Data-driven product ranking: A hybrid ranking approach

2.1 Concepts of IFS and IFMPR

Definition 2.1. [52] Let X be a nonempty set, we call A = {〈 x, μ _A  (x) , ν _A  (x) 〉 |x ∈ X} the intuitionistic fuzzy set (IFSs), where μ _A  (x) and ν _A  (x) are the membership and non-membership functions of the IFS A on X, respectively. μ A : X → [ 0 , 1 ] , x ∈ X → μ A ( x ) ∈ [ 0 , 1 ] ν A : X → [ 0 , 1 ] , x ∈ X → ν A ( x ) ∈ [ 0 , 1 ]

And satisfying that 0 ⩽ μ _A  (x) + ν _A  (x) ⩽1, x ∈ X, π _A  (x) =1 - μ _A  (x) - ν _A  (x) , x ∈ X, which denotes the hesitancy or uncertainty of the element x ∈ X to the set A. The ordered pair (μ _A  (x) , ν _A  (x)) is called an intuitionistic fuzzy value (IFV).

Definition 2.2. [53] For an IFN α = (μ _α, ν _α), we call s (α) = μ _α - ν _α the score function of α, and h (α) = μ _α + ν _α the accuracy function of α. To compare two IFNs α₁ = (μ _α1, ν _α1) and α₂ = (μ _{α 2} , ν _α2), the following laws can be given:

( 1 ) If s ( α 1 ) > s ( α 2 ) , then α 1 > α 2 ; ( 2 ) If s ( α 1 ) = s ( α 2 ) , then ( a ) If h ( α 1 ) > h ( α 2 ) , then α 1 > α 2 ; ( b ) If h ( α 1 ) = h ( α 2 ) , then α 1 = α 2 .

Definition 2.3. [54] Let X is a fixed set, and the intuitionistic fuzzy multiplicative set (IMS) is defined as: D = ( < x , ρ D ( x ) , σ D ( x ) > | x ∈ X )

Where (ρ _D  (x) , σ _D  (x)) is the intuitionistic multipliers number (IMN), ρ _D  (x) and σ _D  (x) are the membership and non-membership of each element x respectively, and satisfy 1/9 ⩽ ρ _D  (x) , σ _D  (x) ⩽9, ρ _D  (x) σ _D  (x) ⩽ 1, ∀ x ∈ X, ρ _D  (x) and σ _D  (x) are represented by Saaty’s scale (see Table 1).

Definition 2.4. [55] For the IFMN α = (ρ _α, σ _α), we call it a score function about s (α) = ρ _α/σ _α, which is an exact function about h (α) = ρ _ασ _α. To compare two IFMNs α₁ = (ρ _α1, σ _α1) , α₂ = (ρ _α2, σ _α2), the following comparison rules for intuitionistic fuzzy numbers can be used:

( 1 ) If s ( α 1 ) > s ( α 2 ) , then α 1 > α 2 ; ( 2 ) If s ( α 1 ) = s ( α 2 ) , then ( a ) If h ( α 1 ) > h ( α 2 ) , then α 1 > α 2 ; ( b ) If h ( α 1 ) = h ( α 2 ) , then α 1 = α 2 .

The following operation rules are also met:

α 1 ⊕ α 2 = ( ρ α 1 , σ α 1 ) ⊕ ( ρ α 2 , σ α 2 ) = ( ( 1 + 2 ρ α 1 ) ( 1 + 2 ρ α 2 ) - 1 2 , 2 σ α 1 σ α 2 ( 2 + 2 σ α 1 ) ( 2 + 2 σ α 2 ) - σ α 1 σ α 2 ) α 1 ⊗ α 2 = ( ρ α 1 , σ α 1 ) ⊗ ( ρ α 2 , σ α 2 ) = ( 2 ρ α 1 ρ α 2 ( 2 + 2 ρ α 1 ) ( 2 + 2 ρ α 2 ) - ρ α 1 ρ α 2 , ( 1 + 2 σ α 1 ) ( 1 + 2 σ α 2 ) - 1 2 )

Definition 2.5. [55] If X = {x₁, x₂, ⋯ , x_n} is an alternative set, the preference relation of intuitionistic fuzzy multiplicative consistency (IFMPR) can be expressed as A = (α _ij ) _n×n ⊂ X × X. α _ij  = (ρ _{α ij} , σ _{α ij} ) (i, j = 1, 2, ⋯ , n) is the IFMNs, ρ _{α ij} represents the preference degree of alternative x _i over x _j , and σ _{α ij} indicates the degree of preference of the alternative x _i overx _j . ρ _{α ij} and σ _{α ij} satisfy ρ _{α ij}  = σ _{α ji} , σ _{α ij}  = ρ _{α ji} , ρ _{α ii}  = σ _{α ii}  = 1, for all i, j = 1, 2, ⋯ , n. For convenience, (ρ _{α ij} , σ _{α ij} ) will be expressed as (ρ _ij , σ _ij ) in the rest of this article.

2.2 Summary of IFMBW [56]

The steps of Intuitionistic fuzzy multiplicative best-worst method (IFMBWM) are described as follows:

Step 1: Determine a set of decision criteria C = {C₁, C₂, . . . , C _m }, and the decision maker compares the criteria set by using Saaty’s scale (Table 2) to obtain the preference relationship IFMPR matrix A = (α _ij ) _n×n of Intuitive Fuzzy multiplication consistency.

A = ( ( ρ 11 , σ 11 ) ( ρ 12 , σ 12 ) ⋯ ( ρ 1 n , σ 1 n ) ( ρ 21 , σ 21 ) ( ρ 22 , σ 22 ) ⋯ ( ρ 2 n , σ 2 n ) ⋮ ⋮ ⋱ ⋮ ( ρ n 1 , σ n 1 ) ( ρ n 2 , σ n 2 ) ⋯ ( ρ nn , σ nn ) ) n × n

Step 2: Sort the standards according to IFMPR to determine the best standard C _B and the worst standard C _W , C _B  = C₁ ≻ C₂ ≻ ⋯ ≻ C _n  = C _W .

Step 3: Suppose that the optimal weight vector W * = w 1 * , w 2 * , ⋯ , w n * T , w j * = ( τ j * , υ j * ) ( j ∈ N ) is IFNs, τ j * can be solved by minimizing the sum of the maximum absolute differences |τ _best /τ _j  - ρ_best,j| and |τ _j /τ _worst  - ρ_j,worst|, υ j * can be solved by minimizing the sum of the maximum absolute differences |υ _best /υ _j  - σ_best,j| and |υ _j /υ _worst  - σ_j,worst|. The following mathematical models can be established: min ξ s . t . | τ best / τ j - ρ best , j | ⩽ ξ , | τ j / τ worst - ρ j , worst | ⩽ ξ , ∑ j = 1 n τ j = 1 , τ 1 ⩾ τ 2 ⩾ ⋯ ⩾ τ n , ξ ⩾ 0 , τ j ⩾ 0 , for all j ∈ N .(2.1) min ζ s . t . | υ best / υ j - σ best , j | ⩽ ζ , | υ j / υ worst - σ j , worst | ⩽ ζ , ∑ j = 1 n υ j = 1 , υ 1 ⩽ υ 2 ⩽ ⋯ ⩽ υ n , ζ ⩾ 0 , υ j ⩾ 0 , for all j ∈ N .(2.2)

The standard intuitionistic fuzzy multiplication optimal weight vector can be easily obtained by solving models 2.1 and 2.2: W * = w 1 * , ⋯ , w n * T = ( ( τ 1 * , υ 1 * ) , ⋯ ( τ n * , υ n * ) ) T

DEA is a typical nonparametric linear programming performance evaluation model. The concept of single input and single output engineering efficiency is extended to the effectiveness evaluation of the same DMU with multiple inputs and outputs, which greatly enriches the production function theory and its application technology in microeconomics. At the same time, subjective factors are avoided, algorithms are simplified the advantages of reducing errors cannot be underestimated. To judge whether the decision-making unit is DEA effective is essentially to judge whether the decision-making unit falls on the production frontier of the production possibility set. The production frontier is the Pareto surface of linear multi-objective programming, which is composed of the effective part of data envelopment surface. Generally, DEA models are divided into output oriented and input-oriented models. The output-oriented DEA model maximizes the output of a given number of input factors, and the output-oriented DEA model minimizes the input factors required for a given output level. Suppose there are n DMUs to be evaluated, and each DMU has m input and n output. In more precise form, the input-oriented DEA-CCR model is as follows [57]: θ o CCR = max ∑ i = m + 1 m + s w i y io s . t : ∑ i = m + 1 m + s w i y ij - ∑ i = 1 m w i x ij ⩽ 0 , j = 1 , ⋯ , n , ∑ i = 1 m w i x io = 1 , w i ⩾ 0 , i = 1 , ⋯ , m + s .(2.3)

Where, x _ij , y _ij respectively represents the i ^th input and r ^th output of the evaluated j ^th DMU, and w₁, ⋯ , w _m , w_m+1, ⋯ , w_m+s respectively represents the weight of the input and output. Moreover, x _ij , y _ij are known parameters and w _i are unknown variables. The efficiency score of the DMU to be evaluated is expressed as θ o CCR , when the efficiency value is equal to 1, the DMU is effective; When the efficiency value is less than 1, the DMU is weakly efficient.

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3.2 Sentiment analysis (SA)

As Web 2.0 continues to evolve, the number of OCR has increased dramatically. the impact of OCRs on purchase decisions between consumers is also increasing, and researchers are increasingly using SA to aid their decision-making process. SA is the fine-grained study of people’s opinions, sentiments, emotions and attitudes, and context mining of text is used to identify and extract subjective information from textual data. The aim of this section is to calculate a sentiment score for each feature of each product; note that here the sentiment score is denoted as IFV. Most current research on online reviews only considers positive and negative reviews, and there is a lack of research on neutral reviews, which can lead to a loss of information for decision making. This is because neutral OCRs can also be used to avoid retaliation from sellers, but are not necessarily objective. Therefore, this paper considers a combination of positive, neutral and negative emotions in OCR, enabling consumers to make faster and more accurate purchase decisions; helping merchants to further upgrade their products.

This section contains three parts, 1. Clustering of OCR based on key attribute; 2. Sentiment analysis of OCR using Naive Bayes; 3. Building an IF decision matrix based on key attribute.

In the decision-making process in real life, it is very important to consider the preferences of decision makers. Decision makers’ preferences are usually hesitant and uncertain. Therefore, in order to reduce the flexibility of the traditional DEA model DMU in choosing weights in the intuitionistic fuzzy environment, this paper uses the method of weight restriction to incorporate decision makers’ preferences into the DEA model. A new integrated IFMBWM-DEA model is proposed, which comprehensively considers the positive, neutral and negative online comments of online consumers, making the ranking of alternatives more objective in the intuitionistic fuzzy environment.

Since the IFMBWM model (2.1) and model (2.2) are nonlinear minimum models, which may produce multiple optimal solutions [58], we consider the following corresponding linear models (3.7) and (3.8) of BWM. min ξ s . t . | τ best - τ j ρ best , j | ⩽ ξ | τ j - τ worst ρ j , worst | ⩽ ξ ∑ j = 1 n τ j = 1 τ 1 ⩾ τ 2 ⩾ ⋯ ⩾ τ n ξ ⩾ 0 , τ j ⩾ 0 , for all j ∈ N(3.7) min ζ s . t . | υ best - υ j σ best , j | ⩽ ζ | υ j - υ worst σ j , worst | ⩽ ζ ∑ j = 1 n υ j = 1 υ 1 ⩽ υ 2 ⩽ ⋯ ⩽ υ n ζ ⩾ 0 , υ j ⩾ 0 , for all j ∈ N(3.8)

The equality constraints ∑ i = 1 n τ i = 1 , ∑ j = 1 n υ j = 1 in IFMBWM model (3.7) and model (3.8) are different from those ∑ i = 1 m ν i x io = 1 in DEA-CCR model (2.3), so the following DEA model is considered: max ∑ i = m + 1 m + s w i y io - θ o CCR ∑ i = 1 m w i x io s . t . ∑ i = m + 1 m + s w i y ij - θ j CCR ∑ i = 1 m w i x ij ⩽ 0 ⋯ j = 1 , ⋯ , n , ∑ i = 1 m + s w i = 1 , w i ⩾ 0 , i = 1 , ⋯ , m + s .(3.9)

Where, θ j CCR is the estimated efficiency score of the j ^th DMU in the model (3.9). M. Zohrehbandian et al. have proved that the optimal solution of the model is the same, in which the constraint ∑ i = 1 m w i x io = 1 in model (3.3) is replaced by ∑ i = 1 m + s ω i = 1 , which is similar to the weight normalization in IFMBWM [59]. Assuming that the optimal weight vector W * = ( w 1 * , w 2 * , ⋯ w n * ) T , w i * = ( τ i * , υ i * ) ( i ∈ N ) is IFMNs, taking the membership degree as an example, the proposed IFMBWM-DEA model is as follows: max f 1 = ∑ i = m + 1 m + s τ i y io - θ o CCR ∑ i = 1 m τ i x io max f 2 = - ξ s . t . ∑ j = m + 1 m + s τ i y ij - θ j CCR ∑ i = 1 m τ i x ij ⩽ 0 ⋯ j = 1 , ⋯ , n , ∑ i = 1 m + s τ i = 1 , | τ best - τ i ρ best , i | ⩽ ξ , i = 1 , ⋯ , m + s , | τ i - τ worst ρ i , worst | ⩽ ξ , i = 1 , ⋯ , m + s , τ 1 ⩾ τ 2 ⩾ ⋯ ⩾ τ n , ξ ⩾ 0 , τ i ⩾ 0 , i = 1 , ⋯ , m + s .(3.10)

The first objective function and the first constraint belong to DEA model; The second objective function and the third and fourth constraints are about inputs in BWM; The third objective function and the fifth and sixth constraints belong to the output in BWM; Equality constraints ∑ i = 1 m + s τ i = 1 belong to DEA and BWM. Since the model (3.10) is a multi-objective programming model, the parameter method and constraint ɛ>, Min max method and multi-objective programming model [60]. In this paper, the min max method is used to solve the model, which can be easily converted into a linear model, as shown below: min α s . t . f 1 * - ( ∑ i = m + 1 m + s τ i y io - θ o CCR ∑ i = 1 m τ i x io ) ⩽ α , f 2 * - ( - ξ ) ⩽ α , ∑ j = m + 1 m + s τ i y ij - θ j CCR ∑ i = 1 m τ i x ij ⩽ 0 , j = 1 , ⋯ , n , ∑ i = 1 m + s τ i = 1 , | τ best - τ i ρ best , i | ⩽ ξ , i = 1 , ⋯ , m + s , | τ i - τ worst ρ i , worst | ⩽ ξ , i = 1 , ⋯ , m + s , τ 1 ⩾ τ 2 ⩾ ⋯ ⩾ τ n , ξ , ψ ⩾ 0 , τ i ⩾ 0 , i = 1 , ⋯ , m + s .(3.11)

By solving the model (3.11), we can get the first part of the optimal weight of intuitionistic fuzzy multiplication ( τ 1 * , ⋯ , τ m * , τ m + 1 * , ⋯ , τ m + s * ) T , the membership of the intuitionistic fuzzy multiplication weight about input and output. In the same way, we can solve the second part of the optimal weight of intuitionistic fuzzy multiplication ( υ 1 * , ⋯ , υ m * , υ m + 1 * , ⋯ , υ m + s * ) T , the non-membership part of the input and output intuitionistic fuzzy multiplication weights, so we can get the optimal weight of W * = ( w 1 * , w 2 * , ⋯ w n * ) T = ( ( τ 1 * , υ 1 * ) , ( τ 2 * , υ 2 * ) , ⋯ , ( τ n * , υ n * ) ) T . Then, the efficiency score of the j ^th DMU is calculated as follows: θ j IFMBWM - DEA = ∑ i = m + 1 m + s w i * ⊗ y ˜ ij ∑ i = 1 m w i * ⊗ x ˜ ij(3.12)

The efficiency obtained from the solution is also an intuitionistic fuzzy number. According to definition 2.4, compare the efficiency and rank the products.

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Preprocess the online consumer comment data after data cleaning. After Chinese word segmentation, deactivation words and part of speech tagging, TF-IDF algorithm is used to extract candidate keywords in online consumer comments, and the TOP200 words with the highest frequency are reserved. After removing unqualified words, K-means clustering algorithm is used to calculate the best category attribution based on the similarity between points and create normalized labels, The K-means clustering diagram is shown in Fig. 1 below. It can be seen from Fig. 3 that when k = 6, the clustering effect is better. Therefore, words with similar meanings are classified into the same group, and a total of six key attributes are clustered, namely after-sales service, quality, logistics, price, appearance and gifts. The key attributes are shown in table.

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Fig. 3

K-means clustering diagram when k = 6.

The purpose of this section is to calculate the emotion score of key attributes of replaceable products, w- here the emotion score is expressed by IFVs. This paper considers both positive and negative online consumer comments, so that potential consumers can make purchase decisions more quickly and accurately; It is also very helpful for merchants to further upgrade their products and plan publicity. First, the “match” function in R language is used to cluster the online consumer comments of alternative products according to the key attributes. The results of the number of OCRs clustered into the key attributes are shown in Table 3.

Then the preprocessed word vector is transformed, the classifier is trained, and then the weighted naive Bayes is used to give weight to the emotional polarity of each emotional word in combination with the sentence structure, and then the weighted sum is used to obtain the emotional polarity score of online consumer comments. The polarity results of emotional analysis are shown in Table 4, where POS, neu and neg respectively represent the number of online consumer comments with positive, neutral and negative emotional polarity.

Finally, the performance scores of key features are constructed into intuitionistic fuzzy numbers. First, convert the data in Table 4 into intuitionistic fuzzy numbers (such as Eqs. (3.4), (3.5) and (3.6) in section 3.2.3.), and then take the performance scores obtained according to the key features as the output in the DEA model. At the same time, because DEA model requires that decision-making units must have input variables, all decision-making units are given the same virtual input variables x ˜ ij = ( 0.5 , 0.5 ) . The input and output of IFMBWM-DEA model are shown in Table 5.

First, we invite experts to use Saaty’s scale to compare the key attributes C = {C₁, C₂, . . . , C₆} extracted from online consumer reviews, and obtain the preference relationship matrix A of the consistency of intuitionistic fuzzy multiplication. The preference of intuitionistic fuzzy multiplication for virtual input is (1, 1). A = ( ( 1 , 1 ) ( 1 5 , 4 ) ( 6 5 , 1 3 ) ( 2 5 , 4 3 ) ( 4 9 , 7 4 ) ( 8 7 , 3 4 ) ( 4 , 1 5 ) ( 1 , 1 ) ( 3 , 1 4 ) ( 8 3 , 1 4 ) ( 9 4 , 5 8 ) ( 7 , 1 9 ) ( 1 3 , 6 5 ) ( 1 4 , 3 ) ( 1 , 1 ) ( 1 9 , 5 ) ( 1 7 , 3 ) ( 7 4 , 2 7 ) ( 4 3 , 2 5 ) ( 1 4 , 8 3 ) ( 5 , 1 9 ) ( 1 , 1 ) ( 6 5 , 4 7 ) ( 3 , 1 7 ) ( 7 4 , 4 9 ) ( 5 8 , 9 4 ) ( 3 , 1 7 ) ( 4 7 , 6 5 ) ( 1 , 1 ) ( 5 4 , 2 7 ) ( 3 4 , 8 7 ) ( 1 9 , 7 ) ( 2 7 , 7 4 ) ( 1 7 , 3 ) ( 2 7 , 5 4 ) ( 1 , 1 ) ) 6 × 6

According to the algorithm for sorting standards proposed by [56], the outgoing degrees of all standard nodes can be calculated, D 1 out = 2 , D 2 out = 5 , D 3 out = 1 , D 4 out = 4 , D 5 out = 3 , D 6 out = 0 . Thus, the best standard C _B  = C₂ and the worst standard C _W  = C₆ can be determined. The weight of the standard needs to be satisfied τ₂ ⩾ τ₄ ⩾ τ₅ ⩾ τ₁ ⩾ τ₃ ⩾ τ₆, υ₂ ⩽ υ₄ ⩽ υ₅ ⩽ υ₁ ⩽ υ₃ ⩽ υ₆. By substituting the data into the model (3.11) and model (3.12), the optimal weight results of intuitionistic fuzzy multiplication can be solved as Table 6.

The efficiency score and ranking results of alternative products can be obtained by substituting the obtained optimal weight into Eq. (4.12), as shown in Table 7 below.

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5.1 Comparison of whether or not to consider the preferences of decision makers

In order to verify whether the proposed consideration of the preference of decision makers will have an effect on the ranking of alternatives, we in contrast the DEA methods of whether to pay attention to the preference of decision makers. In order to save space, only the final results are displayed. The results are shown in Table 7.

It can be viewed from Table 7 that the ranking results of these two methods are obviously different. This is mainly due to the fact considering the preference of decision makers, the weight of attributes will have an effect on the dominance of alternative products, and then affect the final ranking of alternative products. In short, thinking about the preference of decision makers will affect the final ranking of alternative products by influencing the weight of attributes.

5.2 Comparison between the proposed method and other existing methods

The proposed IFMBWM-DEA is compared with IF-VIKOR [61] and IF-TOPSIS [62] methods.

(1) Comparison with the IF-TOPSIS method

The IF-TOPSIS product ranking method focuses on normalizing the original data matrix, determining the weight coefficients of the attributes based on expert recommendations, then calculating the weighted Euclidean distance and proximity between the alternative product and the best or worst solution, and ranking the alternative products based on proximity. The attribute weights are w = [0.15, 0.25, 0.1, 0.2, 0.15, 0.05, 0.1], and the steps of the IF-TOPSIS method are as follows.

Step 1: Identify positive and negative ideal solutions.

The laptop’s positive ideal solution (PIS) A and negative ideal solution (NIS) A+^– are defined as follows. A + = { a j + , max i = 1 m 〈 a ij 〉 ; j = 1 , 2 , ⋯ , n } A - = { a j - , min i = 1 m 〈 a ij 〉 ; j = 1 , 2 , ⋯ , n }

Step 2: Calculate the Euclidean distance between each alternative product and the positive and negative ideal solution. D i + = ∑ j = 1 n w j d ( a ij , a j + ) D i - = ∑ j = 1 n w j d ( a ij , a j - )

Step 3: Calculate proximity. CI i = D i - D i + + D i - , i = 1 , 2 , ⋯ , m

The results of the IF-TOPSIS method, which calculates the positive and negative ideal distances and similar proximity of the substitutable products, are shown in the Table 8 for the 15 laptops.

(2) Comparison with the IF-VIKOR method

IF-VIKOR is a MCDM based on ideal point trade-off ranking, characterized by the ability to combine maximizing group utility and minimizing individual regret to achieve a preferred choice of finite decision options. Based on the data in Table 5, group utility and individual regret are determined, and then the group utility value and the trade-off value are solved for; the smaller the trade-off value, the better the alternative. the steps of the IF-VIKOR method are as follows.

Step 1: Calculate each attribute for positive and negative intuitionistic fuzzy ideal solutions. d i + = 1 2 ( | u ij - u j + | + | v ij - v j + | + | π ij - π j + | ) d i - = 1 2 ( | u ij - u j - | + | v ij - v j - | + | π ij - π j - | ) π i + = 1 - u j + - v j + , π i - = 1 - u j - - v j -

Step 2: Determine the positive and negative intuitionistic fuzzy ideal solutions of the intuitionistic fuzzy synthesis decision matrix. r + = 〈 u + , v + 〉 = 〈 max u , min v 〉 , ( j = 1 , 2 , ⋯ , n ) r - = 〈 u - , v - 〉 = 〈 min u , max v 〉 , ( j = 1 , 2 , ⋯ , n )

Step 3: Calculate the utility value U _i , individual regret value K _i and trade-off value for each option Z _i . U i = ∑ j = 1 n ( w j d ( r j + , r ij ) d ( r j + , r j - ) ) , ( i = 1 , 2 , ⋯ , m K i = max ( w j d ( r j + , r ij ) d ( r j + , r j - ) ) , ( i = 1 , 2 , ⋯ , m Z i = λ U i - min i U i max i U i - min i U i + ⋯ 1 - λ ( U i - min i U i max i U i - min i U i , ( i = 1 , 2 , ⋯ , m

In the above equation, w _i are the weights of the attributes of the integrated intuitionistic fuzzy decision matrix, and λ (0 ⩽ λ ⩽ 1) are the compromise coefficients. In the article, λ = 0.5,a compromise and balance approach are taken.

Step 4: Rank the alternatives according to the compromise value, the larger the Z _i , the worse the plan; the smaller the Z _i , the better the plan.

Based on the above steps of the IF-VIKOR method, the group utility value, individual regret value and compromise value of the alternative products were calculated and the results of the ranking of the 15 laptops are shown in the Table 9.

Comparing the results of ranking products using the DEA method in section 5.1, we can see that whether decision preferences are considered has a significant impact on consumers making purchase decisions. The results of ranking products by IF-TOPSIS, IF-VIKOR in section 5.2 can be seen in Fig. 4, the results of ranking products by the IFMBWM-DEA method are not identical to those of the IF-TOPSIS and IF-VIKOR methods. So we checked the correlation between the proposed method and the other MCDM methods using the Spearman correlation coefficient, which checks the relationship between the rankings obtained from the different MCDM methods, and the calculated results are shown in Table 10. It can be seen from Table 10 that although the ranking results are not identical, there is a high correlation coefficient.

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Fig. 4

Ranking results.

The reason for the incomplete consistency of the ranking results between these methods is because that the proposed method considers consumers’ own purchase preference situations. The IF-TOPSIS and IF-VOKOR methods assume that consumers are perfectly rational when purchasing laptops, but are not perfectly rational in the actual purchase decision process [63]. Therefore, the OCR-based method of product ranking is more reasonable.

Although many websites now provide quantitative benchmarks for ranking products, it is still recommended that consumers make their purchase decisions through OCR. In contrast, the method proposed in this paper extracts key attributes from OCR as evaluation indicators, integrates positive, neutral and negative sentiment orientations, and considers the decision maker’s own preferences, making it more objective and realistic and simplifying the decision-making process.