Dynamic network intelligent hybrid recommendation algorithm and its application in online shopping platform

Abstract

With the rapid development of e-commerce, whether network intelligent recommendation can attract customers has become a measure of customer retention on online shopping platforms. In the literature about network intelligent recommendation, there are few studies that consider the difference preference of customers in different time periods. This paper proposes the dynamic network intelligent hybrid recommendation algorithm distinguishing time periods (DIHR), it is a integrated novel model combined with the DEMATEL and TOPSIS method to solved the problem of network intelligent recommendation considering time periods. The proposed method makes use of the DEMATEL method for evaluating the preference relationship of customers for indexes of merchandises, and adopt the TOPSIS method combined with intuitionistic fuzzy number (IFN) for assessing and ranking the merchandises according to the indexes. We specifically introduce the calculation steps of the proposed method, and then calculate its application in the online shopping platform.

Keywords

DIHR recommendation algorithm network intelligent recommendation system online shopping platform

1 Introduction

With the rapid development of online shopping platforms, people enjoy more convenience brought by online shopping. At the same time, due to the improvement of living standards and the rapid development of economy, the number of people shopping on e-commerce platforms also increases dramatically every year. In recent years, various e-commerce platforms have sprung up, and the competition has become more and more fierce. Each e-commerce platform attracts customers through its unique advantages, such as ease of operation, logistics distribution and shopping discounts.According to ii-media Research, the online retail volume in the first quarter of 2019 has reached 4.816.06 trillion CNY, accounting for 24.7% of the total retail sales of consumer goods. Ii-media consulting analysts believe that advances in mobile terminals and payment technology have boosted the penetration rate of e-commerce. At present, online shopping has become an important consumption habit of consumers, and e-commerce system of China has been developed. In the rapid development of e-commerce, there are also some problems. The resources on the Internet are very rich, but it also increases the search time of customers, making it difficult for customers to buy the most satisfactory products in a short time.

With the development of Internet technology, the operation of the e-commerce platforms become more humanized. It can be able to develop personalized interface according to the customer’s preferences. Personalized merchandise browsing and recommendation based on customers is an important evaluation index that affects customers’ satisfaction with the operation of the internet shopping platform. At present, most online shopping platforms predict the merchandises that customers may be interested in by analyzing their purchase records and browsing records. Meanwhile, customers can refuse the platform to push related commodities again, if they are not interested in the commodities or such commodities. This setting not only shortens the search time of customers, but also can promote merchandises according to customers’ preferences, which greatly improves the potential revenue of the platform.

However, when many online shopping platforms push merchandises, it tend to list everything a customer has ever bought. The recommended order of merchandises is mostly random. Or the similar merchandises that the customer has bought are recommended at random. If only the purchase records of customers are considered, the purchase records of each customer will be very numerous and miscellaneous. And not every customer will have the patience to browse the recommendation pages all the time due to the limited number of recommendation pages. In other words, a recommendation method that only considers a customer’s preference for similar types or styles of merchandises in the purchase record will result in too large a number of recommended merchandises. Meanwhile, the existing intelligent recommendation methods seldom consider the combination of different commodities and the internal relation of the combination.

Based on this, this paper tries to propose a dynamic network intelligent hybrid recommendation algorithm distinguishing time periods (DIHR) model which considers the order of customers’ preference by combining the customers’ habit preference of purchasing merchandises. In considering that the TOPSIS method is a comprehensive evaluation method for multi-objective decision of limit solution. After the same trend and normalization of the original data, the effect of different index dimensions is eliminated. It can make full use of the information of the original data, fully reflect the gap between various schemes, and objectively reflect the actual situation. It has advantages of real, intuitive and reliable. The Dematel method is a methodology for understanding complex and difficult problems in the real world proposed by scholars A. Gabus and E. Fontela of Battelle laboratory in the United States at a conference in Geneva in 1971. It is a systematic analysis method using graph theory and matrix tools. And it is a comprehensive method for building and analyzing a structural model involving causal relationships between complex factors [1]. Considering that this paper needs to analyze the relationship between the merchandises purchased by customers and rank the merchandises. Therefore, it is most appropriate to adopt these two methods in this paper.

In this method, the authors count the merchandises and types of the customers purchase records, analyze the relationship between the merchandises purchased by customers by combining the DEMATEL method, and rank all merchandises according to their preference degree by combining the TOPSIS method. The aim is to build an optimal network intelligent recommendation system that is most conforms to personalized preferences of the customers. This method improves the limitation of the previous intelligent recommendation algorithm that only considers the merchandise preference of the customer, but does not compare and rank the preferred merchandises. It can provide a scientific and reasonable reference for e-commerce platform and has practical application value. This method can promote the development of network platform, if it can be adopted. Meanwhile, it expands the algorithm design of intelligent recommendation system and enriches the application field and value of decision theory.

The rest of this paper is organized as follows: in Section 2, the author describes the research problems of this paper on the basis of introducing the literature of network intelligence recommendation. In Section 3, the author formulates the research problem and then set the parameters, analyze the relationship between the merchandises purchased by customers and rank them according to the preference degree. In Section 4, an example illustrating the feasibility and effectiveness of the proposed method are presented. Finally, the conclusions and the future research directions are presented in Section 5.

2 Related work

There are some methods to make scheme recommendation according to customer preference in the literature of network recommendation. Recommendation Systems are playing more and more important role in our life, representing useful tools helping customers to find “what you need” and “guess what you like” from huge amount of candidates. They denote a meaningful response to the phenomenon of information overload, with the purpose to predict customer’s preferences providing suggestions about candidates that could be of interest [2, 3]. At present, there are many research results about network recommendation systems [4, 5], which are based on social network media or considering customer collaborative filtering. The algorithm research of intelligent recommendation system belongs to group decision, and there are abundant research results on group decision making [6 –9].

In a collaborative filtering method [10], the recommendation is in turn performed by filtering and evaluating candidates with ratings from other customers. The neighborhood-based approaches are the most popular prediction methods which are widely adopted in commercial collaborative filtering methods [11, 12]. Popular neighborhood based collaborative filtering approaches can be classified as customer based approaches and item-based approaches. Customer-based approaches predict the ratings of active customers based on the ratings of their similar ones, and item-based approaches predict the ratings of active customers based on the computed information of items similar to those chosen by the active customer. However, there is drawbacks to this calculation. On one hand, most of the algorithms of customer collaborative filtering need customer evaluation. In China, most customers have a moderate character and will habitually give favorable comments, so their comments will not have a general reference value. On the other hand, this calculation, which takes into account the degree of activity between customers and candidates, is more about recommending popular candidates to customers. Such recommendations may be more concerned with “guess what you like” than “what you need”.

There are also a number of studies that consider more about “what you need”. Deldjoo et al. [13] proposed a recommendations through assessed W. R. T. relevance metrics and compared with existing content-based recommendation systems that exploit explicit features such as movie genre. Son and Kim [14] proposed method employs centrality and clustering techniques to consider the mutual relationships among items, as well as determine the structural patterns of these interactions. This mechanism ensures that a variety of items are recommended to the customer, which improves the performance. Sappelli et al. [15] evaluated context-aware recommendation systems for information re-finding by knowledge workers, identified four criteria that are relevant for evaluating the quality of knowledge worker support and compared three different context-aware recommendation methods for information re-finding in a writing support task. There is also a lot of research on intelligent recommendation system of social network [16 –21].

However, the following cases are seldom considered in the literature. In different online shopping platforms, different customers have their own unique shopping habits. Some customers are accustomed to buying accessories such as a mouse and keyboard after buying a computer, but will not buy the mouse and keyboard when not buying computer. Some customers buy many related products such as toner cartridges when buying digital products such as printers, or not buying all of them at all.

We noticed that shopping habits and preferences of customers may vary in different time periods. There are already some applications that consider time periods for intelligent recommendation, such as a map navigation application that can recommend the best route based on a combination of time periods and customer preferences, and a network short video platform that recommends short videos based on customer browsing preferences and time periods, and so on. However, the intelligent hybrid recommendation considering the time periods and customer preference is still rare in the online shopping platform.

Among the literature of the TOPSIS method and the DEMATEL method, only a few of them are considered in combination [22, 23], and there is a lack of intelligent recommendation algorithm considering different time periods [24 –26]. In this paper, the DEMATEL method will be used to analyze the relationship between the merchandises purchased by customers in different time periods. By calculating customers’ preferences in consumption behaviors and habits, the customers’ preference for merchandises in a specific time is classified and sorted adopting the TOPSIS method combined with intuitionistic fuzzy number. Finally, intelligent recommendation results that satisfy customers’ personalized shopping habits and preferences in different time periods are obtained.

3 DIHR method combined with fuzzy DEMATEL and TOPSIS method

In this section, we formalize the problem that we study in this paper and define the notations which are utilized in this paper at first. Then, we calculate the habits of customers’ preferences for indexes of merchandises in different time periods. For different time periods, the merchandises that conform to customers’ habits are ranked according to customers’ preference degree. Finally, the network intelligent recommendation algorithm by using DIHR method for time periods division which satisfy customers’ personalized habits is obtained.

3.1 Problem formulation

There are a great variety of merchandises in the internet shopping platform. Let P ={ p₁, p₂, ⋯ , p_m } be the set of the indexes of merchandises, P consists of p_i, and p_i denotes the ith index, for i = 1, 2, ⋯ m. In this proposed model, the relationship among the indexes of merchandise is determined by using the modified fuzzy the DEMATEL method. Let A be the direct relation fuzzy matrix, here is a (m × m) matrix, m represents the number of index. The direct relation matrices are all obtained by holding a pair-wise comparison among the indexes themselves in which A_ij indicates the degree to which the index p_i affects indexp_j. Let Q ={ q₁, q₂, ⋯ , q_n } be the different time periods, Q consists of q_k, and q_k denotes the k th time period, for k = 1, 2, ⋯ n. It is assumed that customers have different habits of purchasing preference for merchandises in different time periods. Then, the relationship between indexes of merchandises is also different in different time periods. Therefore, let A^k be the direct relation fuzzy matrix in the time period t_k, and $A_{ij}^{k}$ be the degree to which the index p_i affects index p_j in the q_k time period. Let C ={ c₁, c₂, ⋯ , c_l }be the set of the merchandises, C consists of c_h, and c_hdenotes the ith merchandise, for h = 1, 2, ⋯ l.

3.2 Calculation of the habits of customers’ preferences for merchandises in different time periods

In this section, we will use the DEMATEL method to calculate the preference relationship of customers for indexes of merchandises in different time periods. The specific calculation steps are as follows.

Step 1 Obtain the direct relation matrix

Generally, the effects of the indexes of merchandises on each other are expressed in terms of linguistic expressions. In order to translate the linguistic expression into the mathematical form, we use real numbers to express the degree of influence between merchandises. The measures of relationship which are used to build A matrix are given in Table 1.

Table 1
Merchandises relationship linguistic terms and values

Linguistic terms Linguistic values

No influence (No) 1

Very low influence (VL) 2

Low influence (L) 3

High influence (H) 4

Very high influence (VH) 5

Linguistic terms	Linguistic values
No influence (No)	1
Very low influence (VL)	2
Low influence (L)	3
High influence (H)	4
Very high influence (VH)	5

The relationship among the indexes of merchandises could be held within the matrix A which is given in Equation (1). The relationship among the indexes in different time period could be held within the matrix A^k which is given in Equation (2). $A = [\begin{matrix} 0 & A_{12} & \dots & A_{1 m} \\ A_{21} & 0 & \dots & A_{2 m} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ A_{m 1} & A_{m 2} & \dots & 0 \end{matrix}]$ (1) $A^{k} = {[\begin{matrix} 0 & A_{12} & \dots & A_{1 m} \\ A_{21} & 0 & \dots & A_{2 m} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ A_{m 1} & A_{m 2} & \dots & 0 \end{matrix}]}^{k}$ (2) here, A consists of A_ij, i = 1, 2, ⋯ m, j = 1, 2, ⋯ m, k = 1, 2, ⋯ n. When i = j, A^k = 0. The following A^k has the same meaning.

Step 2 Transform the direct relation matrix into the normal direct relation matrix

The maximum value of normalization is determined as follows: $Maxvar = \max (\sum_{i = 1}^{m} \sum_{j = 1}^{m} A^{k})$ (3)

By normalizing the initial direct-relation fuzzy matrix, the normalizing direct-relation fuzzy matrix X^k can be obtained as Equation (4).: $x_{ij}^{k} = {(A^{k} / M a xvar)}_{m \times m}$ and $X^{k} = [\begin{matrix} x_{11}^{k} & x_{12}^{k} & \dots & x_{1 m}^{k} \\ x_{21}^{k} & x_{22}^{k} & \dots & x_{2 m}^{k} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ x_{m 1}^{k} & x_{m 2}^{k} & \dots & x_{mm}^{k} \end{matrix}]$ (4)

here, $x_{ij}^{k}$ denotes the normal direct relation rating of customer for the index p_iagainst index p_j in the q_ktime period.

Step 3 Calculate the total relation matrix

The direct relation matrix of the normalization multiplies itself denotes the increased indirect relation between the indexes. The total relation matrix T^k can be obtained by adding up all the indirect effects. $T^{k} = lim_{m \to \infty} (X_{1}^{k} + X_{2}^{k} + \dots + X_{m}^{k}) = X^{k} (I - X^{k})^{- 1}$

here, I is the identity matrix, the matrix with a diagonal of 1 and 0 everywhere else. And the matrix could be represented as the Equation (5). $T^{k} = [\begin{matrix} t_{11}^{k} & t_{12}^{k} & \dots & t_{1 m}^{k} \\ t_{21}^{k} & t_{22}^{k} & \dots & t_{2 m}^{k} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ t_{m 1}^{k} & t_{m 2}^{k} & \dots & t_{mm}^{k} \end{matrix}]$ (5)

here, $t_{ij}^{k}$ denotes the total relation rating of customer for the index p_iagainst index p_j in the q_k time period.

Step 4 Calculate the relevant elements

According to the total relation matrix, the influence degree, influenced degree, center degree and cause degree of each elements can be obtained through further calculation.

Let $D_{i}^{k}$ be the influence degree which refers to the sum of the values of each row of matrix T^k, indicating the total influence of the corresponding elements of each row on all other elements. The influence degree $D_{i}^{k}$ can be obtained in the Equation (6). $D_{i}^{k} = \sum_{j = 1}^{m} t_{ij}^{k}, i = 1, 2, \dots m$ (6)

Let $C_{j}^{k}$ be the influenced degree which refers to the sum of the values of each column of matrix T^k, indicating the total influence of the corresponding elements of each column on all other elements. The influenced degree $C_{j}^{k}$ can be obtained in the Equation (7). $C_{j}^{k} = \sum_{i = 1}^{m} t_{ij}^{k}, j = 1, 2, \dots m$ (7)

The center degree represents the position of the element in the evaluation index system and the degree of its effect. The center degree M^k is obtained by adding the influence degree and the influenced degree of the element. The center degree M^k can be obtained in the Equation (8). $M^{k} = D_{i}^{k} + C_{j}^{k}$ (8)

The cause degree R^k is obtained by minus the influence degree and the influenced degree of the element. If the causal degree is greater than 0, it indicates that the element has a great influence on other elements, which is called the causal element. On the contrary, it is called the result element. The cause degree R^k can be obtained in the Equation (9). $R^{k} = D_{i}^{k} - C_{j}^{k}$ (9)

Step 5 Calculating the weights of indexes.

The expected prominence and relation values are calculated, importance of each index can be obtained in the Equation (10).

$w_{i}^{k} = \sqrt{{(M^{k})}^{2} + {(R^{k})}^{2}}$ (10)

Therefore, the normalized importance of each index can be obtained in the Equation (11).

$W^{k} = w_{i}^{k} / \sum_{i = 1}^{m} w_{i}^{k}$ (11) here W^k represents the final weights of the indexes to be used in the decision making process later. Through the calculation of the above steps, the preference degree of customers for the index in the q_k time period is obtained. The preference degree of customers for the index p_i here is identified as the weight of the index.

3.3 Ranking the merchandises according to customers’ shopping habits and preferences

In this section, according to the TOPSIS method, the ranking of the merchandises which be recommended to the customer can be obtained. The details are as follows:

Step 1 Determining the merchandise and getting the assessment of the customers

First, the preferences degree of merchandises will be listed separately by the customer. Generally, the preferences degree of customers for merchandises is expressed by language. To translate the language into mathematical form, here we use intuitionistic fuzzy sets to indicate the degree of influence between merchandises. In this paper, the customer’s evaluation of goods mainly depends on the customer’s subjective judgment, so the intuitionistic fuzzy decision matrix is adopted. However, the ranking results of alternative service providers by the TOPSIS method are not affected by human factors, and the results are quantified and objective, so that the evaluation process is characterized by the combination of subjective and objective, and the evaluation results are more reasonable.

The intuitionistic fuzzy set was first proposed by Atanassov as an expansion and development of Zadeh fuzzy set theory [27]. Compared with Zadeh fuzzy set theory, intuitionistic fuzzy set has a new attribute parameter- non-membership function, which reflects the fuzziness nature of the objective world more delicately, and it has been widely used in the field of multi-attribute decision making. Intuitionistic fuzzy sets have the following properties:

Definition 1 Let X be a non-empty set, an intuitionistic fuzzy set A on X is: $A = {〈 x, u_{A} (x), μ_{A} (x) 〉} | x \in X,$ $u_{A} (x) : X \to [0, 1],$ $μ_{A} (x) : X \to [0, 1]$

here, u_A (x) and μ_A (x) are the membership function and the non-membership function of A respectively. For, ∀x ∈ X, 0 ⩽ u_A (x) + μ_A (x) ⩽1, then the function 〈u_A (x) , μ_A (x) 〉 be called intuitionistic fuzzy number. The function π_A (x) is called the hesitation of the element x to belong to X, here π_A (x) =1 - u_A (x) - μ_A (x).

Definition 2 Let α = 〈u_α (x) , μ_α (x) 〉 and β = 〈u_β (x) , μ_β (x) 〉 be two intuitionistic fuzzy numbers, then

$\bar{α} = 〈 μ_{α} (x), u_{α} (x) 〉$ $α \cap β = 〈 min {u_{α} (x), u_{β} (x)}, max {μ_{α} (x), μ_{β} (x)} 〉$ $α \cup β = 〈 max {u_{α} (x), u_{β} (x)}, min {μ_{α} (x), μ_{β} (x)} 〉$ $α \oplus β = 〈 u_{α} (x) + u_{β} (x) - u_{α} (x) \cdot u_{β} (x), μ_{α} (x) \cdot μ_{β} (x) 〉$ $α \otimes β = 〈 u_{α} (x) \cdot u_{β} (x), μ_{α} (x) + μ_{β} (x) - μ_{α} (x) \cdot μ_{β} (x) 〉$ $λ α = 〈 1 - (1 - u_{α} (x))^{λ}, μ_{α} (x)^{λ} 〉, λ > 0$ $α^{λ} = 〈 u_{α} (x)^{λ}, 1 - (1 - μ_{α} (x))^{λ} 〉, λ > 0$

The assessment values are be represented in E matrix. The matrix could be represented as the Equation (12). $E = [\begin{matrix} e_{11} & e_{12} & \dots & e_{1 l} \\ e_{21} & e_{22} & \dots & e_{2 l} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ e_{m 1} & e_{m 2} & \dots & e_{ml} \end{matrix}]$ (12)

here, $e_{ih} = 〈 u_{ih} (x), μ_{ih} (x) 〉$ denotes the specific assessment of the merchandise c_hgiven by customer for index, i = 1, 2, ⋯ m, h = 1, 2, ⋯ l.

Step 2 Calculating weighted normalized decision matrix

The weighted matrix in different time period is calculated on the basis of the different weights of indexes of merchandises given by customers. Then, the weighted normalized matrix can be obtained as the Equation (13). $v_{ih}^{k} = w_{i}^{k} * e_{ih}$ (13)

The weighted decision matrix can be obtained as the Equation (14). $E_{w}^{k} = {[v_{ih}^{k}]}_{m \times l} = {[\begin{matrix} v_{11} & v_{12} & \dots & v_{1 l} \\ v_{21} & v_{22} & \dots & v_{2 l} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ v_{m 1} & v_{m 2} & \dots & v_{ml} \end{matrix}]}^{k}$ (14)

Step 3 Determining the ideal solutions

Then, let the ideal solution of intuitionistic fuzzy and the nadir solution of intuitionistic fuzzy are respectively be defined as follows:

$A^{+} = (〈 u_{i 1}^{+} (x), μ_{i 1}^{+} (x) 〉, 〈 u_{i 2}^{+} (x), μ_{i 2}^{+} (x) 〉 . . ., 〈 u_{in}^{+} (x), μ_{in}^{+} (x) 〉)$ $A^{-} = (〈 u_{i 1}^{-} (x), μ_{i 1}^{-} (x) 〉, 〈 u_{i 2}^{-} (x), μ_{i 2}^{-} (x) 〉 . . ., 〈 u_{in}^{-} (x), μ_{in}^{-} (x) 〉)$

the set of ideal and nadir solutions are determined by the customer respectively. The ideal and nadir solutions are calculated in Equation (15) and Equation (16). $v_{ih}^{+} = max {v_{ih}^{k} | i = 1, . . ., m}, h = 1, . . ., l$ (15) $v_{ih}^{-} = min {v_{ih}^{k} | i = 1, . . ., m}, h = 1, . . ., l$ (16)

here, ${\begin{matrix} u_{ih}^{+} = max_{0 ⩽ h ⩽ 1} {{\bar{u}}_{ih}^{k}} \\ μ_{ih}^{+} = min_{0 ⩽ h ⩽ 1} {{\bar{μ}}_{ih}^{k}} \end{matrix},$ ${\begin{matrix} u_{ih}^{-} = min_{0 ⩽ h ⩽ 1} {{\bar{u}}_{ih}^{k}} \\ μ_{ih}^{-} = max_{0 ⩽ h ⩽ 1} {{\bar{μ}}_{ih}^{k}} \end{matrix}, i = 1, 2, \dots m$

Step 4 Computing the distance of each merchandise from ideal solution

Let $d_{ih}^{+}$ and $d_{ih}^{-}$ denote the distances of the index p_i and the merchandise c_hin the q_k time period to ideal and nadir solutions. The distances of each merchandise from ideal and nadir solutions are calculated in Equation (17) and Equation (18).

$\begin{matrix} d_{ih}^{+} = \sqrt{\sum_{i = 1}^{m} ({\bar{v}}_{ih}^{k} - v_{ih}^{+})^{2}} \\ = \sqrt{\frac{1}{2} \sum_{i = 1}^{m} [({\bar{u}}_{ih}^{k} (x) - u_{ih}^{+} (x))^{2} + ({\bar{μ}}_{ih}^{k} (x) - μ_{ih}^{+} (x))^{2} + ({\bar{π}}_{ih}^{k} (x) - π_{ih}^{+} (x))^{2}]}, \end{matrix}$ (17)

$\begin{matrix} d_{ih}^{-} = \sqrt{\sum_{i = 1}^{m} ({\bar{v}}_{ih}^{k} - v_{ih}^{-})^{2}} \\ = \sqrt{\frac{1}{2} \sum_{i = 1}^{m} [({\bar{u}}_{ih}^{k} (x) - u_{ih}^{-} (x))^{2} + ({\bar{μ}}_{ih}^{k} (x) - μ_{ih}^{-} (x))^{2} + ({\bar{π}}_{ih}^{k} (x) - π_{ih}^{-} (x))^{2}]}, \end{matrix}$ (18) here, ${\begin{matrix} {\bar{π}}_{ih} (x) = 1 - {\bar{u}}_{ih}^{k} (x) - {\bar{μ}}_{ih}^{k} (x) \\ π_{ih}^{+} (x) = 1 - u_{ih}^{+} (x) - μ_{ih}^{+} (x) \\ π_{ih}^{-} (x) = 1 - u_{ih}^{-} (x) - μ_{ih}^{-} (x) \end{matrix}$

Step 5 Computing the relative degree of closeness

Let ${cl}_{ih}^{k} = ({cl}_{1 h}^{k}, {cl}_{2 h}^{k}, \dots, {cl}_{ml}^{k})$ denote the closeness of the customer considers the merchandise c_h of the index p_i to his ideal solutions, the relative degree of closeness is calculated as Equation (19): ${cl}_{ih}^{k} = \frac{d_{ih}^{-}}{d_{ih}^{-} + d_{ih}^{+}}$ (19)

Step 6 Ranking the merchandises

Finally, let $R_{h}^{k} = (r_{1 h}^{k}, r_{2 h}^{k}, \dots, r_{ih}^{k}, . . ., r_{mh}^{k})$ denote the ranking vector of the merchandiser c_hfor the indexes, and $r_{ih}^{k}$ denote the ranking value of the merchandise c_h for the index p_i in the q_k time period, for i = 1, 2, . . . , m, h = 1, 2, . . . , l, k = 1, 2, ⋯ n. The sequence value $r_{ih}^{k}$ can be determined according to the closeness ${cl}_{ih}^{k}$ calculated in the previous step, and the larger the ${cl}_{ih}^{k}$ , the smaller the $r_{ih}^{k}$ . In other words, the smaller the $r_{ih}^{k}$ , the higher the preference degree of the merchandise c_h to the index p_iin the q_k time period.

4 An illustrative application

There are many different types of merchandises available in the online shopping platform and there is a strict competition among the merchandises. Due to the large number of options, reasonable recommendations are particularly necessary. Recommending merchandises according to customers’ preferences can not only greatly improve shopping efficiency, but also improve customers’ satisfaction with shopping experience. For online shopping platforms, intelligent recommendation can not only increase the sales volume of merchandises, but also attract and retain customers. In the case study, for the convenience of understanding, an e-commerce platforms that the time periods can be divided more concentrated will be adopted, similar to the online shopping platform of catering industry.

4.1 Background

There may be big differences in customer preferences between seasons, or at different times periods of one day. Let’s assume that this is a food supermarket-type online shopping platform. There are a total of twelve indexes when a customer purchase merchandises P ={ p₁, p₂, ⋯ , p₁₂ }, they are calories (p₁), fat (p₂), sugar content (p₃), packaging (p₄), taste (p₅), volume (p₆), brand (p₇), positioning (p₈), advertising (p₉), eating methods (p₁₀), easy to cook or not (p₁₁), nutrition or not (p₁₂). And there are a total of fourteen kinds of merchandises to choose from C ={ c₁, c₂, ⋯ , c₁₄ }. Customers may come to the online shopping platform at three time periods a day to select merchandises Q_k ={ q₁, q₂, q₃ }. The implementation steps of the proposed network intelligent hybrid recommendation algorithm distinguishing time periods along with the model development steps are defined as follows.

4.2 Relationship among indexes of merchandises by using the DEMATEL method

In this section, we use the DEMATEL method to calculate the preferences of customers for different indexes of merchandises p_iin the q_k time period. The specific steps are as follows:

A^k matrix is built upon getting the linguistic assessment terms from the customer. Linguistic terms are given in Table 1. Table 2–4 shows the linguistic assessments of the decision maker on the relationship among the indexes of merchandises among the different time periods.

Table 2
The assessment of the customer in the q₁ time period

A ¹ p ₁ p ₂ p ₃ p ₄ p ₅ p ₆ p ₇ p ₈ p ₉ p ₁₀ p ₁₁ p ₁₂

p ₁ 0 H L No VL H VH H L VL No VH

p ₂ L 0 H VH L VL H H No H L H

p ₃ No L 0 VH H VH L No VL H VH H

p ₄ No H H 0 VL VH H L H L H VH

p ₅ H L VH H 0 No L VH L H VH L

p ₆ L No L H L 0 H H VL H H VH

p ₇ L VL VH H VH L 0 H L H VL H

p ₈ L VH No H No H L 0 VH H VH No

p ₉ VH L H No H VH H L 0 L VL No

p ₁₀ L VH L H No VL VH H H 0 L VL

p ₁₁ L VH H H No VH No L No H 0 VH

p ₁₂ H L No VH VL VH L No VH L VL 0

A ¹	p ₁	p ₂	p ₃	p ₄	p ₅	p ₆	p ₇	p ₈	p ₉	p ₁₀	p ₁₁	p ₁₂
p ₁	0	H	L	No	VL	H	VH	H	L	VL	No	VH
p ₂	L	0	H	VH	L	VL	H	H	No	H	L	H
p ₃	No	L	0	VH	H	VH	L	No	VL	H	VH	H
p ₄	No	H	H	0	VL	VH	H	L	H	L	H	VH
p ₅	H	L	VH	H	0	No	L	VH	L	H	VH	L
p ₆	L	No	L	H	L	0	H	H	VL	H	H	VH
p ₇	L	VL	VH	H	VH	L	0	H	L	H	VL	H
p ₈	L	VH	No	H	No	H	L	0	VH	H	VH	No
p ₉	VH	L	H	No	H	VH	H	L	0	L	VL	No
p ₁₀	L	VH	L	H	No	VL	VH	H	H	0	L	VL
p ₁₁	L	VH	H	H	No	VH	No	L	No	H	0	VH
p ₁₂	H	L	No	VH	VL	VH	L	No	VH	L	VL	0

Table 3

The assessment of the customer in the q₂ time period

A ²	p ₁	p ₂	p ₃	p ₄	p ₅	p ₆	p ₇	p ₈	p ₉	p ₁₀	p ₁₁	p ₁₂
p ₁	0	No	L	H	VH	VL	VH	H	No	L	No	L
p ₂	L	0	H	VL	VH	No	L	H	VH	H	L	H
p ₃	H	L	0	VH	L	L	H	VH	H	No	L	VH
p ₄	L	H	No	0	H	L	VH	No	VH	L	H	L
p ₅	H	VH	L	VL	0	No	VL	VH	H	H	L	No
p ₆	H	L	VH	VL	No	0	H	L	VH	No	H	VL
p ₇	No	VH	L	VL	H	VL	0	H	VH	L	No	H
p ₈	L	H	No	H	VH	VH	H	0	L	VH	VH	No
p ₉	VH	No	VH	No	L	No	VH	L	0	H	VH	VH
p ₁₀	H	VH	VH	H	VH	H	H	L	VL	0	L	H
p ₁₁	VH	H	H	L	H	VL	L	VH	VH	H	0	No
p ₁₂	H	L	No	H	VH	H	No	VH	H	VL	No	0

Table 4

The assessment of the customer in the q₃ time period

A ³	p ₁	p ₂	p ₃	p ₄	p ₅	p ₆	p ₇	p ₈	p ₉	p ₁₀	p ₁₁	p ₁₂
p ₁	0	VH	L	H	VL	No	VH	H	H	VL	L	VH
p ₂	VH	0	VL	H	VH	L	No	H	VL	VH	No	H
p ₃	H	VH	0	L	H	VH	VL	VL	VH	H	L	No
p ₄	H	No	L	0	VL	No	H	VH	H	L	VL	VH
p ₅	H	VH	VL	L	0	L	L	H	H	No	VH	VL
p ₆	H	No	VH	No	L	0	H	H	L	H	VL	VH
p ₇	VH	No	H	VL	No	H	0	H	VH	L	L	H
p ₈	L	L	H	VH	No	L	L	0	VL	H	No	VH
p ₉	No	H	L	H	No	VH	H	VL	0	VH	L	H
p ₁₀	H	L	VH	No	VL	H	L	L	H	0	VH	No
p ₁₁	L	H	L	No	VH	L	No	H	No	VL	0	VH
p ₁₂	L	VH	H	L	H	VL	No	L	H	VH	No	0

Due to the space limitation, here we select the q₁ time period and list its calculation steps in detail. The direct relation matrix A¹ can be obtained as Table 5 according to Table 1. And the normal direct relation matrix X¹ can be obtained by using the Equation (4). Table 6 shows the normalized direct relation matrix for the indexes of merchandises.

Table 5

The direct relation matrix in the q₁ time period

A ¹	p ₁	p ₂	p ₃	p ₄	p ₅	p ₆	p ₇	p ₈	p ₉	p ₁₀	p ₁₁	p ₁₂
p ₁	0	4	3	1	2	4	5	4	3	2	1	5
p ₂	3	0	4	5	3	2	4	4	1	4	3	4
p ₃	1	3	0	5	4	5	3	1	2	4	5	4
p ₄	1	4	4	0	2	5	4	3	4	3	4	5
p ₅	4	3	5	4	0	1	3	5	3	4	5	3
p ₆	3	1	3	4	3	0	4	4	2	4	4	5
p ₇	3	2	5	4	5	3	0	4	3	4	2	4
p ₈	3	5	1	4	1	4	3	0	5	4	5	1
p ₉	5	3	4	1	4	5	4	3	0	3	2	1
p ₁₀	3	5	3	4	1	2	5	4	4	0	3	2
p ₁₁	3	5	4	4	1	5	1	3	1	4	0	5
p ₁₂	4	3	1	5	2	5	3	1	5	3	2	0

Table 6

The normalized direct relation matrix in the q₁ time period

X ¹	p ₁	p ₂	p ₃	p ₄	p ₅	p ₆	p ₇	p ₈	p ₉	p ₁₀	p ₁₁	p ₁₂
p ₁	0.00	0.10	0.07	0.02	0.05	0.10	0.12	0.10	0.07	0.05	0.02	0.12
p ₂	0.07	0.00	0.10	0.12	0.07	0.05	0.10	0.10	0.02	0.10	0.07	0.10
p ₃	0.02	0.07	0.00	0.12	0.10	0.12	0.07	0.02	0.05	0.10	0.12	0.10
p ₄	0.02	0.10	0.10	0.00	0.05	0.12	0.10	0.07	0.10	0.07	0.10	0.12
p ₅	0.10	0.07	0.12	0.10	0.00	0.02	0.07	0.12	0.07	0.10	0.12	0.07
p ₆	0.07	0.02	0.07	0.10	0.07	0.00	0.10	0.10	0.05	0.10	0.10	0.12
p ₇	0.07	0.05	0.12	0.10	0.12	0.07	0.00	0.10	0.07	0.10	0.05	0.10
p ₈	0.07	0.12	0.02	0.10	0.02	0.10	0.07	0.00	0.12	0.10	0.12	0.02
p ₉	0.12	0.07	0.10	0.02	0.10	0.12	0.10	0.07	0.00	0.07	0.05	0.02
p ₁₀	0.07	0.12	0.07	0.10	0.02	0.05	0.12	0.10	0.10	0.00	0.07	0.05
p ₁₁	0.07	0.12	0.10	0.10	0.02	0.12	0.02	0.07	0.02	0.10	0.00	0.12
p ₁₂	0.10	0.07	0.02	0.12	0.05	0.12	0.07	0.02	0.12	0.07	0.05	0.00

Then, the total relation matrix T¹ can be obtained by using the Equation (5). Table 7 shows the total direct relation matrix of the case study.

Table 7

The total direct relation matrix in the q₁ time period

T ¹	p ₁	p ₂	p ₃	p ₄	p ₅	p ₆	p ₇	p ₈	p ₉	p ₁₀	p ₁₁	p ₁₂
p ₁	0.53	0.69	0.66	0.69	0.51	0.75	0.74	0.66	0.61	0.67	0.60	0.74
p ₂	0.64	0.66	0.73	0.84	0.57	0.77	0.77	0.71	0.61	0.77	0.70	0.78
p ₃	0.60	0.73	0.65	0.84	0.59	0.83	0.75	0.65	0.63	0.78	0.75	0.79
p ₄	0.63	0.78	0.76	0.76	0.57	0.87	0.80	0.72	0.70	0.78	0.75	0.83
p ₅	0.70	0.78	0.80	0.86	0.53	0.80	0.80	0.78	0.69	0.82	0.79	0.80
p ₆	0.64	0.69	0.71	0.81	0.56	0.72	0.77	0.71	0.63	0.77	0.72	0.80
p ₇	0.67	0.74	0.79	0.85	0.64	0.82	0.72	0.75	0.69	0.81	0.71	0.81
p ₈	0.63	0.75	0.65	0.79	0.51	0.79	0.73	0.61	0.67	0.75	0.72	0.69
p ₉	0.66	0.69	0.70	0.71	0.57	0.79	0.74	0.67	0.55	0.72	0.65	0.68
p ₁₀	0.63	0.75	0.70	0.79	0.51	0.75	0.78	0.70	0.66	0.66	0.68	0.72
p ₁₁	0.62	0.75	0.71	0.79	0.51	0.81	0.69	0.67	0.59	0.75	0.61	0.78
p ₁₂	0.62	0.67	0.62	0.77	0.51	0.77	0.70	0.60	0.65	0.69	0.62	0.64

According to the total relation matrix, the influence degree, influenced degree, center degree and cause degree of each elements can be obtained by using the Equation (6)- (11). and showed as the Table 8.

Table 8

The relevant elements in the q₁ time period

	p ₁	p ₂	p ₃	p ₄	p ₅	p ₆	p ₇	p ₈	p ₉	p ₁₀	p ₁₁	p ₁₂
$D_{i}^{1}$	7.86	8.56	8.59	8.95	9.16	8.52	8.99	8.29	8.11	8.32	8.27	7.87
$C_{j}^{1}$	7.56	8.70	8.46	9.50	6.58	9.46	8.98	8.23	7.70	8.97	8.30	9.06
M ¹	15.41	17.26	17.05	18.45	15.74	17.98	17.97	16.53	15.81	17.29	16.56	16.93
R ¹	0.30	-0.13	0.13	-0.55	2.58	–0.95	0.01	0.06	0.42	-0.65	-0.03	-1.18
$w_{i}^{1}$	15.41	17.26	17.05	18.46	15.52	18.01	17.97	16.53	15.80	17.30	16.56	16.97
W ¹	0.076	0.085	0.084	0.091	0.077	0.089	0.089	0.081	0.078	0.085	0.082	0.084

The relationship among indexes of merchandises in the rest of the time periods are calculated in the similar way. Table 9 shows the weight of the index in the different time periods.

Table 9

The weight of the index in the different time periods

	p ₁	p ₂	p ₃	p ₄	p ₅	p ₆	p ₇	p ₈	p ₉	p ₁₀	p ₁₁	p ₁₂
W ¹	0.076	0.085	0.084	0.091	0.077	0.089	0.089	0.081	0.078	0.085	0.082	0.084
W ²	0.081	0.086	0.084	0.078	0.089	0.070	0.084	0.092	0.090	0.087	0.083	0.076
W ³	0.090	0.086	0.089	0.077	0.077	0.082	0.079	0.085	0.087	0.087	0.072	0.089

4.3 Rank among merchandises according the preferences by using the TOPSIS method

In this step, TOPSIS method is applied. First, fifteen different kinds of merchandises are assessed by the customer. The evaluation matrix of intuitionistic fuzzy set E is obtained in Table 10.

Table 10
The evaluation of the customer to merchandises for indexes

c ₁ c ₂ c ₃ c ₄ c ₅ c ₆ c ₇

p ₁ 〈0.74, 0.13〉〈0.78, 0.14〉〈0.81, 0.16〉〈0.69, 0.11〉〈0.56, 0.14〉〈0.70, 0.17〉〈0.79, 0.13〉

p ₂ 〈0.68, 0.20〉〈0.70, 0.12〉〈0.63, 0.17〉〈0.58, 0.20〉〈0.78, 0.18〉〈0.77, 0.11〉〈0.67, 0.14〉

p ₃ 〈0.58, 0.25〉〈0.72, 0.28〉〈0.58, 0.24〉〈0.66, 0.14〉〈0.68, 0.11〉〈0.72, 0.08〉〈0.77, 0.11〉

p ₄ 〈0.63, 0.09〉〈0.69, 0.16〉〈0.72, 0.08〉〈0.71, 0.16〉〈0.72, 0.09〉〈0.67, 0.09〉〈0.70, 0.10〉

p ₅ 〈0.70, 0.16〉〈0.81, 0.09〉〈0.78, 0.21〉〈0.77, 0.19〉〈0.75, 0.20〉〈0.69, 0.15〉〈0.75, 0.18〉

p ₆ 〈0.64, 0.16〉〈0.61, 0.19〉〈0.71, 0.11〉〈0.58, 0.08〉〈0.69, 0.17〉〈0.71, 0.13〉〈0.61, 0.23〉

p ₇ 〈0.76, 0.15〉〈0.72, 0.17〉〈0.59, 0.23〉〈0.83, 0.05〉〈0.61, 0.20〉〈0.69, 0.12〉〈0.77, 0.08〉

p ₈ 〈0.51, 0.20〉〈0.58, 0.13〉〈0.69, 0.27〉〈0.71, 0.24〉〈0.56, 0.14〉〈0.47, 0.23〉〈0.77, 0.19〉

p ₉ 〈0.61, 0.18〉〈0.78, 0.15〉〈0.66, 0.19〉〈0.67, 0.16〉〈0.65, 0.13〉〈0.74, 0.11〉〈0.66, 0.08〉

p ₁₀ 〈0.57, 0.19〉〈0.68, 0.11〉〈0.56, 0.22〉〈0.59, 0.23〉〈0.56, 0.17〉〈0.61, 0.21〉〈0.65, 0.17〉

p ₁₁ 〈0.67, 0.19〉〈0.56, 0.14〉〈0.56, 0.33〉〈0.47, 0.28〉〈0.57, 0.24〉〈0.68, 0.14〉〈0.53, 0.27〉

p ₁₂ 〈0.71, 0.18〉〈0.68, 0.14〉〈0.65, 0.19〉〈0.57, 0.28〉〈0.61, 0.28〉〈0.64, 0.31〉〈0.72, 0.13〉

c ₈ c ₉ c ₁₀ c ₁₁ c ₁₂ c ₁₃ c ₁₄

p ₁ 〈0.80, 0.09〉〈0.67, 0.28〉〈0.66, 0.12〉〈0.75, 0.15〉〈0.62, 0.09〉〈0.57, 0.29〉〈0.68, 0.17〉

p ₂ 〈0.83, 0.08〉〈0.58, 0.23〉〈0.62, 0.21〉〈0.80, 0.14〉〈0.68, 0.12〉〈0.67, 0.13〉〈0.74, 0.11〉

p ₃ 〈0.76, 0.15〉〈0.66, 0.19〉〈0.71, 0.15〉〈0.72, 0.08〉〈0.73, 0.14〉〈0.77, 0.20〉〈0.76, 0.14〉

p ₄ 〈0.72, 0.12〉〈0.48, 0.29〉〈0.69, 0.16〉〈0.74, 0.16〉〈0.77, 0.15〉〈0.73, 0.16〉〈0.72, 0.18〉

p ₅ 〈0.75, 0.14〉〈0.73, 0.22〉〈0.79, 0.18〉〈0.79, 0.13〉〈0.71, 0.11〉〈0.81, 0.13〉〈0.75, 0.15〉

p ₆ 〈0.70, 0.13〉〈0.58, 0.24〉〈0.68, 0.15〉〈0.63, 0.14〉〈0.59, 0.24〉〈0.81, 0.08〉〈0.66, 0.18〉

p ₇ 〈0.45, 0.36〉〈0.52, 0.27〉〈0.61, 0.26〉〈0.58, 0.23〉〈0.63, 0.19〉〈0.71, 0.16〉〈0.77, 0.07〉

p ₈ 〈0.73, 0.15〉〈0.63, 0.17〉〈0.55, 0.27〉〈0.70, 0.18〉〈0.45, 0.35〉〈0.78, 0.06〉〈0.63, 0.18〉

p ₉ 〈0.68, 0.23〉〈0.54, 0.25〉〈0.61, 0.14〉〈0.67, 0.15〉〈0.59, 0.17〉〈0.68, 0.14〉〈0.59, 0.23〉

p ₁₀ 〈0.66, 0.09〉〈0.57, 0.24〉〈0.66, 0.25〉〈0.61, 0.09〉〈0.66, 0.12〉〈0.73, 0.13〉〈0.78, 0.09〉

p ₁₁ 〈0.68, 0.11〉〈0.76, 0.08〉〈0.71, 0.15〉〈0.63, 0.21〉〈0.53, 0.34〉〈0.66, 0.21〉〈0.71, 0.13〉

p ₁₂ 〈0.77, 0.08〉〈0.69, 0.16〉〈0.81, 0.01〉〈0.77, 0.12〉〈0.72, 0.26〉〈0.61, 0.14〉〈0.62, 0.32〉

	c ₁	c ₂	c ₃	c ₄	c ₅	c ₆	c ₇
p ₁	〈0.74, 0.13〉	〈0.78, 0.14〉	〈0.81, 0.16〉	〈0.69, 0.11〉	〈0.56, 0.14〉	〈0.70, 0.17〉	〈0.79, 0.13〉
p ₂	〈0.68, 0.20〉	〈0.70, 0.12〉	〈0.63, 0.17〉	〈0.58, 0.20〉	〈0.78, 0.18〉	〈0.77, 0.11〉	〈0.67, 0.14〉
p ₃	〈0.58, 0.25〉	〈0.72, 0.28〉	〈0.58, 0.24〉	〈0.66, 0.14〉	〈0.68, 0.11〉	〈0.72, 0.08〉	〈0.77, 0.11〉
p ₄	〈0.63, 0.09〉	〈0.69, 0.16〉	〈0.72, 0.08〉	〈0.71, 0.16〉	〈0.72, 0.09〉	〈0.67, 0.09〉	〈0.70, 0.10〉
p ₅	〈0.70, 0.16〉	〈0.81, 0.09〉	〈0.78, 0.21〉	〈0.77, 0.19〉	〈0.75, 0.20〉	〈0.69, 0.15〉	〈0.75, 0.18〉
p ₆	〈0.64, 0.16〉	〈0.61, 0.19〉	〈0.71, 0.11〉	〈0.58, 0.08〉	〈0.69, 0.17〉	〈0.71, 0.13〉	〈0.61, 0.23〉
p ₇	〈0.76, 0.15〉	〈0.72, 0.17〉	〈0.59, 0.23〉	〈0.83, 0.05〉	〈0.61, 0.20〉	〈0.69, 0.12〉	〈0.77, 0.08〉
p ₈	〈0.51, 0.20〉	〈0.58, 0.13〉	〈0.69, 0.27〉	〈0.71, 0.24〉	〈0.56, 0.14〉	〈0.47, 0.23〉	〈0.77, 0.19〉
p ₉	〈0.61, 0.18〉	〈0.78, 0.15〉	〈0.66, 0.19〉	〈0.67, 0.16〉	〈0.65, 0.13〉	〈0.74, 0.11〉	〈0.66, 0.08〉
p ₁₀	〈0.57, 0.19〉	〈0.68, 0.11〉	〈0.56, 0.22〉	〈0.59, 0.23〉	〈0.56, 0.17〉	〈0.61, 0.21〉	〈0.65, 0.17〉
p ₁₁	〈0.67, 0.19〉	〈0.56, 0.14〉	〈0.56, 0.33〉	〈0.47, 0.28〉	〈0.57, 0.24〉	〈0.68, 0.14〉	〈0.53, 0.27〉
p ₁₂	〈0.71, 0.18〉	〈0.68, 0.14〉	〈0.65, 0.19〉	〈0.57, 0.28〉	〈0.61, 0.28〉	〈0.64, 0.31〉	〈0.72, 0.13〉
	c ₈	c ₉	c ₁₀	c ₁₁	c ₁₂	c ₁₃	c ₁₄
p ₁	〈0.80, 0.09〉	〈0.67, 0.28〉	〈0.66, 0.12〉	〈0.75, 0.15〉	〈0.62, 0.09〉	〈0.57, 0.29〉	〈0.68, 0.17〉
p ₂	〈0.83, 0.08〉	〈0.58, 0.23〉	〈0.62, 0.21〉	〈0.80, 0.14〉	〈0.68, 0.12〉	〈0.67, 0.13〉	〈0.74, 0.11〉
p ₃	〈0.76, 0.15〉	〈0.66, 0.19〉	〈0.71, 0.15〉	〈0.72, 0.08〉	〈0.73, 0.14〉	〈0.77, 0.20〉	〈0.76, 0.14〉
p ₄	〈0.72, 0.12〉	〈0.48, 0.29〉	〈0.69, 0.16〉	〈0.74, 0.16〉	〈0.77, 0.15〉	〈0.73, 0.16〉	〈0.72, 0.18〉
p ₅	〈0.75, 0.14〉	〈0.73, 0.22〉	〈0.79, 0.18〉	〈0.79, 0.13〉	〈0.71, 0.11〉	〈0.81, 0.13〉	〈0.75, 0.15〉
p ₆	〈0.70, 0.13〉	〈0.58, 0.24〉	〈0.68, 0.15〉	〈0.63, 0.14〉	〈0.59, 0.24〉	〈0.81, 0.08〉	〈0.66, 0.18〉
p ₇	〈0.45, 0.36〉	〈0.52, 0.27〉	〈0.61, 0.26〉	〈0.58, 0.23〉	〈0.63, 0.19〉	〈0.71, 0.16〉	〈0.77, 0.07〉
p ₈	〈0.73, 0.15〉	〈0.63, 0.17〉	〈0.55, 0.27〉	〈0.70, 0.18〉	〈0.45, 0.35〉	〈0.78, 0.06〉	〈0.63, 0.18〉
p ₉	〈0.68, 0.23〉	〈0.54, 0.25〉	〈0.61, 0.14〉	〈0.67, 0.15〉	〈0.59, 0.17〉	〈0.68, 0.14〉	〈0.59, 0.23〉
p ₁₀	〈0.66, 0.09〉	〈0.57, 0.24〉	〈0.66, 0.25〉	〈0.61, 0.09〉	〈0.66, 0.12〉	〈0.73, 0.13〉	〈0.78, 0.09〉
p ₁₁	〈0.68, 0.11〉	〈0.76, 0.08〉	〈0.71, 0.15〉	〈0.63, 0.21〉	〈0.53, 0.34〉	〈0.66, 0.21〉	〈0.71, 0.13〉
p ₁₂	〈0.77, 0.08〉	〈0.69, 0.16〉	〈0.81, 0.01〉	〈0.77, 0.12〉	〈0.72, 0.26〉	〈0.61, 0.14〉	〈0.62, 0.32〉

Due to the space limitation, here we select the q₁ time period and list its calculation steps in detail. The weighted normalized matrix in the q₁ time period can be obtained by using the Equation (14) and shows as the Table 11.

Table 11

The weighted normalized matrix in the q₁time period

E ¹	c ₁	c ₂	c ₃	c ₄	c ₅	c ₆	c ₇
p ₁	〈0.097, 0.856〉	〈0.109, 0.861〉	〈0.119, 0.870〉	〈0.085, 0.846〉	〈0.060, 0.861〉	〈0.087, 0.847〉	〈0.112, 0.856〉
p ₂	〈0.092, 0.872〉	〈0.097, 0.835〉	〈0.081, 0.860〉	〈0.071, 0.872〉	〈0.121, 0.864〉	〈0.117, 0.829〉	〈0.090, 0.846〉
p ₃	〈0.070, 0.890〉	〈0.101, 0.809〉	〈0.070, 0.887〉	〈0.087, 0.848〉	〈0.091, 0.831〉	〈0.101, 0.809〉	〈0.116, 0.831〉
p ₄	〈0.087, 0.803〉	〈0.101, 0.846〉	〈0.109, 0.795〉	〈0.107, 0.846〉	〈0.109, 0.803〉	〈0.096, 0.803〉	〈0.104, 0.811〉
p ₅	〈0.089, 0.868〉	〈0.120, 0.831〉	〈0.110, 0.887〉	〈0.107, 0.880〉	〈0.101, 0.883〉	〈0.086, 0.864〉	〈0.101, 0.876〉
p ₆	〈0.087, 0.850〉	〈0.120, 0.831〉	〈0.110, 0.887〉	〈0.107, 0.880〉	〈0.101, 0.883〉	〈0.086, 0.864〉	〈0.101, 0.876〉
p ₇	〈0.119, 0.845〉	〈0.107, 0.854〉	〈0.076, 0.877〉	〈0.146, 0.766〉	〈0.080, 0.867〉	〈0.099, 0.828〉	〈0.123, 0.799〉
p ₈	〈0.056, 0.878〉	〈0.068, 0.848〉	〈0.091, 0.899〉	〈0.095, 0.891〉	〈0.064, 0.853〉	〈0.050, 0.888〉	〈0.112, 0.874〉
p ₉	〈0.071, 0.875〉	〈0.111, 0.862〉	〈0.081, 0.879〉	〈0.083, 0.867〉	〈0.079, 0.853〉	〈0.100, 0.842〉	〈0.081, 0.821〉
p ₁₀	〈0.069, 0.868〉	〈0.092, 0.829〉	〈0.067, 0.879〉	〈0.073, 0.883〉	〈0.067, 0.860〉	〈0.077, 0.876〉	〈0.085, 0.860〉
p ₁₁	〈0.087, 0.898〉	〈0.092, 0.829〉	〈0.067, 0.879〉	〈0.073, 0.883〉	〈0.067, 0.860〉	〈0.077, 0.876〉	〈0.085, 0.860〉
p ₁₂	〈0.099, 0.866〉	〈0.091, 0.848〉	〈0.084, 0.870〉	〈0.068, 0.899〉	〈0.076, 0.899〉	〈0.082, 0.906〉	〈0.101, 0.843〉
	c ₈	c ₉	c ₁₀	c ₁₁	c ₁₂	c ₁₃	c ₁₄
p ₁	〈0.115, 0.833〉	〈0.081, 0.908〉	〈0.079, 0.851〉	〈0.100, 0.866〉	〈0.071, 0.833〉	〈0.062, 0.910〉	〈0.083, 0.874〉
p ₂	〈0.140, 0.807〉	〈0.071, 0.883〉	〈0.079, 0.876〉	〈0.128, 0.846〉	〈0.092, 0.835〉	〈0.090, 0.841〉	〈0.108, 0.829〉
p ₃	〈0.113, 0.853〉	〈0.087, 0.870〉	〈0.099, 0.853〉	〈0.101, 0.809〉	〈0.104, 0.848〉	〈0.116, 0.874〉	〈0.113, 0.848〉
p ₄	〈0.109, 0.825〉	〈0.058, 0.893〉	〈0.101, 0.846〉	〈0.115, 0.846〉	〈0.125, 0.841〉	〈0.112, 0.846〉	〈0.109, 0.856〉
p ₅	〈0.101, 0.860〉	〈0.096, 0.890〉	〈0.113, 0.876〉	〈0.113, 0.855〉	〈0.091, 0.844〉	〈0.120, 0.855〉	〈0.101, 0.864〉
p ₆	〈0.102, 0.834〉	〈0.074, 0.881〉	〈0.096, 0.845〉	〈0.085, 0.839〉	〈0.076, 0.881〉	〈0.137, 0.799〉	〈0.092, 0.858〉
p ₇	〈0.052, 0.913〉	〈0.063, 0.890〉	〈0.080, 0.887〉	〈0.074, 0.877〉	〈0.085, 0.863〉	〈0.104, 0.850〉	〈0.123, 0.789〉
p ₈	〈0.101, 0.858〉	〈0.077, 0.866〉	〈0.063, 0.899〉	〈0.093, 0.870〉	〈0.047, 0.918〉	〈0.115, 0.796〉	〈0.077, 0.870〉
p ₉	〈0.085, 0.892〉	〈0.059, 0.898〉	〈0.071, 0.858〉	〈0.083, 0.862〉	〈0.067, 0.871〉	〈0.085, 0.858〉	〈0.067, 0.892〉
p ₁₀	〈0.088, 0.815〉	〈0.069, 0.886〉	〈0.088, 0.889〉	〈0.077, 0.815〉	〈0.088, 0.835〉	〈0.105, 0.841〉	〈0.121, 0.815〉
p ₁₁	〈0.289, 0.834〉	〈0.110, 0.813〉	〈0.097, 0.856〉	〈0.078, 0.880〉	〈0.060, 0.915〉	〈0.085, 0.880〉	〈0.097, 0.846〉
p ₁₂	〈0.116, 0.809〉	〈0.094, 0.857〉	〈0.130, 0.800〉	〈0.116, 0.837〉	〈0.101, 0.893〉	〈0.076, 0.848〉	〈0.078, 0.909〉

After finding the weighted normalized decision matrix, the set of ideal and nadir solutions determined by the customer respectively. The ideal and nadir solutions are obtained by using Equation (15) and Equation (16). The A⁺ and A^- sets of the merchandises are computed as follows:

$\begin{matrix} A^{+} = (〈 0.119, 0.833 〉, 〈 0.140, 0.807 〉, 〈 0.116, 0.809 〉, \\ 〈 0.125, 0.795 〉, 〈 0.120, 0.831 〉, 〈 0.137, 0.799 〉, \\ 〈 0.146, 0.766 〉, 〈 0.115, 0.796 〉, 〈 0.111, 0.821 〉, \\ 〈 0.121, 0.815 〉, 〈 0.110, 0.813 〉, 〈 0.130, 0.800 〉)^{T} \end{matrix}$ $\begin{matrix} A^{+} = (〈 0.060, 0.910 〉, 〈 0.071, 0.883 〉, 〈 0.070, 0.890 〉, \\ 〈 0.058, 0.893 〉, 〈 0.086, 0.890 〉, 〈 0.074, 0.881 〉, \\ 〈 0.052, 0.913 〉, 〈 0.047, 0.918 〉, 〈 0.059, 0.898 〉, \\ 〈 0.067, 0.889 〉, 〈 0.051, 0.915 〉, 〈 0.068, 0.909 〉)^{T} \end{matrix}$

Then, the distance of each merchandise from ideal solution are calculated by using Equation (17) and (18) respectively. Finally, the relative degree of closeness of the customer considers the merchandise are calculated by using Equation (19). The distance values are given in Table 12.

Table 12

The distance of each merchandise from ideal solution and merchandise from ideal solution

	c ₁	c ₂	c ₃	c ₄	c ₅	c ₆	c ₇	c ₈	c ₉	c ₁₀	c ₁₁	c ₁₂	c ₁₃	c ₁₄
$d_{ih}^{+}$	0.196	0.167	0.210	0.196	0.192	0.175	0.162	0.178	0.282	0.250	0.229	0.265	0.225	0.231
$d_{ih}^{-}$	0.139	0.171	0.143	0.177	0.136	0.171	0.184	0.184	0.142	0.167	0.181	0.155	0.199	0.190
${cl}_{ih}^{1}$	0.416	0.506	0.405	0.475	0.415	0.494	0.531	0.508	0.334	0.401	0.441	0.368	0.469	0.451

The distance of each merchandise from ideal solution and the relative degree of closeness of the customer considers the merchandise in the rest of the time periods are calculated in the similar way. Table 13 shows the relative distance of each merchandise in the different time periods.

Table 13

The relative distance of each merchandise in the different time periods

	c ₁	c ₂	c ₃	c ₄	c ₅	c ₆	c ₇	c ₈	c ₉	c ₁₀	c ₁₁	c ₁₂	c ₁₃	c ₁₄
${cl}_{ih}^{1}$	0.416	0.506	0.405	0.475	0.415	0.494	0.531	0.508	0.334	0.401	0.441	0.368	0.469	0.451
${cl}_{ih}^{2}$	0.404	0.511	0.394	0.464	0.413	0.487	0.534	0.508	0.338	0.393	0.442	0.366	0.469	0.449
${cl}_{ih}^{3}$	0.407	0.513	0.404	0.463	0.410	0.485	0.537	0.521	0.331	0.405	0.449	0.371	0.465	0.441

Finally, the ranking value of the merchandise in different time periods can be obtained as Table 14. That is, the smaller the ranking, the higher the preference degree of the merchandise to the customer.

Table 14

The relative distance of each merchandise in the different time periods

	c ₁	c ₂	c ₃	c ₄	c ₅	c ₆	c ₇	c ₈	c ₉	c ₁₀	c ₁₁	c ₁₂	c ₁₃	c ₁₄
$R_{h}^{1}$	9	3	11	5	10	4	1	2	14	12	8	13	6	7
$R_{h}^{2}$	10	2	11	6	9	4	1	3	14	12	8	13	5	7
$R_{h}^{3}$	10	3	12	6	9	4	1	2	14	11	7	13	5	8

As the most preferred merchandise should simultaneously have the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution, which also certainly reflects the rational of human choice.

The above results show that even if the customers have the same evaluation on the merchandises, there will still be such a situation. When visiting the same online shopping platform in different time periods of the day, the merchandises recommended by the platform are quite different due to the differences in the degree of merchandise preference in different time periods.

At present, most online shopping platforms in China recommend merchandises randomly selected according to customers’ previous orders, or give priority to customers according to the frequency of their purchases. Such recommendation method is difficult to consider the real demand of customers when the quantity of merchandises is very large. The hybrid algorithm of network intelligent recommendation considering time period proposed in this paper, can satisfy customers’ personalized and targeted recommendation when they come to the online shopping platform at any time.

5 Conclusions

To solve the problem that online shopping platforms will be able to more accurately recommend products that match customers’ preferences when they shop online. In this way, the time that the customers spend on searching for products and browsing for unrelated products can be reduced, the satisfaction of customers with the online shopping platform can be improved, and the utilization rate and praise rate of the online shopping platform can be ultimately increased.

To improve the existing intelligent recommendation algorithm. In this paper, a integrated novel model combined the DEMATEL and TOPSIS method with intuitionistic fuzzy number (IFN) is proposed to solved the problem of the dynamic network intelligent hybrid recommendation algorithm distinguishing time periods (DIHR). Because the shopping habits and preferences of customers may vary in different time periods, we considered the interrelationship between the indexes that the customer considered when purchasing merchandises over different time periods. Subsequently, according to the customer’s evaluation of the merchandises according to the index, the personalized recommendation in different time periods can be obtained. Specifically, it has the following conclusions though combining the practical problems of online shopping platform.

(1) The DEMATEL method is considered to calculate the preference relationship of customers for indexes of merchandises. At the same time, a differentiated approach to the relationship degree of indexes provided by customer is adopted to overcome the shortcomings of the existing research methods to deal with the preference relation by considering the different time periods in intelligent recommendation algorithm.

(2) The optimization model of the ranking among the merchandises according to the index in different time periods is constructed combined the TOPSIS method with intuitionistic fuzzy number (IFN) to determine the ranking vector of merchandises. It can be seen that the determined ranking can reflect the will of the customer in different time periods as much as possible.

In the actual process of network intelligent recommendation, the quantity of merchandises is very large, and the classification of merchandises is also very important. How to establish a hierarchical intelligent recommendation algorithm for big data is our next research direction. Moreover, the differential treatment of indicators is also a subject worthy of further study. Therefore, the next step is to propose a method of decision-making which is as fair as possible for the differentiation index system of customers’ preference.

Footnotes

Acknowledgments

This work was supported by National Natural Science Funds of China (No. 72071152), the Xi’an Science and Technology Projects (No. XA2020-RKXYJ-0086), the Youth Innovation Team of Shaanxi Universities, the Natural Science Foundation Research Project of Shaanxi Province (No. 2020JQ-334), the Personnel and Talents Special Project of Fundamental Research Funds for the Central Universities, the poverty alleviation Special Project of Fundamental Research Funds for the Central Universities.

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Dynamic network intelligent hybrid recommendation algorithm and its application in online shopping platform

Abstract

Keywords

1 Introduction

2 Related work

3 DIHR method combined with fuzzy DEMATEL and TOPSIS method

3.1 Problem formulation

3.2 Calculation of the habits of customers’ preferences for merchandises in different time periods

Table 1 Merchandises relationship linguistic terms and values Linguistic terms Linguistic values No influence (No) 1 Very low influence (VL) 2 Low influence (L) 3 High influence (H) 4 Very high influence (VH) 5

4.1 Background

4.2 Relationship among indexes of merchandises by using the DEMATEL method

Footnotes

Acknowledgments

References

Table 1
Merchandises relationship linguistic terms and values

Linguistic terms Linguistic values

No influence (No) 1

Very low influence (VL) 2

Low influence (L) 3

High influence (H) 4

Very high influence (VH) 5