} = p^{(k)} / \sum_{k = 1}^{# L (p)} p^{(k)}, k = 1, 2, \dots, # L (p) \end{aligned}$
(2)

It should be noted that assigning unknown probabilities to linguistic terms in an average way is the most common and primitive way.
Definition 5.
Assume that there are two different normalized PLTS $L_{1} (p)$ and $L_{2} (p)$ , $L_{1} (p) = {L_{1}^{(k)} (p_{1}^{(k)}) ∣ k = 1, 2, \dots, # L_{1} (p)}$ , $L_{2} (p) = {L_{2}^{(k)} (p_{2}^{(k)}) ∣ k = 1, 2, \dots, # L_{2} (p)}$ , and let $L_{1} (p) = # L_{2} (p)$ . Furthermore, we assume that $L_{1} (p)$ and $L_{2} (p)$ are the ordered PLTS. The deviation between the PLTSs $L_{1} (p)$ and $L_{2} (p)$ is expressed by the following equation:
$\begin{aligned} d (L_{1} (p), L_{2} (p)) = \sqrt{\sum_{k = 1}^{# L_{1} (p)} (p_{1}^{(k)} r_{1}^{(k)} - p_{2}^{(k)} r_{2}^{(k)})^{2} / # L_{1} (p)} \end{aligned}$
(3)

Where, $r_{1}^{(k)}$ and $r_{2}^{(k)}$ are the subscripts of the linguistic terms $L_{1}^{(k)}$ and $L_{2}^{(k)}$ respectively.
Definition 6.
Let $L (p) = {L^{(k)} (p^{(k)}) ∣ k = 1, 2, \dots, # L (p)}$ be a PLTS and $r^{(k)}$ be the subscript of the linguistic term $L^{(k)}$ . Then the score of $L (p)$ is defined as:
$\begin{aligned} E (L (p)) = s_{\bar{α}} \end{aligned}$
(4)

Where, $\bar{α} = \sum_{k = 1}^{# L (p)} r^{(k)} p^{(k)} / \sum_{k = 1}^{# L (p)} p^{(k)}$ .

For two PLTSs $L_{1} (p)$ and $L_{2} (p)$ , if $E (L_{1} (p)) > E (L_{2} (p))$ , then $L_{1} (p) > L_{2} (p)$ ; if $E (L_{1} (p)) < E (L_{2} (p))$ , then $L_{1} (p) = L_{2} (p)$ ; if $L_{1} (p) < L_{2} (p)$ , according to Pang’s method, we should further calculate the deviation degree $σ (L (p))$ of $L_{1} (p)$ and $L_{2} (p)$ , where:
$\begin{aligned} σ (L (p)) = {(\sum_{k = 1}^{# L (p)} {(p^{(k)} (r^{(k)} - \bar{α}))}^{2})}^{1 / 2} / \sum_{k = 1}^{# L (p)} p^{(k)} \end{aligned}$
(5)

For two PLTSs $L_{1} (p)$ and $L_{2} (p)$ , with $E (L_{1} (p)) = E (L_{2} (p))$ , if $σ (L_{1} (p)) > σ (L_{2} (p))$ , then $L_{1} (p) < L_{2} (p)$ ; if $σ (L_{1} (p)) < σ (L_{2} (p))$ , then $L_{1} (p) > L_{2} (p)$ ; if $σ (L_{1} (p)) = σ (L_{2} (p))$ , then $L_{1} (p)$ is indifferent to $L_{2} (p)$ .

Pang et al. [21] first proposed the concept of the score of PLTS, Wu et al. [28] further introduced a fresh score function of PLTS and proved that the proposed score function is better than the previous score function. The score function is shown as follows.
Definition 7.
Let
$\begin{aligned} L (p) = {L^{(k)} (p^{(k)}) ∣ L^{(k)} \in S, p^{(k)} ⩾ 0, k = 1, 2, \dots, # L (p), \sum_{k = 1}^{# L (p)} p^{(k)} ⩽ 1} \end{aligned}$

be a PLTS based on $S = {s_{α} | α = - τ, \dots, 0, \dots, τ}$ and $α^{(l)}$ be the subscript of $L (p)$ , then the score function of $L (p)$ is
$\begin{aligned} E (L (p)) = \sum_{l = 1}^{# L (p)} (\frac{α^{(l)} + τ}{2 τ} p^{(l)}) / \sum_{l = 1}^{# L (p)} p^{(l)} \end{aligned}$
(6)
2.5. Preference ranking organization method for enrichment evaluations (PROMETHEE)

Preference ranking organization method for enrichment evaluations (PROMETHEE) is a multi-attribute decision-making method based on the priority relationship [25]. Based on the pairwise comparison of the schemes, it fully considers the decision makers’ preference of all attributes, making the evaluation results more convincing. The main steps of the method are as follows: (1) Construct an evaluation function matrix. Let $A = {A_{1}, \dots, A_{i}, \dots, A_{n}}$ be the set of alternatives, $C = {C_{1}, \dots, C_{j}, \dots, C_{m}}$ be the set of attributes, $ω = {ω_{1}, \dots, ω_{j}, \dots, ω_{m}}$ be the set of attribute weights. Then, according to decision makers’ evaluation values, an evaluation matrix is available; (2) To determine the preference function Let $P$ be the preference function which indicates the priority between two different alternatives. For example, $P_{j} (A_{i}, A_{s})$ means the priority of $A_{i}$ over $A_{s}$ under attribute $C_{j}$ ; (3) Determine the priority index. In this method, the priority index is defined as $H (A_{i}, A_{s}) = \sum_{j = 1}^{m} ω_{j} P_{j} (A_{i}, A_{s})$ which represents the priority index of $A_{i}$ over $A_{s}$ ; (4) Calculate the outflow flow, inflow flow, and net flow of the alternatives. Outflow flow, inflow flow, and net flow are defined as $Φ^{+} (A_{i})$ , $Φ^{-} (A_{i})$ and $Φ (A_{i})$ respectively; (5) Rank the options according to alternatives’ net flow value. There are six forms of preference functions in the PROMETHEE method, which are general guidelines, U-shaped guidelines, Linear guidelines, multi-level guidelines, Linear non-differentiable interval criteria, and Gaussian criteria, respectively.

3. An interval-valued probabilistic linguistic PROMETHEE method for products ranking

Considering that most existing studies do not take additional customer reviews into account, we propose a novel IVPLTs-PROMETHEE product ranking method through online customer reviews taking initial Online customer reviews and additional online customer reviews into consideration simultaneously. The proposed product ranking method has a clear decision-making process, shown in Figure 1. And the main steps of this method can be concluded as follows:

Step 1. Online review information acquisition;

Step 2. Online review preprocessing and feature extraction;

Step 3. Sentiment analysis and emotional information fusion;

Step 4. Calculate comprehensive attribute weights;

Step 5. Product ranking by IVPLTS-PROMETHEE method.

We’ll expand around these steps in more detail in the following sections.

Figure 1.

Flow chart of product selection method considering sentiment intensity of additional online reviews.

3.1. Problem description

During the process of online shopping, it refers to the decision makers or buyers, alternative products, and Online customer reviews of the products containing product feature information. It is said that the product ranking problem is a typical multi-attribute decision problem (MADM) [17]. In this problem, there exist the elements of products, product features, and Online customer reviews on alternative products. Products are treated as alternatives and product key features are attributes. According to the above analysis, to describe the product ranking decision problem through Online customer reviews, some symbols and variables are shown below.

(1)
$A = {A_{1}, \dots A_{i}, \dots, A_{n}}$ , $B = {b_{1}^{t}, \dots, b_{i}^{t}, \dots, b_{n}^{t}}$ stand for the set of alternative products that consumers care about; and number of initial reviews of each alternative in $t$ stage, respectively.
(2)
$F = {f_{1}, \dots, f_{j}, \dots, f_{m}}$ , $D = {D_{1}, \dots, D_{j}, \dots, D_{m}}$ , $D_{j} = {D_{j}^{- 1}, D_{j}^{0}, D_{j}^{1}}$ express the set of collection of feature words extracted from all alternative product reviews, sentiment intensity level dictionary and sentiment intensity level dictionary of $f_{j}$ , respectively.
(3)
$T = {1, \dots, t, \dots, s}$ , $P = {ρ_{1}, ρ_{2}, \dots, ρ_{s}}$ , $ω = {ω_{1}, \dots, ω_{j}, \dots, ω_{m}}$ stand for the set of the multiple comment stages, weight of each comment stage, weights of different product features.
(4)
$s_{ikt}$ , $W (s_{ikt})$ , $L_{i j}^{t} (p)$ express the $k$ -th review of the product $A_{i}$ in $t$ stage, preprocessing result of $s_{ikt}$ and probabilistic linguistic value for the alternative product $A_{i}$ in $t$ stage concerning each attribute $f_{j}$ , respectively.

3.2. Sentiment analysis

To solve the product ranking problem, the first step is to obtain and preprocess Online customer reviews information related to the alternative products. Next, product feature extraction technology is used to obtain product features that consumers care about. Then, we can further use sentiment analysis technology to obtain the sentiment score of each review.

(1) Online review prepossessing and product feature extraction

Obtaining reviews of relevant products is a fundamental task in conducting sentiment analysis. In this paper, we acquire review information through crawler software and then preprocess the review information, turning the initial qualitative Online customer reviews information into quantitative data that can be calculated. This process normally consists of three steps: word segmentation, part-of-speech (POS) tagging, and stopping word removal. We use ICTCLAS 2016 (a Chinese word separation system) and python programming to help us achieve the above operations. For example, “the phone is very nice” can get “phone/n very/d nice/a” after being processed, where “n”, “d” and “a” stand for nouns, adverbs, and adjectives, respectively. Then, we can obtain the set of preprocessed comment words for each review. Let $s_{ikt}$ denote the k-th review of the product $A_{i}$ in $t$ stage and $W (s_{ikt})$ denote the preprocessing result of $s_{ikt}$ . Then the LDA algorithm is used to extract product features that consumers care about contained in reviews, which are noted $F = {f_{1}, \dots, f_{j}, \dots, f_{m}}$ . On this basis, a sentiment analysis method based on a sentiment dictionary is applied to get the emotional orientation contained in each comment.

(2) Sentiment analysis

Considering that different products have different review contexts, to improve the accuracy of sentiment analysis, our paper uses a sentiment analysis method based on a sentiment dictionary to obtain consumers’ emotional orientation contained in each review. The main contribution of sentiment analysis can be concluded as follows:

① Establish the dictionary of sentiment intensity reference words. To improve the quality of sentiment intensity analysis, we establish the dictionary of sentiment intensity reference words, dictionaries of degree adverbs, and negatives based on the HowNet sentiment dictionary in advance. Then, the sentiment words extracted from the Online customer reviews are classified according to the pre-built sentiment intensity reference set following the principle of synonym grouping.

② Obtain the set of sentiment intensity levels dictionary of each product feature. We can obtain $D$ , the set of sentiment intensity levels dictionary of each product feature, where $D = {D_{1}, \dots, D_{j}, \dots D_{m}}$ . Among $D_{j} = {D_{j}^{- 1}, D_{j}^{0}, D_{j}^{1}}$ stands for the sentiment dictionary of $f_{j}$ and $D_{j}^{- 1}, D_{j}^{0}, D_{j}^{1}$ are the set of sentiment intensity reference words that represents ‘bad’, the set of sentiment intensity reference words that represents ‘medium’, and the set of sentiment intensity reference words that represents ‘good’, respectively.

③ Establish the dictionary of degree adverbs. In this paper, we divide the sentiment intensity into 5 levels. let $D_{d - a}$ denote the dictionary of degree adverbs. Let $D_{neg}$ denote the dictionary of negatives. Then, let $s_{ikt}^{j}$ denote the sentiment score for the $k$ -th review of the product $A_{i}$ under $f_{j}$ in $t$ stage which can be determined by the following algorithm:

\begin{aligned} s_{ikt}^{j} = D_{j} (s_{ikt}^{j}) D_{d - a} (s_{ikt}^{j}) (- 1)^{N_{neg} (s_{ikt}^{j})} \end{aligned}

(7)

Where $D_{j} (s_{i k}^{j})$ denote the score of sentiment intensity reference words. If $W (s_{ikt}) \cap D_{j}^{1} \neq \emptyset$ and $W (s_{ikt}) \cap D_{j}^{- 1} = \emptyset$ , then $D_{j} (s_{ikt}^{j}) = 1$ ; If $W (s_{i k}) \cap D_{j}^{- 1} \neq \emptyset$ and $W (s_{ikt}) \cap D_{j}^{1} = \emptyset$ , then $D_{j} (s_{ikt}^{j}) = - 1$ ; If $W (s_{ikt}) \cap D_{j}^{- 1} \neq \emptyset$ and $W (s_{ikt}) \cap D_{j}^{1} \neq \emptyset$ , then $D_{j} (s_{ikt}^{j}) = 0$ . $D_{d - a} (s_{ikt}^{j})$ denotes the score of degree adverbs. If $W (s_{ikt}^{j}) \cap D_{a - d} = \emptyset$ , $D_{d - a} (s_{ikt}^{j}) = 1$ ; if $W (s_{ikt}^{j}) \cap D_{a - d} \neq \emptyset$ , $D_{d - a} (s_{ikt}^{j}) = 2$ . $(- 1)^{N_{neg} (s_{ikt}^{j})}$ denotes the score of negatives and $N (s_{ikt}^{j})$ denotes the number of negatives in $s_{ikt}^{j}$ . It is obvious that $s_{ikt}^{j}$ varies from $-$ 2 to 2.

3.3. The shift from sentiment score to PLTS

In this section, the conversion of Online customer reviews information to PLTS will be introduced in detail. In 3.2, the sentiment score of each review can be obtained, based on which, we can further establish the sentiment indicator vector $R_{ikt}^{j}$ for the k-th review of the product $A_{i}$ about the feature $f_{j}$ in $t$ stage.

\begin{aligned} R_{ikt}^{j} = (s_{ikt}^{1 j}, s_{ikt}^{2 j}, s_{ikt}^{3 j}, s_{ikt}^{4 j}, s_{ikt}^{5 j}) = {\begin{array}{l} (1, 0, 0, 0, 0), s_{ikt}^{j} = - 2 \\ (0, 1, 0, 0, 0), s_{ikt}^{j} = - 1 \\ (0, 0, 1, 0, 0), s_{ikt}^{j} = 0 \\ (0, 0, 0, 1, 0), s_{ikt}^{j} = 1 \\ (0, 0, 0, 0, 1), s_{ikt}^{j} = 2 \end{array} \end{aligned}

(8)

From Eq. (8), the sentiment indication vector has five possible cases, which point to five different sentiment scores. From a statistical point of view, the frequency of occurrence of these five different sentiment scores can be transformed into the probability of their occurrence. Let $S = {S_{- 2}, S_{- 1}, S_{0}, S_{1}, S_{2}}$ be the LTS used for evaluation, where $S_{- 2}$ corresponds to the sentiment indicator vector $(1, 0, 0, 0, 0)$ , $S_{- 1}$ corresponds to the sentiment indicator vector $(0, 1, 0, 0, 0)$ , $S_{0}$ corresponds to the sentiment indicator vector $(0, 0, 1, 0, 0)$ , $S_{1}$ corresponds to the sentiment indicator vector $(0, 0, 0, 1, 0)$ , $S_{2}$ corresponds to the sentiment indicator vector $(0, 0, 0, 0, 1)$ , respectively. Further, based on the sentiment indicator vector $R_{ikt}^{j}$ , the sentiment distribution of each feature of the alternative products can be counted. Let $T_{i t}^{j} = (a_{i t}^{j}, b_{i t}^{j}, c_{i t}^{j}, d_{i t}^{j}, e_{i t}^{j})$ be the sentiment distribution vector for product $A_{i}$ about $f_{j}$ in $t$ stage, which can be calculated as follows.

\begin{aligned} T_{i t}^{j} = (a_{i t}^{j}, b_{i t}^{j}, c_{i t}^{j}, d_{i t}^{j}, e_{i t}^{j}) = (\sum_{k = 1}^{b_{i}^{t}} s_{ikt}^{1 j}, \sum_{k = 1}^{b_{i}^{t}} s_{ikt}^{2 j}, \sum_{k = 1}^{b_{i}^{t}} s_{ikt}^{3 j}, \sum_{k = 1}^{b_{i}^{t}} s_{ikt}^{4 j}, \sum_{k = 1}^{b_{i}^{t}} s_{ikt}^{5 j}) \end{aligned}

(9)

Let $P_{i t}^{j} (a)$ , $P_{i t}^{j} (b)$ , $P_{i t}^{j} (c)$ , $P_{i t}^{j} (d)$ , $P_{i t}^{j} (e)$ denote the probability of occurrence of each sentiment intensity of product $A_{i}$ with respect to $f_{j}$ in $t$ stage, respectively, where

\begin{aligned} P_{i t}^{j} (a) = \frac{a_{i t}^{j}}{a_{i t}^{j} + b_{i t}^{j} + c_{i t}^{j} + d_{i t}^{j} + e_{i t}^{j}} = \frac{\sum_{k = 1}^{b_{j}} s_{ikt}^{1 j}}{\sum_{k = 1}^{b_{i}^{t}} s_{ikt}^{1 j} + \sum_{k = 1}^{b_{i}^{t}} s_{ikt}^{2 j} + \sum_{k = 1}^{b_{i}^{t}} s_{ikt}^{3 j} + \sum_{k = 1}^{b_{i}^{t}} s_{ikt}^{4 j} + \sum_{k = 1}^{b_{i}^{t}} s_{ikt}^{5 j}} \end{aligned}

(10)

The calculation steps of $P_{i t}^{j} (b)$ , $P_{i t}^{j} (c)$ , $P_{i t}^{j} (d)$ , and $P_{i t}^{j} (e)$ are similar to $P_{i t}^{j} (a)$ .

After the above transformation, it is easy to get the probabilistic linguistic value $L_{i j}^{t} (p)$ of the product $A_{i}$ concerning the product feature $f_{j}$ in $t$ stage which contains complete probabilistic information. Then, the sentiment score of each review is transformed into probabilistic linguistic information.

3.4. Interval-valued probability linguistic terms sets (IVPLTS)

Usually, when consumers post an initial review of a purchased product, they will post additional reviews after a period of use. Additional comments tend to contain richer consumer emotion orientation and utility evaluation of products. To fully characterize the consumer’s two-stage Online customer reviews, the IVPLTS is proposed in this section.

Definition 8.
Let $IVL (p)$ be an IVPLTS which can be defined as:
$\begin{aligned} IVL (p) = {L^{(k)} ({\underline{p}}^{(k)}, {\bar{p}}^{(k)}) ∣ L^{(k)} \in S, 0 ⩽ {\underline{p}}^{(k)} ⩽ {\bar{p}}^{(k)} ⩽ 1, k = 1, 2, \dots, # IVL (p)} \end{aligned}$
(11)

Where, $L^{(k)} ({\underline{p}}^{(k)}, {\bar{p}}^{(k)})$ is the linguistic term $L^{(k)}$ associated with probability interval $({\underline{p}}^{(k)}, {\bar{p}}^{(k)})$ , ${\underline{p}}^{(k)}$ is the minimum probability among multi-stage assessment, ${\bar{p}}^{(k)}$ is the maximum probability in multi-stage assessment, and $# IVL (p)$ is the number of all different linguistic terms in $IVL (p)$ .

Note that if ${\underline{p}}^{(k)} = {\bar{p}}^{(k)}$ , IVPLTS is transformed to PLTS and IVPLTS is a general form of PLTS.

After proposing the concept of IVPLTS, we notice that in some cases the occurrence probabilities information of linguistic terms is incomplete owing to the lack of some people’s opinions or the divergence or the hesitance of people’s opinions. Incompleteness can be divided into two cases, the first is the lack of partial linguistic terms, and the second is the lack of information on the occurrence probability of linguistic terms. To solve this problem, we propose a method to maximize the accommodation of missing information. Assume that $I V L (p) = {L^{(k)} ({\underline{p}}^{(k)}, {\bar{p}}^{(k)}) ∣ L^{(k)} \in S, 0 ⩽ {\underline{p}}^{(k)} ⩽ {\bar{p}}^{(k)} ⩽ 1, k = 1, 2, \dots, # I V L (p)}$ be an incomplete IVPLTs To convert it to a normalized IVPLTS, we add ${s_{k} | s_{k} \in S - I V L (p)}$ to $I V L (p)$ and let its occurrence probability be (0, 1).

Based on the proposed normalization method, we propose a conversion function to convert IVPLTS to PLTS. At the same time, a more intuitive and understandable IVPLTS comparison method is proposed.
Definition 9.
Let $I V L (p) = {L^{(k)} ({\underline{p}}^{(k)}, {\bar{p}}^{(k)}) ∣ L^{(k)} \in S, 0 ⩽ {\underline{p}}^{(k)} ⩽ {\bar{p}}^{(k)} ⩽ 1, k = 1, 2, \dots, # I V L (p)}$ be normalized IVPLTs and $o = [\underline{p}, \bar{p}] \to p$ be the conversion function through which we can turn normalized IVPLTS into PLTS.
$\begin{aligned} o (\underline{p}, \bar{p}) = χ \underline{p} + (1 - χ) \bar{p} = \hat{p} \end{aligned}$
(12)

Where, $χ$ is the positioning coefficient, usually, the value is 0.5.

After applying transformation functions to the $I V L (p)$ , we can get $L (p)$ , $L (p) = {L^{(k)} (p^{(k)}) | L^{(k)} \in S, 0 ⩽ p^{(k)} ⩽ 1, k = 1, 2, \dots, # L (p)}$ . It should be pointed out that the PLTS obtained here is different from the PLTS in the previous literature [21, 16], specifically in that the sum of probabilities of linguistic terms is not less than or equal to 1. Next, we propose a more intuitive and easy-to-understand method for comparing PLTS sizes with the help of images. The comparison method can be seen below.

Figure 2.
Five basic attitudes of decision makers present by broken lines.

As shown in Figure 2, there are 5 broken lines in the figure, which can be used to represent the five basic attitudes of decision makers which can be seen in Table 1.

Table 1
Five basic attitudes.

Attitude PLTS

Very bad ${\bar{L (p)}}_{1} = {s_{o} (0.75), s_{1} (0.75), s_{2} (0.5), s_{3} (0.25), s_{4} (0.25)}$

Bad ${\bar{L (p)}}_{2} = {s_{o} (0.75), s_{1} (0.75), s_{2} (0.5), s_{3} (0.5), s_{4} (0.5)}$

Medium ${\bar{L (p)}}_{3} = {s_{o} (0.5), s_{1} (0.5), s_{2} (0.5), s_{3} (0.5), s_{4} (0.5)}$

Good ${\bar{L (p)}}_{4} = {s_{o} (0.5), s_{1} (0.5), s_{2} (0.5), s_{3} (0.75), s_{4} (0.75)}$

Very good ${\bar{L (p)}}_{5} = {s_{o} (0.25), s_{1} (0.25, s_{2} (0.5), s_{3} (0.75), s_{4} (0.75)}$

The relationship between them is that ${\bar{L (p)}}_{5} ≻ {\bar{L (p)}}_{4} ≻ {\bar{L (p)}}_{3} ≻ {\bar{L (p)}}_{2} ≻ {\bar{L (p)}}_{1}$ . To compare the sizes of different PLTS, we first map them to a two-dimensional coordinate system and then calculate their distances to the 5 polylines respectively. The distance calculation formula is $d = min_{t} {\sum_{k = 1}^{# L (p)} (p^{(k)} - p_{t}^{(k)})^{2}}$ , $t = 1, 2, 3, 4, 5$ , where $p_{t}^{(k)}$ represents probability corresponding to the $k$ -th probabilistic language term in PLTS for the $t$ -th attitude. We determine the attitude of PLTS by judging the nearest polyline and then comparing the size of different PLTS.
Definition 10.
Let ${I V L}_{1} (p) = {L_{1}^{(k)} ({\underline{p}}_{1}^{(k)}, {\bar{p}}_{1}^{(k)}) ∣ L_{1}^{(k)} \in S, 0 ⩽ {\underline{p}}_{1}^{(k)} ⩽ {\bar{p}}_{1}^{(k)} ⩽ 1, k = 1, 2, \dots, # {I V L}_{1} (p)}$ and ${I V L}_{2} (p) = {L_{2}^{(k)} ({\underline{p}}_{2}^{(k)}, {\bar{p}}_{2}^{(k)}) ∣ L_{2}^{(k)} \in S, 0 ⩽ {\underline{p}}_{2}^{(k)} ⩽ {\bar{p}}_{2}^{(k)} ⩽ 1, k = 1, 2, \dots, # {I V L}_{2} (p)}$ be any two IVPLTSs based on $S = {s_{α} | α = τ, \dots, 0, \dots, τ}$ and $α^{(k)}$ be the subscript of a linguistic term $L^{(k)}$ .

Let $Δ$ and $Δ^{- 1}$ be the transformation function and the reverse transformation function, respectively, where
$\begin{aligned} Δ (α^{(k)}) & = \frac{α^{(k)} + τ}{2 τ} = υ \end{aligned}$
(13)

$\begin{aligned} Δ^{- 1} (υ) & = (2 υ - 1) τ = α^{(k)} \end{aligned}$
(14)

By transformation function $Δ$ , we can transform the linguistic interval $[- τ, τ]$ into a numerical interval $[0, 1]$ , and the reverse transformation function $Δ^{- 1}$ performs the opposite.
Definition 11.
Let $I V L (p) = {L^{(k)} ({\underline{p}}^{(k)}, {\bar{p}}^{(k)}) ∣ L^{(k)} \in S, 0 ⩽ {\underline{p}}^{(k)} ⩽ {\bar{p}}^{(k)} ⩽ 1, k = 1, 2, \dots, # I V L (p)}$ be a normalized IVPLTs based on $S = {s_{α} | α = τ, \dots, 0, \dots, τ}$ , where $[{\underline{p}}^{(k)}, {\bar{p}}^{(k)}]$ is a probability interval of linguistic term $L^{(k)}$ , $α^{(k)}$ be the subscript of $L^{(k)}$ Let $θ$ be the probability interval width and $ψ_{k}$ be the probability interval reliability function through which we can compare the magnitude of the precision of different probability intervals. Let $p^{(k)}$ be the compromise probability of $[{\underline{p}}^{(k)}, {\bar{p}}^{(k)}]$ . Then, we propose a new expectation value function $E (I V L P)$ for IVPLTS, where:
$\begin{aligned} θ_{k} & = {\bar{p}}^{(k)} - {\underline{p}}^{(k)} \end{aligned}$
(15)

$\begin{aligned} ψ_{k} & = \cos \frac{π}{2} θ_{k} \end{aligned}$
(16)

$\begin{aligned} p^{(k)} & = \cos \frac{π}{2} θ_{k} \cdot o ({\underline{p}}^{(k)}, {\bar{p}}^{(k)}) \end{aligned}$
(17)

$\begin{aligned} E (I V L (p)) & = \sum_{k = 1}^{# I V L (p)} (Δ (α^{(k)}) p^{(k)}) / \sum_{l = 1}^{# L (p)} p^{(k)} \end{aligned}$
(18)

By Eq. (18), we can get the decision matrix composed of the expectation value of ${I V L}_{i j} (p)$ .

After we give the concept of IVPLTS, we also propose the corresponding comparison method, operation rules, and expectation value calculation formula. More research on the properties of IVPLTS will be carried out in follow-up studies.
3.5. Calculation of the weights of each product feature

Attitude	PLTS
Very bad	${\bar{L (p)}}_{1} = {s_{o} (0.75), s_{1} (0.75), s_{2} (0.5), s_{3} (0.25), s_{4} (0.25)}$
Bad	${\bar{L (p)}}_{2} = {s_{o} (0.75), s_{1} (0.75), s_{2} (0.5), s_{3} (0.5), s_{4} (0.5)}$
Medium	${\bar{L (p)}}_{3} = {s_{o} (0.5), s_{1} (0.5), s_{2} (0.5), s_{3} (0.5), s_{4} (0.5)}$
Good	${\bar{L (p)}}_{4} = {s_{o} (0.5), s_{1} (0.5), s_{2} (0.5), s_{3} (0.75), s_{4} (0.75)}$
Very good	${\bar{L (p)}}_{5} = {s_{o} (0.25), s_{1} (0.25, s_{2} (0.5), s_{3} (0.75), s_{4} (0.75)}$

In the process of calculating product attribute weights, it is necessary to consider consumers’ individual preferences and product objective evaluation information from Online customer reviews simultaneously, and then obtain a comprehensive weight of product features. In this part, we calculate the objective weight of product attributes through the entropy weight method. Considering the product feature preference information given by the customer, we can finally get the comprehensive weight through maximizing deviation method. The specific calculation steps are as follows:

(1) Determine the subjective weights of product attributes

For customers, they usually hold a subjective preference for each attribute of products before making a choice. Based on this, different weights will be given to the product attributes according to the degree of importance. Therefore, we can obtain the weight information of each attribute of the products given by the customer in advance and let $ω^{*} = (ω_{1}^{*}, \dots, ω_{j}^{*}, \dots, ω_{m}^{*})$ be the subjective weight vector.

(2) Determine the objective weights of product attributes

The entropy weight method is an objective weighting determination method which is often used in solving attribute weight solving problems. The method mainly includes five steps:

① Normalize the indicators. After converting the review information into IVPLTS and using the conversion function proposed in the paper to convert it into PLTS, then use Eq. (18) to calculate the expectation function value of product $A_{i}$ with respect to attribute $f_{j}$ denoted as $x_{i j}^{*}$ . For benefit and cost attributes, by using $x_{i j} = \frac{x_{i j}^{*} - min_{i} x_{i j}^{*}}{max_{i} x_{i j}^{*} - min_{i} x_{i j}^{*}}$ and $x_{i j} = \frac{max_{i} x_{i j}^{*} - x_{i j}^{*}}{max_{i} x_{i j}^{*} - min_{i} x_{i j}^{*}}$ respectively, we can get corresponding normalized values, and finally, the normalized decision matrix $X_{i j}$ can be obtained.

② Calculate the proportion of each indicator value under each indicator. Use $p_{i j}$ to represent the proportion of the performance value of product $A_{i}$ in the performance value of all products under product attribute $f_{j}$ . The calculation formula is $p_{i j} = \frac{x_{i j}}{\sum_{i = 1}^{n} x_{i j}}$ , $i = 1, \dots, n, j = 1, \dots, m$ .

③ Calculate the entropy value of each attribute. Let $e_{j}$ be the entropy value of $f_{j}$ , where $e_{j} = - \frac{1}{\ln (n)} \sum_{i = 1}^{n} p_{i j} \ln (p_{i j})$ , $j = 1, \dots, m$ .

④ Calculate the information entropy redundancy. Let $d_{j}$ be the information redundancy which can be calculated by $d_{j} = 1 - e_{j}$ , $j = 1, \dots, m$ .

⑤ Calculate the weight of each indicator. Let $ω^{'} = (ω_{1}^{^{'}}, \dots, ω_{j}^{^{'}}, \dots, ω_{m}^{^{'}})$ be the objective weight vector and $ω_{j}^{^{'}}$ can be calculated by $w_{j}^{^{'}} = d_{j} / \sum_{j = 1}^{m} d_{j}$ , $j = 1, \dots, m$ .

In decision-making problems, if all alternatives are undifferentiated with respect to an attribute, then this attribute should be given a small weight. If the alternatives show a large difference regarding an attribute, then that attribute will have an important role in the ranking of the alternatives and should be given a larger weight. Assume that the comprehensive weight vector of the attributes is $ω = (ω_{1}, \dots, ω_{j}, \dots, ω_{m})$ where $ω_{j} = a ω_{j}^{*} + b ω_{j}^{^{'}}$ and $a^{2} + b^{2} = 1$ , $a, b ⩾ 0$ , $j = 1, 2, \dots m$ . Denote that $V_{i j}$ means the distance between the alternative product $i$ and all other alternatives under attribute $f_{j}$ and $V_{i j}$ are defined as follows:

\begin{aligned} V_{i j} = \sum_{k = 1}^{n} ω_{j} d ({I V L}_{i j} (p), {I V L}_{k j} (p)) \end{aligned}

(19)

Where, $d (L_{i j} (p), L_{k j} (p)) = E ({I V L}_{i j} (p)) - E ({I V L}_{k j} (p))$ , $i = 1, 2, \dots, n, j = 1, 2, \dots, m, k = 1, 2, \dots n$ .

Further, let $V_{j}$ express the total deviation of all alternative products from other alternative products under the attribute $f_{j}$ , and then it can be expressed as

\begin{aligned} V_{j} = \sum_{i = 1}^{n} V_{i j} = \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j} d ({I V L}_{i j} (p), {I V L}_{k j} (p)) \end{aligned}

(20)

To make the weights of each product attribute objectively reflect the importance of the product attribute to the consumer’s decision, the total deviation of all product attributes concerning each alternative product should be maximized under the weight vector $ω$ . Therefore, the objective function for maximizing the deviation is constructed as follows.

\begin{aligned} {\begin{cases} max V = \sum_{j = 1}^{m} V_{j} = \sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j} d ({I V L}_{i j} (p), {I V L}_{k j} (p)) \\ = \sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} (a ω_{j}^{*} + b ω_{j}^{^{'}}) d ({I V L}_{i j} (p), {I V L}_{k j} (p)) \\ s . t . a^{2} + b^{2} = 1 \\ a ⩾ 0, b ⩾ 0 \end{cases} \end{aligned}

(21)

Then we use the Lagrange function to solve the model:

\begin{aligned} L (a, b) = \sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} (a ω_{j}^{*} + b ω_{j}^{^{'}}) d ({I V L}_{i j} (p), {I V L}_{k j} (p)) + φ (a^{2} + b^{2} - 1) \end{aligned}

(22)

Where $φ$ stands for the Lagrange parameter.

Then we calculate the partial derivatives with respect to $a, b$ and $α$ , and as follows:

\begin{aligned} {\begin{cases} \frac{\partial L}{\partial a} = \sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j}^{*} d ({I V L}_{i j} (p), {I V L}_{k j} (p)) + 2 a φ = 0 \\ \frac{\partial L}{\partial b} = \sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j}^{^{'}} d ({I V L}_{i j} (p), {I V L}_{k j} (p)) + 2 b φ = 0 \\ \frac{\partial L}{\partial φ} = α^{2} + β^{2} - 1 = 0 \end{cases} \end{aligned}

(23)

And then, we can get $a, b$ and $φ$ as follows, respectively:

\begin{aligned} {\begin{cases} a = \frac{\sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j}^{*} d ({I V L}_{i j} (p), {I V L}_{k j} (p))}{\sqrt{{(\sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j}^{*} d ({I V L}_{i j} (p), {I V L}_{k j} (p)))}^{2} + {(\sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j}^{^{'}} d ({I V L}_{i j} (p), {I V L}_{k j} (p)))}^{2}}} \\ b = \frac{\sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j}^{^{'}} d ({I V L}_{i j} (p), {I V L}_{k j} (p))}{\sqrt{{(\sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j}^{*} d ({I V L}_{i j} (p), {I V L}_{k j} (p)))}^{2} + {(\sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j}^{^{'}} d ({I V L}_{i j} (p), {I V L}_{k j} (p)))}^{2}}} \\ φ = - \frac{1}{2} \sqrt{\begin{array}{l} {(\sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j}^{*} d ({I V L}_{i j} (p), {I V L}_{k j} (p)))}^{2} + {(\sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} ω_{j}^{^{'}} d ({I V L}_{i j} (p), {I V L}_{k j} (p)))}^{2} \end{array}} \end{cases} \end{aligned}

(24)

3.6. IVPLTs-PROMETHEE product ranking method

In contrast to the previous approach of considering only initial reviews, this paper considers both initial and additional Online customer reviews and proposes a composite review-based product selection method that takes the time of publication of the review into account. The language set used in this part is an LTS: $S = {S_{- 2} = very bad, S_{- 1} = b a d, S_{0} = m e d i u m, S_{1} = g o o d, S_{2} = very good}$ , $S_{0}$ stands for the most negative sentiment and $S_{5}$ stands for the most positive sentiment. The probabilistic linguistic term set was first proposed by Pang et al. [21] to provide a new solution for multi-attribute decision-making. Unlike HFLTS, PLST allows decision makers to represent individual preferences with different probabilistic information, whereas HFLTS considers individual decision makers to be consistent when preferring all linguistic term elements.

In the next section, we focus on the extended interval-valued probabilistic linguistic set PROMETHEE approach (IVPLTs-PROMETHEE). PROMETHEE uses the preference function $P_{j} (A_{i}, A_{k})$ to describe the priority of $A_{i}$ over $A_{k}$ under attribute $f_{j}$ . When $P_{j} (A_{i}, A_{k}) = 0$ , it means that there is no difference between the alternative $A_{i}$ and other alternatives on the attribute $f_{j}$ , and when $P_{j} (A_{i}, A_{k}) = 1$ , it means that the alternative $A_{i}$ is strictly better than the alternative $A_{k}$ on the attribute $f_{j}$ .

For two stages of evaluation content, there is inevitably an evaluation bias between the initial and additional reviews. The same attributes of the same product also differ between the two stages of evaluation. A variety of factors can cause evaluation bias. If a consumer buys a product and uses it for a period of time and finds that the product’s performance is temporarily superior and not as good as it actually is, then in his follow-up additional Online customer reviews, the consumer will describe more about the disadvantages of this attribute and the two-stage Online customer reviews of that attribute will inevitably be different. Let $d_{i}^{j} = \sum_{t = 1}^{s - 1} d_{j} (L_{i j}^{t + 1} (p), L_{i j}^{t} (p))$ denote the total deviation between the two stages of evaluation of the alternative product $A_{i}$ regarding attribute $f_{j}$ . The larger the value of $d_{i}^{j}$ , the more ambivalent the consumer is about the product $A_{i}$ and the more controversial product $A_{i}$ is. The construction of the optimization function should fully reflect the difference between the two stages of evaluation information. In the context of the Online customer reviews environment, we need to analyze the preference information contained in Online customer reviews of different stages, and then construct the optimization function MinD, where $o r n e s s (ρ (t))$ reflects the temporal weighting of each stage. A smaller $o r n e s s (ρ (t))$ indicates a greater emphasis on recent data and a larger $o r n e s s (ρ (t))$ indicates a greater emphasis on long-term data The value of $o r n e s s (ρ (t))$ should be determined by the actual situation. Assume that $\underline{E} (L_{i j}^{t} (p)$ , $\bar{E} (L_{i j}^{t} (p)$ stand for the minimum and maximization expectation value of the attribute $f_{j}$ in $t$ stage, which can also be used to represent $t$ -stage consumers’ minimum and maximization willingness to accept the performance of $f_{j}$ in phase $t$ . Let $E ({I V L}_{* j} (p)$ stand for the consensus ideal expectation value of the attribute $f_{j}$ in all stages, which can also be used to represent consumers’ consensus ideal willingness to accept the performance of $f_{j}$ . Then, we can use the ratio of the minimum willingness value and the maximization willingness value to present the minimum satisfaction degree of the attribute $f_{j}$ in $t$ stage. Because the consensus ideal expectation value $E ({I V L}_{* j} (p)$ should be accepted by all DMs, it is necessary to construct an optimization model to determine $E ({I V L}_{* j} (p)$ under the goal of maximizing overall satisfaction. Based on the above analysis, we construct the following two-step optimization model:

\begin{aligned} max F & = \sum_{j = 1}^{m} ω_{j} \prod_{t = 1}^{s} {(\frac{E ({I V L}_{* j} (p))}{\bar{E} (L_{i j}^{t} (p))} - \frac{\underline{E} (L_{i j}^{t} (p))}{\bar{E} (L_{i j}^{t} (p))})}^{ρ_{t}} \end{aligned}

\begin{aligned} min D & = \sum_{i = 1}^{n} \sum_{j = 1}^{m} \sum_{t = 2}^{s} ω_{j} d_{i}^{j} (L_{i j}^{t} (p) ρ_{t}, L_{i j}^{t - 1} (p) ρ_{t - 1}) \end{aligned}

\begin{aligned} s . t . {\begin{cases} o r n e s s (ρ_{t}) = \frac{1}{s - 1} \sum_{t = 1}^{s} (s - t) ρ_{t} = γ, 0 ⩽ γ ⩽ 1 \\ \sum_{t = 1}^{s} ρ_{t} = 1 \\ \underline{E} (L_{i j}^{t} (p) ⩽ E (L_{* j} (p) ⩽ \bar{E} (L_{i j}^{t} (p) \\ \underline{E} (L_{i j}^{t} (p) = {min}_{i} {E (L_{i j}^{t} (p)} \\ \bar{E} (L_{i j}^{t} (p) = {max}_{i} {E (L_{i j}^{t} (p)} \\ \sum_{j = 1}^{m} ω_{j} = 1 \\ i = 1, 2, \dots n; j = 1, 2, \dots, m, t = 1, 2, \dots, s \end{cases} \end{aligned}

(25)

Proof. Model (25) is a two-stage single-objective programming problem. It is readily known from the objective function and the actual meaning of each constraint that the feasible domain of the model exists and is bounded. According to the existence theorem of optimal solutions (a single-objective plan with bounded bounds in any feasible domain must be optimal in its feasible domain), the model surely has an optimal solution.

Then, we propose a new preference function $P_{j} (A_{i}, A_{l})$ , where

\begin{aligned} P_{j} (A_{i}, A_{l}) = {\begin{array}{l} E ({I V L}_{i j} (p)) / E ({I V L}_{* j} (p) - E ({I V L}_{l j} (p)) / E ({I V L}_{* j} (p), \\ E ({I V L}_{i j} (p)) > E ({I V L}_{l j} (p) \\ 0, o t h e r w i s e \end{array} \end{aligned}

(26)

Further $H (A_{i}, A_{k})$ , $Φ^{+} (A_{i})$ , $Φ^{-} (A_{i})$ , $Φ (A_{i})$ can be calculated respectively, where

\begin{aligned} H (A_{i}, A_{k}) & = \sum_{j = 1}^{m} w_{j} p_{j} (A_{i}, A_{k}) \end{aligned}

(27)

\begin{aligned} Φ^{+} (A_{i}) & = \frac{1}{n - 1} \sum_{A_{k}, A_{i} \in A} H (A_{i}, A_{k}) \end{aligned}

(28)

\begin{aligned} Φ^{-} (A_{i}) & = \frac{1}{n - 1} \sum_{A_{k}, A_{i} \in A} H (A_{k}, A_{i}) \end{aligned}

(29)

\begin{aligned} Φ (A_{i}) & = Φ^{+} (A_{i}) - Φ^{-} (A_{i}) \end{aligned}

(30)

Among, $H (A_{i}, A_{k})$ represents the priority index of $A_{i}$ over $A_{k}$ , $Φ^{+} (A_{i})$ is the dominance degree (or positive outranking flow) of the alternative $A_{i}$ over all other alternatives, $Φ^{-} (A_{i})$ is the dominance degree (or negative outranking flow) of all other alternatives over the alternative $A_{i}$ , $Φ (A_{i})$ reflects the relative dominance degree(or net outranking flow) of the alternative $A_{i}$ , and a higher value for $Φ (A_{i})$ indicates a higher priority for the alternative $A_{i}$ .

4. Case studies

At present, among several electronic products trading platforms in China, Jingdong Mall is one of the most popular platforms. Because it not only sells a wide range of electronic products online, but it also owns several physical shopping malls allowing consumers to purchase and experience offline. Jingdong Mall sells a variety of products by setting up its own flagship shops, so the quality of the products is guaranteed and consumers can effectively avoid buying fake products. At the same time, Jingdong Mall provides a convenient way for consumers to post reviews online. Because the Online customer reviews in Jingdong Mall is open source, so we can freely collect and mine Online customer reviews through crawler software or by writing crawler code. Mobile phones are an indispensable tool in today’s society and people’s demand for mobile phones is increasing. To meet the diverse needs of consumers, mobile phone manufacturers frequently launch new mobile phone products to cater to consumers. As a result, consumers are often faced with a hard decision-making situation where they don’t know which mobile phone to purchase. For that we extracted core information about alternative products from the huge number of online customer reviews. Then consumers can quickly have a comprehensive understanding of the alternative products and thus help them choose the best mobile phone more easily. Moreover it is of great relevance that will not only improve the shopping experience of consumers but also improve the effectiveness and user loyalty of Jingdong Mall.

Suppose a college student wants to purchase a mobile phone soon. Given his current financial situation, he has a budget for a phone between 4,000RMB to 5,000 RMB, and he doesn’t know much about mobile phone configurations. With so many mobile phone brands available, he is faced with a myriad of choices. Finally, he decides to choose from five familiar phone brands: Apple, Xiaomi, Huawei, OPPO, and vivo which are denoted as $A_{1} = x i a o m i$ , $A_{2} = a p p l e$ , $A_{3} = h u a w e i$ , $A_{4} = o p p o$ , $A_{5} = v i v o$ . The college student knows little about phones, so he needs to refer to the reviews posted by consumers who have already purchased to help him make the right purchase decision. Generally speaking, a phone that has a high number of positive Online customer reviews indicates that the phone performs better, while a phone that has a high number of negative Online customer reviews indicates that the phone has a poor reputation and may bring an unpleasant user experience. To get a comprehensive understanding of consumers’ reviews of these phones, this paper takes into account both initial and additional reviews and integrates the information from both stages of Online customer reviews to rank the alternative phones. The main four steps involved in ranking alternative products through Online customer reviews are preprocessing, feature extraction, sentiment analysis, and application of product selection methods.

4.1. Online customer reviews preprocessing

First, in order to facilitate access to online customer reviews data, this paper uses Octopus crawler software to crawl two-stage online customer reviews posted by consumers on Jingdong. Due to the limitations of software functions and shopping platform permissions, the amount of reviews data obtained at a time is limited. Therefore, from 2022 to 2023, we obtained more than 150,000 reviews data by obtaining reviews multiple times in time periods. Among them, the data of additional reviews accounted for 2.64% of the total reviews. It shows part of the initial reviews and additional reviews for a cell phone on the Jingdong website in Figure 3.

Figure 3.

Display of initial and additional online reviews.

Second, the crawled review data is often in the form of text, which cannot be used directly for decision analysis (as shown in Figure 3), so the data needs to be cleaned first. The Online customer reviews preprocessing process generally includes word separation, POS tagging, stop word removal, and noise processing. This paper accomplishes the task of data cleaning with the help of python programming and ICTCLAS 2016.

Finally, we use Python software to construct LDA topic clustering model. And each topic represents a product attribute. Then we calculate the number of topics to obtain the relevant feature words of each topic (as shown in Figure 4). For some high-frequency product feature words that appear in the reviews but are not included under each topic, they are categorized under the corresponding topics by manual identification. Finally, we obtain the product attributes that consumers pay attention to. Based on this, we can obtain the product attributes: $f_{1} = p r e f e r e n c e$ , $f_{2} = p h o t o g r a p h$ , $f_{3} = battery life$ , $f_{4} = s c r e e n$ , $f_{5} = a p p e a r a n c e$ .

4.2. Application of proposed product sorting methods

After the review data has been acquired and cleaned, it needs to be further analyzed to transform the review text information into quantifiable and analyzable PLTS information that can be manipulated. In this process, we first build a feature-based sentiment dictionary based on the HowNet sentiment dictionary and sentiment words involved in all Online customer reviews. This sentiment dictionary contains positive, moderate, neutral, degree adverbs, and negatives. Then, we count the frequency of occurrence of each sentiment score and transform it into PLTS by using Eqs (8)–(10) and use it to characterize initial and additional Online customer reviews. Further, to characterize customers’ emotional orientations in all stages, we transform two-stage PLTS into IVPLTS by Eq. (11). The results are shown in the Table 2.

Table 2
IVPLTS based on two-stage reviews.

Laptops Attributes $S_{- 2}$ $S_{- 1}$ $S_{0}$ $S_{1}$ $S_{1}$

$A_{1}$ Performance (0, 0) (0, 0) (0.114, 0.241) (0.462, 0.673) (0.213, 0.297)

Photograph (0.003, 0.021) (0, 0.221) (0, 0.143) (0.52, 0.68) (0.113, 0.299)

Battery life (0, 0.072) (0, 0.216) (0.32, 0.528) (0.124, 0.474) (0.132, 0.134)

Screen (0.002, 0.104) (0, 0.105) (0.149, 0.213) (0.525, 0.626) (0.057, 0.219)

Appearance (0.002, 0.003) (0, 0) (0.124, 0.218) (0.532, 0.628) (0.245, 0.248)

$A_{2}$ Performance (0, 0.072) (0.091, 0.121) (0.184, 0.221) (0.45, 0.536) (0.159, 0.166)

Photograph (0, 0.002) (0, 0.071) (0.108, 0.48) (0.251, 0.623) (0.198, 0.267)

Battery life (0, 0.098) (0.005, 0.123) (0, 0.211) (0.404, 0.608) (0.164, 0.387)

Screen (0, 0.003) (0, 0.007) (0.232, 0.356) (0.511, 0.569) (0.13, 0.192)

Appearance (0.001, 0.004) (0, 0.021) (0.102, 0.142) (0.539, 0.612) (0.282, 0.297)

$A_{3}$ Performance (0.002, 0.072) (0.091, 0.101) (0.124, 0.221) (0.45, 0.529) (0.166, 0.244)

Photograph (0, 0.001) (0.071, 0.075) (0.224, 0.48) (0.251, 0.458) (0.198, 0.242)

Battery life (0, 0.098) (0, 0.123) (0.082, 0.211) (0.404, 0.426) (0.164, 0.492)

Screen (0, 0.003) (0.007, 0.007) (0.232, 0.522) (0.227, 0.569) (0.192, 0.241)

Appearance (0, 0.004) (0, 0.031) (0.102, 0.219) (0.573, 0.612) (0.177, 0.282)

$A_{4}$ Performance (0.001, 0.05) (0.007, 0.073) (0.206, 0.329) (0.22, 0.662) (0.124, 0.328)

Photograph (0.001, 0.008) (0.021, 0.041) (0.094, 0.108) (0.652, 0.782) (0.102, 0.191)

Battery life (0, 0.001) (0, 0.001) (0.124, 0.389) (0.241, 0.623) (0.253, 0.368)

Screen (0.002, 0.009) (0.157, 0.213) (0.308, 0.342) (0.207, 0.39) (0.109, 0.263)

Appearance (0.001, 0.005) (0.032, 0.09) (0.252, 0.521) (0.326, 0.563) (0.058, 0.152)

$A_{5}$ Performance (0.006, 0.097) (0, 0.087) (0.102, 0.234) (0.432, 0.683) (0.15, 0.209)

Photograph (0, 0) (0.001, 0.013) (0, 0.154) (0.608, 0.642) (0.225, 0.357)

Battery life (0, 0.003) (0.001, 0.009) (0.192, 0.24) (0.529, 0.584) (0.164, 0.278)

Screen (0.001, 0.007) (0.132, 0.149) (0.171, 0.25) (0.329, 0.562) (0.134, 0.265)

Appearance (0.001, 0.004) (0.012, 0.052) (0.129, 0.23) (0.542, 0.671) (0.172, 0.187)

Laptops	Attributes	$S_{- 2}$	$S_{- 1}$	$S_{0}$	$S_{1}$	$S_{1}$
$A_{1}$	Performance	(0, 0)	(0, 0)	(0.114, 0.241)	(0.462, 0.673)	(0.213, 0.297)
	Photograph	(0.003, 0.021)	(0, 0.221)	(0, 0.143)	(0.52, 0.68)	(0.113, 0.299)
	Battery life	(0, 0.072)	(0, 0.216)	(0.32, 0.528)	(0.124, 0.474)	(0.132, 0.134)
	Screen	(0.002, 0.104)	(0, 0.105)	(0.149, 0.213)	(0.525, 0.626)	(0.057, 0.219)
	Appearance	(0.002, 0.003)	(0, 0)	(0.124, 0.218)	(0.532, 0.628)	(0.245, 0.248)
$A_{2}$	Performance	(0, 0.072)	(0.091, 0.121)	(0.184, 0.221)	(0.45, 0.536)	(0.159, 0.166)
	Photograph	(0, 0.002)	(0, 0.071)	(0.108, 0.48)	(0.251, 0.623)	(0.198, 0.267)
	Battery life	(0, 0.098)	(0.005, 0.123)	(0, 0.211)	(0.404, 0.608)	(0.164, 0.387)
	Screen	(0, 0.003)	(0, 0.007)	(0.232, 0.356)	(0.511, 0.569)	(0.13, 0.192)
	Appearance	(0.001, 0.004)	(0, 0.021)	(0.102, 0.142)	(0.539, 0.612)	(0.282, 0.297)
$A_{3}$	Performance	(0.002, 0.072)	(0.091, 0.101)	(0.124, 0.221)	(0.45, 0.529)	(0.166, 0.244)
	Photograph	(0, 0.001)	(0.071, 0.075)	(0.224, 0.48)	(0.251, 0.458)	(0.198, 0.242)
	Battery life	(0, 0.098)	(0, 0.123)	(0.082, 0.211)	(0.404, 0.426)	(0.164, 0.492)
	Screen	(0, 0.003)	(0.007, 0.007)	(0.232, 0.522)	(0.227, 0.569)	(0.192, 0.241)
	Appearance	(0, 0.004)	(0, 0.031)	(0.102, 0.219)	(0.573, 0.612)	(0.177, 0.282)
$A_{4}$	Performance	(0.001, 0.05)	(0.007, 0.073)	(0.206, 0.329)	(0.22, 0.662)	(0.124, 0.328)
	Photograph	(0.001, 0.008)	(0.021, 0.041)	(0.094, 0.108)	(0.652, 0.782)	(0.102, 0.191)
	Battery life	(0, 0.001)	(0, 0.001)	(0.124, 0.389)	(0.241, 0.623)	(0.253, 0.368)
	Screen	(0.002, 0.009)	(0.157, 0.213)	(0.308, 0.342)	(0.207, 0.39)	(0.109, 0.263)
	Appearance	(0.001, 0.005)	(0.032, 0.09)	(0.252, 0.521)	(0.326, 0.563)	(0.058, 0.152)
$A_{5}$	Performance	(0.006, 0.097)	(0, 0.087)	(0.102, 0.234)	(0.432, 0.683)	(0.15, 0.209)
	Photograph	(0, 0)	(0.001, 0.013)	(0, 0.154)	(0.608, 0.642)	(0.225, 0.357)
	Battery life	(0, 0.003)	(0.001, 0.009)	(0.192, 0.24)	(0.529, 0.584)	(0.164, 0.278)
	Screen	(0.001, 0.007)	(0.132, 0.149)	(0.171, 0.25)	(0.329, 0.562)	(0.134, 0.265)
	Appearance	(0.001, 0.004)	(0.012, 0.052)	(0.129, 0.23)	(0.542, 0.671)	(0.172, 0.187)

Figure 4.

Topic coherent index change chart.

Further, we can get $X$ the decision matrix composed of the expectation value of ${I V L}_{i j} (p)$ by Eqs (13)–(18) as follows.

\begin{aligned} X = [\begin{array}{cccccccccccccccccccc} 0.742 & 0.694 & 0.550 & 0.663 & 0.761 \\ 0.656 & 0.636 & 0.685 & 0.709 & 0.782 \\ 0.677 & 0.652 & 0.683 & 0.643 & 0.753 \\ 0.610 & 0.730 & 0.690 & 0.604 & 0.606 \\ 0.658 & 0.792 & 0.742 & 0.647 & 0.714 \end{array}] \end{aligned}

Next, we can calculate product attribute weights. And it is necessary to consider consumers’ individual preferences and product objective evaluation information from Online customer re-views simultaneously. On the one hand, this college has a high preference for the performance of the mobile phone, but not much preference for the photography of the mobile phone. So, in response to consumers’ different preferences for cell phone product attributes, we set consumers’ subjective weights of product attributes as $ω_{1}^{*} = 0.25 ω_{2}^{*} = 0.15$ , $ω_{3}^{*} = 0.25$ , $ω_{4}^{*} = 0.2$ , $ω_{5}^{*} = 0.15$ . On the other hand, we can solve the objective weights of product attributes with the help of entropy weighting method in section 3.4. (2), and we get $ω_{1}^{^{'}} = 0.196$ , $ω_{2}^{^{'}} = 0.144$ , $ω_{3}^{^{'}} = 0.264$ , $ω_{4}^{^{'}} = 0.147$ , $ω_{5}^{^{'}} = 0.245$ . Combined with the attribute weight solving method by using Eqs (19)–(24), we can acquire the final comprehensive attribute weights, where $ω_{1} = 0.230$ , $ω_{2} = 0.219$ , $ω_{3} = 0.201$ , $ω_{4} = 0.198$ , $ω_{5} = 0.152$ . Then, the IVPLTS-PROMETHEE method proposed in our paper is used to rank the alternative products by combining two stages Online customer reviews. In general, compared to initial reviews, additional reviews are often more objective and reliable after consumers have used the product for a period of time, so the orness measure is set to 0.4 in this paper. Then, the stage weights and ideal expectation values can be obtained by Eq. (25). The stage weights are found to be $ρ_{1} = 0.4$ , $ρ_{2} = 0.6$ , and the ideal expectation values are $E (L_{* 1} (p) = 0.775$ , $E (L_{* 2} (p) = 0.839$ , $E (L_{* 3} (p) = 0.853$ , $E (L_{* 4} (p) = 0.737$ , $E (L_{* 5} (p) = 0.792$ . Then, by using Eqs (26)–(30), we can obtain, $Φ^{+} (A_{i}) Φ^{+} (A_{i})$ , $Φ^{+} (A_{i})$ . Based on the value of $Φ (A_{i})$ , we can get the final product ranking result $A_{5} ≻ A_{2} ≻ A_{1} ≻ A_{3} ≻ A_{4}$ . The final ranking results are shown in Table 3 below.

Table 3

The value of outranking flow.

	$Φ^{+} (A_{i})$	$Φ^{-} (A_{i})$	$Φ (A_{i})$
$A_{1}$	0.0503	0.0481	0.0023
$A_{2}$	0.0442	0.0328	0.0114
$A_{3}$	0.0284	0.0335	−0.0052
$A_{4}$	0.0226	0.0737	−0.0511
$A_{5}$	0.0630	0.0203	0.0426

4.3. Comparison of methods

To well show the practicality of the method proposed in this paper, we not only compare the method proposed in this paper with those proposed in previous studies [18, 19, 1, 35, 13], but also with the method proposed in this paper without the additional reviews. Specifically, the method [18, 19] ranks products through online reviews based on sentiment classification and interval-valued intuitionistic fuzzy TOPSIS; the method [1] represents sentiment analysis results of online reviews using interval type-2 fuzzy numbers; the method [35] give a product purchasing recommendation ranking based on multi-attribute online ratings information; the method [13] is useful under probabilistic linguistic circumstances with unknown criteria weights for online customer reviews. It is worth noting that most of the previous studies did not consider the information of the two-stage Online customer reviews, so when comparing the methods, we will gather the information of the two phases with the help of IVPLTS and the expectation function value of PLTS. Usually, different methods could be comparable only if they are used to solve the same problem. However, in most of the existing studies, the product attributes and attribute weights are objectively determined based on online reviews or are subjectively determined by consumers. To compare the result obtained by the proposed method with the results obtained by the existing methods, it is considered that the weights of different attributes are equal, i.e., $ω = (0.2, 0.2, 0.2, 0.2, 0.2)$ . The situation of equal attribute weights can be considered approximately equivalent to the situation that product attributes preference is not considered. The specific ranking results are shown in the Table 4.

Table 4
Comparison between methods.

Method Whether consider additional Online customer reviews Sort results

Our method Yes $A_{5} ≻ A_{2} ≻ A_{1} ≻ A_{3} ≻ A_{4}$

Our method without additional reviews No $A_{2} ≻ A_{5} ≻ A_{1} ≻ A_{4} ≻ A_{3}$

Liu et al. 2017 No $A_{1} ≻ A_{5} ≻ A_{2} ≻ A_{3} ≻ A_{4}$

Bi et al. 2018 No $A_{1} ≻ A_{5} ≻ A_{2} ≻ A_{3} ≻ A_{4}$

Zhang et al. 2019 No $A_{1} ≻ A_{5} ≻ A_{2} ≻ A_{3} ≻ A_{4}$

Li et al. 2020 No $A_{2} ≻ A_{1} ≻ A_{5} ≻ A_{3} ≻ A_{4}$

Method	Whether consider additional Online customer reviews	Sort results
Our method	Yes	$A_{5} ≻ A_{2} ≻ A_{1} ≻ A_{3} ≻ A_{4}$
Our method without additional reviews	No	$A_{2} ≻ A_{5} ≻ A_{1} ≻ A_{4} ≻ A_{3}$
Liu et al. 2017	No	$A_{1} ≻ A_{5} ≻ A_{2} ≻ A_{3} ≻ A_{4}$
Bi et al. 2018	No	$A_{1} ≻ A_{5} ≻ A_{2} ≻ A_{3} ≻ A_{4}$
Zhang et al. 2019	No	$A_{1} ≻ A_{5} ≻ A_{2} ≻ A_{3} ≻ A_{4}$
Li et al. 2020	No	$A_{2} ≻ A_{1} ≻ A_{5} ≻ A_{3} ≻ A_{4}$

According to the Table 4, the same or similar ranking results are obtained by different methods. Compared with other methods, our method considers vivo to be the most suitable phone for the college. The main possible reason is considering two-stage Online customer reviews. Our approach not only takes into account the time weight of Online customer reviews but also fully exploits the consumer preferences contained in reviews. And compared with our method without additional reviews, it shows that by combining information from initial and additional reviews, our approach highlights the value of consistent and contradictory evaluations. Because consumers tend to be more comprehensive and objective in the additional reviews they post after using a product for a period of time and having a better understanding of the product they purchased, and contradictory reviews have been shown to have a higher perception of usefulness. Therefore, the method in this paper is more realistic in reflecting the value of product attributes and provides a more favorable product selection method for consumers.

5. Conclusions

In this paper, we study the product selection problem in the context of Online customer reviews and propose an extended IVPLTS-PROMETHEE product ranking method. According to the model and case analysis, some conclusions are given as follows.

(1)

In the proposed method, to identify the positive, neutral, and negative sentiment orientations of Online customer reviews, an algorithm based on sentiment dictionary is proposed. The algorithm has a clear logic and is a valuable attempt at refining more valuable information for product ranking through Online customer reviews. Then, we introduce IVPLTSs to present the sentiment analysis result of Online customer reviews. It achieves the transformation of text information to interval probabilistic linguistic information and provides an effective tool to make use of two-stage Online customer reviews for product ranking.

(2)

This paper provides a new method to deal with the product ranking problem through Online customer reviews. It applies a new combination weighting method to calculate attribute weights considering individual preferences and collective external evaluation simultaneously. We further establish a model to calculate the ideal expectation value of attributes and stage weights for final product ranking.

In the follow-up research, we will consider developing a support system based on the proposed method to improve consumers’ shopping experiences. Moreover, the deeper research on sentiment analysis and more properties of IVPLTS are also worth paying attention to.

Footnotes

Acknowledgments

This work is partially funded by the National Natural Science Foundation of China (71503103; 72372059); National Social Science Foundation of China (19FGLB031; 22AJL002); Outstanding Youth in Social Sciences of Jiangsu Province; Qinglan Project of Jiangsu Province, and the Fundamental Research Funds for the Central Universities (JUSRP622047; JUSRP321016), the Tender Project from Wuxi Federation of Philosophy and Social Sciences (WXSK24-A-05) and Engineering Research Center of Integration and Application of Digital Learning Technology, Ministry of Education (1321005) and Social Science Fund of Qinghai Province (23YQA-003) and Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX24_2486). Even so, this work does not involve any conflict of interest.

Conflict of interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.

Data availability statement

The data used to support the findings of this study will be considered by the corresponding author.

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