An improved Interval-valued intuitionistic fuzzy MCGDM for the evaluation of agricultural products live-streaming e-commerce platform

Abstract

A crucial step for agricultural product merchants to achieve profitable and sustainable development in the live-streaming e-commerce age is evaluating the risk of the agricultural products live-streaming e-commerce platform. However, there isn’t much reliable research available right now on the risk evaluation of platforms. Therefore, this study suggests an improved risk evaluation method based on interval-valued intuitionistic fuzzy multi-criteria group decision-making (MCGDM). This method determines the decision-maker weight for the risk criterion according to the levels of professionalism of the decision-makers in the risk criterion and uses the VIse Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method to rate the risk of the alternative agricultural products live-streaming e-commerce platforms. The viability and dependability of the approach described in this work are demonstrated using a case study. The strengths and weaknesses of this approach are illustrated by a comparative analysis. With the help of this paper, agricultural product merchants will be able to identify the live-streaming e-commerce platform that carries the least amount of overall risk and work toward the paper’s stated objectives of sustainable development in addition to developing and enhancing theoretical research findings in the field.

Keywords

Live-streaming e-commerce platform risk assessment MCGDM interval-valued intuitionistic fuzzy number professionalism of decision makers

1 Introduction

To support the development of the agricultural industry, countries have enacted a series of policies. For example, from 2009 to 2016, the United States financed 1,389,400 rural development projects with a funding amount of US$253,434 million. From 2015 to 2020, the UK allocated 138 million pounds to support agricultural diversification. China’s No. 1 Central Document in 2022 pointed out that the project of prospering agriculture through a digital business should be implemented, including using modern information technology to help rural revitalization [1]. In this context, agricultural products live-streaming e-commerce has shown strong development potential and has gradually become a window and bridge between rural specialty products and the global consumer market. In addition to policy support, the rapid application and popularization of 5 G communication technology and online payment in recent years have provided technical support for agricultural products live-streaming e-commerce [2, 3]. With COVID-19 raging, the shift in consumer shopping habits from offline to online has provided market development opportunities for agricultural products live-streaming e-commerce [4]. All of these make the agricultural products live-streaming e-commerce develop rapidly and become a new driving force for rural revitalization. The 2020 Taobao live-streaming data analysis report shows that by the end of 2019, there were 1.4 million live-streaming related to agricultural products on Taobao, covering 31 provinces and more than 2,000 counties, driving more than 60,000 new farmers to join [5].

The agricultural products live-streaming e-commerce refers to agricultural products merchants sell their products through the mode of live-streaming [6, 7]. Choosing a live-streaming e-commerce platform to settle in is the primary step for agricultural product merchants to develop a live-streaming e-commerce business. At present, there are many live-streaming e-commerce platforms in the market, including not only Taobao, JD.com, Pinduoduo, and other retail platforms, but also some short video platforms, such as TikTok and Quick Hand [8]. In order to achieve healthy and sustainable development, when agricultural product merchants choose a platform to settle in, they must first conduct a comprehensive analysis of the risks of alternative live-streaming e-commerce platforms and take comprehensive risk as the key decision-making basis for entering the platform [9]. Regarding the risks brought by the live-streaming e-commerce platform to agricultural products merchants, a comprehensive analysis can be made from the four dimensions, namely the platform’s information security strategy [10, 11], digital management system [12, 13], technology [14] and operation and maintenance [15, 16]. Whether the information security strategy adopted by the live-streaming e-commerce platform is feasible is directly related to whether agricultural product merchants can maintain their market competitiveness. Whether the digital management system of the live-streaming e-commerce platform is effective plays a crucial role in the entire operation and management of the platform. Whether the technology of the live-streaming e-commerce platform is mature in live-streaming also directly affects the long-term development of agricultural products live-streaming e-commerce. Operation and maintenance risks include various risks in the daily operation and maintenance process of the live-streaming e-commerce platform. Considering the characteristics that agricultural products are perishable and difficult to store, we focus on whether the platform cold chain logistics is standardized. To sum up, the risk assessment of the agricultural products live-streaming e-commerce platform can start from the four dimensions, including information security strategy, digital management system, technology, and maintenance, and determine four risk criteria, including the perfection of information security strategy, the standardization of the digital management system, the professionalism of live-streaming technology, and the standardization of cold chain logistics.

How should agricultural product merchants assess the risks of live-streaming e-commerce platforms, identify the platform with the lowest overall risk, and then provide a decision-making basis for their entry into the platform, given the abundance of alternative live-streaming e-commerce platforms and the various risks they may bring? This work specifically seeks to investigate this issue. Specifically, this paper will use the improved interval-valued intuitionistic fuzzy MCGDM method to evaluate the risk of live-streaming e-commerce platforms. The method determines the weight of the decision maker for the criterion according to the professionalism of the decision maker and solves the problem of unscientific evaluation caused by assigning the same weight to different decision-makers in the same criterion. At the same time, this method uses the VIKOR method to rank the alternative agricultural products live-streaming e-commerce platforms. The VIKOR method can provide a variety of compromise solutions for agricultural product merchants, which is more in line with the decision-making habits of decision-makers. The research in this paper can not only promote and enhance the theoretical research results in the field of agricultural products live-streaming e-commerce, but also provide practical guidance for agricultural products merchants to determine the live-streaming e-commerce platform with the lowest comprehensive risk, which can help achieve the sustainable development goal of agricultural products live-streaming e-commerce. In addition, the research in this paper can also urge agricultural products live-streaming e-commerce platforms to reduce their own risks, thus promoting the benign and healthy development of the industry and helping to realize rural revitalization.

The rest of this paper is structured as follows. Section 2 reviews the relevant literature. Section 3 introduces the model for risk assessment of agricultural products live-streaming e-commerce platforms. Section 4 conducts a case study to demonstrate the feasibility of the method proposed in this paper. Finally, conclusions are drawn in Section 5 and future research directions are proposed.

2 Literature review

2.1 Risks of agricultural products live-streaming e-commerce

As a new driving force for rural revitalization, agricultural products live-streaming e-commerce has not only ushered in opportunities such as the increasingly solid industrial foundation, the implementation of several policies and projects that benefit farmers, and the integrated development of urban and rural “dual circulation” e-commerce markets, but also faced with some risks. For example, Zan [17] believes that there are problems in the agricultural products live-streaming e-commerce industry such as exaggerated propaganda, inferior quality, low standardization, weak brand awareness, insufficient supporting services, imperfect platform supervision, and homogenization of live-streaming content in agricultural products and live-streaming e-commerce. Ren [18] believes that agricultural product live-streaming is constrained by product guidelines, live-streaming talents, network technology, and operational experience. Wang and Fang [19] believe that the rapid development of agricultural products live-streaming e-commerce makes the supply chain face problems such as weak supply capacity, slow response speed, and low supply chain coordination and sharing. Liu [20] believes that some inherent shortcomings of the agricultural product supply chain and live-streaming e-commerce restrict the organic integration of the agricultural product supply chain. Yuan and Zhang [21] believe that the current agricultural products live-streaming presents difficulties in the production and reproduction of social capital, including the lack of social capital among farmers, the lack of trust in the online agricultural product sales model, the lack of rich reciprocity norms, and the lack of agricultural products branding. The above study shows that there are many risks in the agricultural products live-streaming e-commerce industry, mainly focusing on information security strategy, digital management systems, technology, and cold chain logistics, with cold chain logistics receiving the most attention. Therefore, we identified four risk evaluation criteria from the above four dimensions, including the perfection of information security strategy, the standardization of the digital management system, the professionalism of live-streaming technology, and the standardization of cold chain logistics.

2.2 Risk assessment methods

As an emerging industry, there are few authoritative research on the risk assessment of agricultural products live-streaming e-commerce platforms at present. But the research on risk assessment in other fields can still be used for reference. By reviewing the literature, it is found that in the previous research on risk assessment, scholars mostly use methods related to Ana-lytic Hierarchy Process (AHP) [22], neural networks [23], and fuzzy MCGDM [24]. Risk evaluation models based on AHP and neural networks are mostly used to study the evaluation system of risks in an unambiguous environment. The models achieve a more comprehensive description of the operating mechanism of each element of the risk management process by refining and quantifying the evaluation system. However, the risk of live-streaming e-commerce platforms, risk evaluation environment, and decision makers’ thinking are all uncertain. Meanwhile, this paper focuses on how to build a valid and reliable evaluation model. Both of the above methods are too inapplicable when evaluating the risk of agricultural products live-streaming e-commerce platforms. The risk evaluation method based on fuzzy MCGDM is concerned with precisely the risk evaluation problem in a fuzzy environment. The method can be adapted to different evaluation problems by constructing different evaluation models. Therefore, this paper will use the risk evaluation method based on fuzzy MCGDM to assess the risk of agricultural products live-streaming e-commerce platforms.

Fuzzy MCGDM is to gather the preferences of group members in a fuzzy environment to form group preferences, and then sort the decision-making schemes according to the group’s preferences or choose the most preferred scheme for the group [25]. Among them, the processing of fuzzy information, the determination of decision makers’ weights, the aggregation of decision makers’ opinions, and the ordering of schemes are the key issues involved in the risk assessment method of fuzzy MCGDM. In this regard, scholars have carried out a lot of related research. For example, in terms of the processing of fuzzy information, Darko and Liang [26] used q-step orthogonal pair fuzzy sets. Chen et al. [27] used interval type-2 fuzzy sets. Haiyun et al. [28] used mixed interval-valued intuitionistic fuzzy sets. Compared with q-step orthogonal pair fuzzy sets and interval type-2 fuzzy sets, interval-valued intuitionistic fuzzy sets consider both affiliation, disaffiliation, and hesitation, and are more accurate and flexible in dealing with uncertain information. Therefore, this paper will use the interval-valued intuitionistic fuzzy numbers to process the uncertainty evaluation information of agricultural products live-streaming e-commerce platforms. In terms of assembling the opinions of decision-makers, Kamal and Shyi [29] proposed an advanced linguistic intuitionistic fuzzy weighted average aggregation operator. Rahman et al. [30] introduced the Pythagorean fuzzy ordered weighted average aggregation operator. Zhao et al. [31] used an n-dimensional interval-valued intuitionistic fuzzy weighted average (IIFWA) operator. These three aggregation methods are aimed at different processing environments of fuzzy information. Considering that interval intuitionistic fuzzy sets are used in this paper to process evaluation information, this paper will use the n-dimensional IIFWA operator to gather decision makers’ opinions. In terms of ranking the schemes, Yu [32] utilized the Shapley value method. You [33] and Hang [34] used the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS). Wang et al. [35] used VIKOR. Compared with Shapley value and TOPSIS, VIKOR can consider both group utility maximization and individual regret minimization as well as incorporating decision makers’ subjective preferences, and thus has higher ranking stability and reliability. This paper will use VIKOR to rank alternatives.

When applying the fuzzy MCGDM approach to assess the risk of agricultural products live-streaming e-commerce platforms, determining the weight of decision-makers is a crucial issue. Regarding the research on determining the weights of decision makers, previous scholars have achieved rich results. For example, Peng [36] set decision-maker weights in the form of interval-valued intuitionistic fuzzy numbers. Fang [37] determined the weights of decision-makers by constructing a mathematical model. The method proposed by Zhang [38] innovatively uses entropy and cross-entropy to determine the expert weights. The method proposed by Yi [39] takes into account both historical evaluation information and current evaluation information to obtain more scientific and reasonable expert weights. Although the above methods are very effective in determining the weights of decision makers, the decision maker has the same weight for different criteria, which may be unreasonable and unrealistic. In actual decision-making problems, due to the limited professional background and knowledge level of each decision maker, each decision maker is usually only good at some fields, but not all fields. A decision-maker is only good at evaluating certain criteria, not all criteria. Because of this, this study proposes a method for determining the decision-maker weight for the risk criterion according to the levels of professionalism of the decision-makers in the risk criterion.

In summary, considering the uncertainty of the risk, the uncertainty of risk evaluation environment and the uncertainty of decision makers’ thinking, as well as the purpose of this paper intending to establish a reliable risk evaluation model, this paper decides to adopt an improved fuzzy MCGDM method to evaluate the risk of agricultural products live-streaming e-commerce platform. The method uses interval-valued intuitionistic fuzzy sets to deal with uncertain information, which is more accurate and flexible; it uses n-dimensional IIFWA operators to gather decision makers’ opinions, which is more suitable for the research context of this paper; it uses the VIKOR method to rank alternatives, which is more stable and reliable; in addition, the method proposes a method to determine the decision maker weights for the criteria, which is more suitable for the realistic research context.

3 Overview of interval-valued intuitionistic fuzzy sets

Due to the limited cognitive level of decision-makers and the complexity and uncertainty of the risks of agricultural products live-streaming e-commerce platforms, it is very difficult to describe the risk with an exact value. Therefore, this paper uses interval-valued intuitionistic fuzzy numbers to process the evaluation information given by decision-makers. A brief introduction to the basic theory of interval-valued intuitionistic fuzzy sets is given below.

Definition 1. [40] Let X be a non-empty set, A ={ < x, u_A (x) , v_A (x) > |x ∈ X } is an intuitionistic fuzzy set. where, u_A (x) and v_A (x) represent the affiliation and non-affiliation of the element x belonging to the set X respectively, and satisfy the condition 0 ⩽ u_A (x) + v_A (x) ⩽1, ∀ x ∈ X. Since it is difficult to express the complexity and uncertainty of objective things with exact real values, it is proposed to extend the intuitionistic fuzzy set with interval-valued numbers u_A (x) and v_A (x), where u_A (x) v_A (x) respectively satisfy u_A (x) ⊂ [0, 1] , v_A (x) ⊂ [0, 1], and sup u_A (x) + sup v_A (x) ⩽1, ∀ x ∈ X.

Definition 2. [41] Let X be a non-empty set, { < x, [u_A (x) ^-, u_A (x) ⁺] , [v_A (x) ^-, v_A (x) ⁺] > |x ∈ X } be an interval-valued intuitionistic fuzzy set, and < [u_A (x) ^-, u_A (x) ⁺] , [v_A (x) ^-, v_A (x) ⁺]> is called interval-valued intuitionistic fuzzy number. where, [u_A (x) ^-, u_A (x) ⁺] and [v_A (x) ^-, v_A (x) ⁺] represent the interval affiliation and interval non-affiliation of the element x belonging to the set X respectively, and satisfy the conditions [u_A (x) ^-, u_A (x) ⁺] ⊆ [0, 1] , [v_A (x) ^-, v_A (x) ⁺] ⊆ [0, 1], and u_A (x) ⁺ + v_A (x) ⁺ ⩽ 1, ∀ x ∈ X.

Definition 3. [42] Let α = ([a₁, b₁] , [c₁, d₁]) , β = ([a₂, b₂] , [c₂, d₂]) be any two interval-valued intuitionistic fuzzy numbers, then the algorithm is:

α + β = ([a₁ + a₂ - a₁a₂, b₁ + b₂ - b₁b₂] , [c₁c₂, d₁d₂]);

α · β = ([a₁a₂, b₁b₂] , [c₁ + c₂ - c₁c₂, d₁ + d₂ d₁d₂]);

$λ α = ([1 - {(1 - a_{1})}^{λ}, 1 - {(1 - b_{1})}^{λ}], [c_{1}^{λ}, d_{1}^{λ}])$ ;

$α^{λ} = ([a_{1}^{λ}, b_{1}^{λ}], [1 - {(1 - c_{1})}^{λ}, 1 - {(1 - d_{1})}^{λ}])$ .

Definition 4. [42] Let α = ([a₁, b₁] , [c₁, d₁]) , β = ([a₂, b₂] , [c₂, d₂]) be any two interval-valued intuitionistic fuzzy numbers, then the normalized Hamming distance between them is

$\begin{matrix} d (α, β) = & \frac{1}{4} (| a_{1} - a_{2} | + | b_{1} - b_{2} | \\ + | c_{1} - c_{2} | + | d_{1} - d_{2} |), \end{matrix}$ (1)

Definition 5. [42] Let H = [α₁, α₂, …, α_n] be a set of interval-valued intuitionistic fuzzy numbers, where α_i = ([a_i, b_i] , [c_i, d_i]) (i = 1, 2, …, n), then the IIFWA is

$\begin{matrix} {IIFWA}_{ω_{i}} (α_{1}, α_{2}, \dots, α_{n}) \\ = \sum_{i = 1}^{n} ω_{i} α_{i} = ([1 - \prod_{i = 1}^{n} {(1 - a_{i})}^{ω_{i}}, \\ 1 - \prod_{i = 1}^{n} {(1 - b_{i})}^{ω_{i}}], [\prod_{i = 1}^{n} c_{i}^{ω_{i}}, \prod_{i = 1}^{n} d_{i}^{ω_{i}}]) \end{matrix},$ (2)

Among them, ω ={ ω₁, ω₂, …, ω_n } is the criterion weight of H = [α₁, α₂, …, α_n], which satisfies $0 ⩽ ω_{i} ⩽ 1, \sum_{i = 1}^{n} ω_{i} = 1, i = 1, 2, \dots, n$ .

4 Risk assessment model of agricultural products live-streaming e-commerce platform

4.1 Problem description

Against the background of the country’s vigorous promotion of the rural revitalization strategy and the rise of live-streaming e-commerce, the agricultural products live-streaming e-commerce has shown a strong momentum of development. Before entering the live-streaming e-commerce platform, agricultural product merchants need to evaluate the risk of the platform. It can help agricultural products merchants determine the platform with the lowest comprehensive risk, to provide a decision-making basis for platform selection decisions. In this paper, an improved risk evaluation method based on interval-valued intuitionistic fuzzy MCGDM is proposed to evaluate the risks of agricultural products live-streaming e-commerce platforms. For convenience, the following notations are used to denote the aggregate quantities involved:

I = { I₁, I₂, …, I_i }: The set of i alternative agricultural products live-streaming e-commerce platforms concerned by agricultural products merchants, where I_l represents the l - th alternative agricultural products live-streaming e-commerce platform, l = 1, 2, …, i.

Q ={ Q_1,, Q₂, …, Q_q }: The set of q risk criteria that decision makers pay attention to when evaluating the risk of the agricultural products live-streaming e-commerce platform, where Q_t represents the t - th risk criterion, t = 1, 2, …, q.

H ={ H₁, H₂, …, H_h }: h decision makers participating in the risk assessment of the agricultural products live-streaming e-commerce platforms, where H_s represents the s - th decision maker, s = 1, 2, …, h.

μ ={ μ₁, μ₂, …, μ_q }: Weight vector of risk criterion, where μ_t represents the weight or importance of the risk criterion Q_t, satisfying μ_t ⩾ 0 and $\sum_{t = 1}^{q} μ_{t} = 1, t = 1, 2, \dots, q$ . In this paper, the weight vector of risk criteria is given by all decision makers after consultation.

$η_{t}^{s}$ : The weight of decision maker H_s for risk criterion Q_t.

$r_{lt}^{s} = ([a_{lt}^{s}, b_{lt}^{s}], [c_{lt}^{s}, d_{lt}^{s}])$ : The risk evaluation value of the decision maker H_s in the risk criterion Q_t of the alternative agricultural products live-streaming e-commerce platform I_l, which is an interval-valued intuitionistic fuzzy number, where $[a_{lt}^{s}, b_{lt}^{s}]$ and $[c_{lt}^{s}, d_{lt}^{s}]$ represent the affiliation and the non-affiliation of the alternative agricultural products live-streaming e-commerce platform I_l in the risk criterion Q_t, respectively, $[a_{lt}^{s}, b_{lt}^{s}] \subseteq [0, 1], [c_{lt}^{s}, d_{lt}^{s}] \subseteq [0, 1], b_{lt}^{s} + d_{lt}^{s} ⩽ 1$ .

$R^{s} = {(r_{lt}^{s})}_{i \times q}$ : The risk assessment matrix of decision maker H_s.

T ={ T¹, T², …, T^v }: The set of evaluation scales about the professionalism of decision makers in risk criteria. In the specific example in the section of 5, the scale set used is in the form of a 5-point scale, namely T ={ T¹ = 1, T² = 2, T³ = 3, T⁴ = 4T⁵ = 5 }, where 1 indicates the least professionalism, and 5 indicates the highest professionalism.

$z_{ot}^{s}$ : The professional score value of decision maker H_s in the risk criterion Q_t of agricultural products live-streaming e-commerce platform from decision maker H_o, where H_o represents the o - th decision, o = 1, 2, …, h.

To illustrate the problem more precisely, 3 hypotheses are given:

Decision makers are all experts in the field of agricultural products live-streaming e-commerce.

Decision makers are able to give reasonable judgments based on the real situation.

The decision maker’s judgment has a certain degree of stability.

4.2 Risk assessment method based on improved interval-valued intuitionistic fuzzy MCGDM

When the risk evaluation method based on improved interval-valued intuitionistic fuzzy MCGDM is used to evaluate the risk of the agricultural products live-streaming e-commerce platforms, the specific evaluation process includes the following four steps: (1) Each decision maker gives the individual risk evaluation matrix of the alternative agricultural products live-streaming e-commerce platform, and the weight vector of the risk criterion is given after consultation by all decision-makers. (2) Use the expert scoring method to determine the decision maker’s weight for the risk criterion. The standard is the level of expertise of the decision-maker. If the decision maker is highly professional about a risk criterion, the decision maker will be given a larger weight about the risk criterion. If the decision maker is less professional about a risk criterion, a smaller weight is given to the decision maker about the risk criterion. (3) The individual risk assessment matrix of all decision-makers is assembled into a comprehensive risk assessment matrix by using the weight of the risk criterion and the decision maker’s weight for the risk criterion. (4) According to the VIKOR method, the risks of the alternative agricultural products live-streaming e-commerce platforms are ranked, to determine the platform with the lowest comprehensive risk.

a. Determination of decision maker weight for risk criteria

The first key point of the risk assessment method of the agricultural products live-streaming e-commerce platform proposed in this paper is to determine the decision maker weight for risk criteria. $η_{t}^{s}$ indicates the weight of decision maker H_s in the risk criterion Q_t. In order to determine the value of $η_{t}^{s}$ , it is necessary to consider the professionalism of the decision makers H_s in the risk criteria Q_t. If decision maker H_s is highly specialized in risk criterion Q_t, give decision maker H_s a larger weight for risk criterion Q_t. If decision maker H_s is weak in risk criterion Q_t, assign decision maker H_s a smaller weight for risk criterion Q_t. Among them, professionalism is a qualitative concept. In order to facilitate the calculation, the professionalism of decision makers in risk criteria is quantified by the expert scoring method. The expert scoring method objectively integrates the experience and subjective judgment of all decision makers, and makes a reasonable estimate of the professionalism of decision makers which are difficult to quantitatively analyze by technical methods. And the calculation is simple and practical. The specific algorithm is as follows:

The decision maker H_O (o = 1, 2, …, h) scores the professionalism of the decision maker H_s in the risk criteria Q_t, and the score is $z_{ot}^{s} (o = 1, 2, \dots, h)$ . When o = s, $z_{st}^{s}$ represents the professional score value of decision makers H_s in the risk criterion Q_t given by himself. When o ≠ s, $z_{ot}^{s} (o = 1, 2, \dots, h, o \neq s)$ represents the professional score value of decision makers H_s in the risk criterion Q_t given by other decision makers H_O (o = 1, 2, …, h, o ≠ s). In the professional scoring process, the scale set used is a set in the form of a v-point scale T = { T¹, T², …, T^v }.

θ is called the control coefficient. The control coefficient θ (0 ⩽ θ ⩽ 1) is introduced to construct the professional comprehensive score $z_{t}^{s}$ of the decision maker H_s in the risk criterion Q_t, which can comprehensively consider the self-scoring $z_{st}^{s}$ and the scoring $z_{ot}^{s}$ of other decision makers, among which:

$z_{t}^{s} = θ z_{st}^{s} + (1 - θ) z_{ot}^{s}$ (3)

By the change in the control coefficient, a trade-off between self-scoring and other decision makers’ scores can be achieved. When η = 1, the weight of decision maker H_s in the risk criterion Q_t only depends on the self-rating of decision maker H_s; When θ = 0, the weight of decision maker H_s in the risk criterion Q_t only depends on the rating of other decision makers. Generally, take θ = 0.5.

Standardize the comprehensive score of the decision maker to obtain the decision maker weight for the risk criterion as follows:

$η_{t}^{s} = \frac{z_{t}^{s}}{\sum_{s = 1}^{h} z_{t}^{s}}$ (4)

b. Construction of comprehensive interval-valued intuitionistic fuzzy risk assessment matrix

When evaluating the risks of agricultural products live-streaming e-commerce platforms, in order to comprehensively consider the evaluation information of all decision makers, it is necessary to integrate the individual risk evaluation matrices of all decision makers into a comprehensive risk evaluation matrix. According to equation (3) and (4), the decision maker weight matrix for the risk criteria of the agricultural products live-streaming e-commerce platform is obtained, and the risk criteria weight vector is given by the decision makers after consultation. Then, equation (2) is used to assemble the interval-valued intuitionistic fuzzy risk evaluation matrix of all decision makers to construct a comprehensive interval intuitionistic fuzzy risk evaluation matrix R = (r_lt) _i×q, in which:

$\begin{matrix} R = {(r_{lt})}_{i \times q} = (\sum_{s = 1}^{h} η_{t}^{s} r_{lt}^{s}) \\ = (\begin{matrix} [1 - \prod_{s = 1}^{h} {(1 - a_{lt}^{s})}^{η_{t}^{s}}, 1 - \prod_{s = 1}^{h} {(1 - b_{lt}^{s})}^{η_{t}^{s}}] \\ [\prod_{s = 1}^{h} {(c_{lt}^{s})}^{η_{t}^{s}}, \prod_{s = 1}^{h} {(d_{lt}^{s})}^{η_{t}^{s}}] \end{matrix}) \end{matrix}$ (5)

c. Ranking of risks of agricultural products live-streaming e-commerce platforms

The second key point of the risk evaluation method based on interval-valued intuitionistic fuzzy MCGDM proposed in this paper is to rank the risk of alternative agricultural products live-streaming e-commerce platforms. Compared with the Shapley value method [28] and the TOPSIS method [29, 30], The VIKOR method used in this paper can consider group utility values and individual regret values [31], and provide a variety of compromise schemes for agricultural merchants by changing the decision mechanism coefficients, which can provide more comprehensive decision suggestions for agricultural products merchants while conforming more to the decision making habits of decision makers. Specific steps are as follows:

1) Determine the positive ideal point and negative ideal point of each criterion:

$\begin{matrix} r_{t}^{+} = max_{1 ⩽ l ⩽ i} r_{lt} \\ = ([max_{1 ⩽ l ⩽ i} a_{lt}, max_{1 ⩽ l ⩽ i} b_{lt}], [min_{1 ⩽ l ⩽ i} c_{lt}, min_{1 ⩽ l ⩽ i} d_{lt}]) \\ r_{t}^{-} = min_{1 ⩽ l ⩽ i} r_{lt} \\ = ([min_{1 ⩽ l ⩽ i} a_{lt}, min_{1 ⩽ l ⩽ i} b_{lt}], [max_{1 ⩽ l ⩽ i} c_{lt}, max_{1 ⩽ l ⩽ i} d_{lt}]), \\ t = 1, 2, \dots, q \end{matrix}$ (6)

2) Calculate group utility value, individual regret value and compromise value:

$S_{l} = \sum_{t = 1}^{q} ω_{t} \frac{d (r_{t}^{+}, r_{lt})}{d (r_{t}^{+}, r_{t}^{-})}$ (7)

$R_{l} = max_{1 ⩽ t ⩽ q} {ω_{t} \frac{d (r_{t}^{+}, r_{lt})}{d (r_{t}^{+}, r_{t}^{-})}}$ (8)

$\begin{matrix} Q_{l} = ɛ \frac{S_{l} - S^{-}}{S^{+} - S^{-}} + (1 - ɛ) \frac{R_{l} - R^{-}}{R^{+} - R^{-}} \end{matrix}$ (9)

Among them, $S^{+} = max_{1 ⩽ l ⩽ i} S_{l}, S^{-} = min_{1 ⩽ l ⩽ i} S_{l}, R^{+} = max_{1 ⩽ l ⩽ i} R_{l},$ $R^{-} = min_{1 ⩽ l ⩽ i} R_{l}$ , ɛ is called the decision-making mechanism coefficient, ɛ > 0.5 indicates that the decision is based on a decision-making mechanism that maximizes group utility, ɛ < 0.5 indicates that the decision is based on a decision-making mechanism that minimizes individual regret, and ɛ = 0.5 indicates that the decision is a consensus decision through negotiation mechanism decision.

3) Sort schemes. Sort each scheme according to S_l, R_l, and Q_l from small to large, and the smaller the value, the better the scheme.

4) Choose a compromise scheme. Sort each scheme according to the compromise value from small to large, denoted as Q⁽¹⁾, Q⁽²⁾, …, Q⁽ⁱ, when Q^l) satisfies the following two conditions:

Condition 1: $Q_{d} - Q_{l} ⩾ \frac{1}{i - 1} (d = 1, 2, \dots, i, d \neq l)$ , Q_d and Q_l are the Q values of Q⁽²⁾ and Q⁽¹ respectively.

Condition 2: Q⁽¹⁾ is also S⁽¹⁾ or R⁽¹⁾ at the same time.

Then Q⁽¹⁾ is a compromise scheme. If the above conditions cannot be satisfied at the same time, a compromise scheme can be obtained according to the following conditions:

If condition 2 is not satisfied, then Q⁽¹Q⁽²⁾ are all compromise schemes,

If the condition 1 is not satisfied, the schemes that satisfy the condition $Q^{(f)} - Q^{(1)} < \frac{1}{i - 1} (f = 1, 2, \dots, i)$ are all compromise schemes.

5 Case and comparative analysis

5.1 Case study

In this section, using the risk assessment method of the agricultural products live-streaming e-commerce platform proposed in this paper helps Horned Pepper to determine the live-streaming e-commerce platform with the lowest comprehensive risk and provides a decision-making basis for its choice of platform. Then the feasibility and effectiveness of the method proposed in this paper are illustrated. Horned Pepper is a local specialty in Gansu Province, China. It has a good reputation for its long Pepper body, thick leather, good color, strong spicy taste, and high oil content. However, due to information asymmetry, the consumer market for Horned Pepper has not been fully opened, and the phenomenon of slow sales, difficult to sell, and expensive to buy has appeared. In this regard, the local government decided to invite experts to identify a platform with the lowest comprehensive risk for Horned Pepper from several alternative live-streaming e-commerce platforms to provide a reference for its choice of live-streaming e-commerce platform to settle in, to help Horned Pepper to carry out new sales model of live-streaming e-commerce, expanding sales channels. The local government invited 4 experts as decision makers to evaluate the risks of 5 alternative agricultural products live-streaming e-commerce platforms concerned farmers. Among them, experts are those who specialize in the field of live-streaming e-commerce, with specialized experience, knowledge, and skills, and reach a certain level of professionalism [43 –45]. The 5 alternative agricultural products live-streaming e-commerce platforms are Taobao, JD.com, Tiktok, Pinduoduo and Kuaishou. The 4 risk criteria used by decision makers to evaluate the risks of agricultural products live-streaming e-commerce platforms are the perfection of information security strategy, the standardization of the digital management system, the professionalism of live-streaming technology, and the standardization of cold chain logistics. The specific evaluation process is as follows:

In the first step, according to the evaluation scale, 4 decision makers evaluated the risks of 5 alternative agricultural products live-streaming e-commerce platforms. The evaluation values are expressed as interval-valued intuitionistic fuzzy numbers to obtain individual risk evaluation matrices, as shown in Table 1. Through the group discussion and negotiation of the decision makers, the weight vector of the risk criterion is jointly given by the 4 decision makers: μ ={ 0.3, 0.1, 0.2, 0.4 }.

Table 1
Individual risk assessment matrix

Q ₁ Q ₂ Q ₃ Q ₄

H ₁ I ₁ ([0.5,0.6], [0.2,0.4]) ([0.7,0.8], [0.1,0.2]) ([0.4,0.5], [0.1,0.2]) ([0.2,0.4], [0.4,0.5])

I ₂ ([0.5,0.6], [0.1,0.2]) ([0.4,0.6], [0.3,0.4]) ([0.4,0.5], [0.1,0.3]) ([0.4,0.5], [0.3,0.4])

I ₃ ([0.5,0.6], [0.1,0.3]) ([0.3,0.5], [0.3,0.4]) ([0.6,0.8], [0.1,0.2]) ([0.3,0.4], [0.3,0.4])

I ₄ ([0.4,0.5], [0.3,0.5]) ([0.4,0.5], [0.3,0.4]) ([0.5,0.7], [0.1,0.3]) ([0.5,0.6], [0.2,0.4])

I ₅ ([0.4,0.5], [0.4,0.5]) ([0.6,0.7], [0.2,0.3]) ([0.4,0.5], [0.2,0.4]) ([0.4,0.6], [0.3,0.4])

H ₂ I ₁ ([0.4,0.7], [0.1,0.3]) ([0.5,0.7], [0.1,0.2]) ([0.4,0.5], [0.1,0.4]) ([0.4,0.5], [0.3,0.5])

I ₂ ([0.3,0.5], [0.2,0.4]) ([0.4,0.5], [0.3,0.4]) ([0.4,0.6], [0.2,0.4]) ([0.4,0.5], [0.4,0.5])

I ₃ ([0.3,0.6], [0.2,0.3]) ([0.3,0.5], [0.3,0.5]) ([0.5,0.7], [0.2,0.3]) ([0.5,0.6], [0.3,0.5])

I ₄ ([0.4,0.6], [0.2,0.3]) ([0.5,0.8], [0.1,0.2]) ([0.4,0.7], [0.2,0.3]) ([0.5,0.7], [0.2,0.3])

I ₅ ([0.3,0.5], [0.4,0.5]) ([0.6,0.7], [0.1,0.3]) ([0.4,0.5], [0.3,0.4]) ([0.6,0.8], [0.1,0.2])

H ₃ I ₁ ([0.4,0.5], [0.2,0.3]) ([0.4,0.6], [0.2,0.3]) ([0.5,0.6], [0.3,0.4]) ([0.4,0.5], [0.2,0.4])

I ₂ ([0.4,0.6], [0.2,0.3]) ([0.4,0.7], [0.1,0.3]) ([0.4,0.5], [0.2,0.4]) ([0.3,0.5], [0.2,0.4])

I ₃ ([0.4,0.6], [0.2,0.4]) ([0.3,0.5], [0.4,0.5]) ([0.6,0.7], [0.1,0.2]) ([0.3,0.5], [0.2,0.4])

I ₄ ([0.4,0.5], [0.2,0.3]) ([0.4,0.6], [0.3,0.4]) ([0.5,0.7], [0.1,0.3]) ([0.5,0.7], [0.1,0.2])

I ₅ ([0.4,0.5], [0.3,0.4]) ([0.4,0.7], [0.1,0.2]) ([0.3,0.5], [0.2,0.4]) ([0.7,0.8], [0.1,0.2])

H ₄ I ₁ ([0.5,0.7], [0.2,0.3]) ([0.5,0.7], [0.1,0.2]) ([0.4,0.6], [0.3,0.4]) ([0.5,0.7], [0.2,0.3])

I ₂ ([0.4,0.6], [0.1,0.3]) ([0.5,0.7], [0.1,0.2]) ([0.3,0.5], [0.3,0.4]) ([0.4,0.6], [0.3,0.4])

I ₃ ([0.4,0.6], [0.2,0.4]) ([0.3,0.4], [0.3,0.5]) ([0.6,0.7], [0.2,0.3]) ([0.4,0.6], [0.3,0.4])

I ₄ ([0.6,0.7], [0.2,0.3]) ([0.5,0.7], [0.1,0.3]) ([0.5,0.6], [0.1,0.3]) ([0.4,0.6], [0.2,0.3])

I ₅ ([0.3,0.6], [0.3,0.4]) ([0.4,0.6], [0.2,0.3]) ([0.2,0.5], [0.3,0.4]) ([0.7,0.8], [0.1,0.2])

		Q ₁	Q ₂	Q ₃	Q ₄
H ₁	I ₁	([0.5,0.6], [0.2,0.4])	([0.7,0.8], [0.1,0.2])	([0.4,0.5], [0.1,0.2])	([0.2,0.4], [0.4,0.5])
	I ₂	([0.5,0.6], [0.1,0.2])	([0.4,0.6], [0.3,0.4])	([0.4,0.5], [0.1,0.3])	([0.4,0.5], [0.3,0.4])
	I ₃	([0.5,0.6], [0.1,0.3])	([0.3,0.5], [0.3,0.4])	([0.6,0.8], [0.1,0.2])	([0.3,0.4], [0.3,0.4])
	I ₄	([0.4,0.5], [0.3,0.5])	([0.4,0.5], [0.3,0.4])	([0.5,0.7], [0.1,0.3])	([0.5,0.6], [0.2,0.4])
	I ₅	([0.4,0.5], [0.4,0.5])	([0.6,0.7], [0.2,0.3])	([0.4,0.5], [0.2,0.4])	([0.4,0.6], [0.3,0.4])
H ₂	I ₁	([0.4,0.7], [0.1,0.3])	([0.5,0.7], [0.1,0.2])	([0.4,0.5], [0.1,0.4])	([0.4,0.5], [0.3,0.5])
	I ₂	([0.3,0.5], [0.2,0.4])	([0.4,0.5], [0.3,0.4])	([0.4,0.6], [0.2,0.4])	([0.4,0.5], [0.4,0.5])
	I ₃	([0.3,0.6], [0.2,0.3])	([0.3,0.5], [0.3,0.5])	([0.5,0.7], [0.2,0.3])	([0.5,0.6], [0.3,0.5])
	I ₄	([0.4,0.6], [0.2,0.3])	([0.5,0.8], [0.1,0.2])	([0.4,0.7], [0.2,0.3])	([0.5,0.7], [0.2,0.3])
	I ₅	([0.3,0.5], [0.4,0.5])	([0.6,0.7], [0.1,0.3])	([0.4,0.5], [0.3,0.4])	([0.6,0.8], [0.1,0.2])
H ₃	I ₁	([0.4,0.5], [0.2,0.3])	([0.4,0.6], [0.2,0.3])	([0.5,0.6], [0.3,0.4])	([0.4,0.5], [0.2,0.4])
	I ₂	([0.4,0.6], [0.2,0.3])	([0.4,0.7], [0.1,0.3])	([0.4,0.5], [0.2,0.4])	([0.3,0.5], [0.2,0.4])
	I ₃	([0.4,0.6], [0.2,0.4])	([0.3,0.5], [0.4,0.5])	([0.6,0.7], [0.1,0.2])	([0.3,0.5], [0.2,0.4])
	I ₄	([0.4,0.5], [0.2,0.3])	([0.4,0.6], [0.3,0.4])	([0.5,0.7], [0.1,0.3])	([0.5,0.7], [0.1,0.2])
	I ₅	([0.4,0.5], [0.3,0.4])	([0.4,0.7], [0.1,0.2])	([0.3,0.5], [0.2,0.4])	([0.7,0.8], [0.1,0.2])
H ₄	I ₁	([0.5,0.7], [0.2,0.3])	([0.5,0.7], [0.1,0.2])	([0.4,0.6], [0.3,0.4])	([0.5,0.7], [0.2,0.3])
	I ₂	([0.4,0.6], [0.1,0.3])	([0.5,0.7], [0.1,0.2])	([0.3,0.5], [0.3,0.4])	([0.4,0.6], [0.3,0.4])
	I ₃	([0.4,0.6], [0.2,0.4])	([0.3,0.4], [0.3,0.5])	([0.6,0.7], [0.2,0.3])	([0.4,0.6], [0.3,0.4])
	I ₄	([0.6,0.7], [0.2,0.3])	([0.5,0.7], [0.1,0.3])	([0.5,0.6], [0.1,0.3])	([0.4,0.6], [0.2,0.3])
	I ₅	([0.3,0.6], [0.3,0.4])	([0.4,0.6], [0.2,0.3])	([0.2,0.5], [0.3,0.4])	([0.7,0.8], [0.1,0.2])

In the second step, according to their subjective judgments, 4 decision makers score the professionalism of all decision makers for each risk criterion. When scoring, the scale set is a set in the form of a 5-point scale, that is T ={ T¹ = 1, T² = 2, T³ = 3, T⁴ = 4, T⁵ = 5 }, where 1 point represent the weakest professionalism, 2 represent weaker professional, 3 represent average professional, 4 represent stronger professional, and 5 points represent the strongest professionalism. so as to obtain the professional scoring matrix of decision makers, as shown in Table 2.

Table 2

Professional scoring matrix

		Q ₁	Q ₂	Q ₃	Q ₄
H ₁	H ₁	3	2	2	3
	H ₂	2	2	3	3
	H ₃	5	4	2	3
	H ₄	3	4	1	4
H ₂	H ₁	2	4	3	3
	H ₂	4	1	3	2
	H ₃	5	5	4	2
	H ₄	3	4	3	4
H ₃	H ₁	4	2	3	2
	H ₂	3	4	4	3
	H ₃	3	4	4	3
	H ₄	4	1	3	3
H ₄	H ₁	4	2	4	4
	H ₂	3	3	4	3
	H ₃	5	5	3	4
	H ₄	3	4	3	5

According to Equation (3), calculate the professional comprehensive score of all decision makers in each risk criterion of the agricultural products live-streaming e-commerce platform. Where, let the control coefficient θ = 0.5, get the professional comprehensive score matrix of decision makers, as shown in Table 3.

Table 3

Professional comprehensive score matrix

	Q ₁	Q ₂	Q ₃	Q ₄
H ₁	6.5	5	6	6
H ₂	6	5	7	5.5
H ₃	9	9	6.5	6
H ₄	6.5	6.5	5	8

According to Equation (4), standardize the professional comprehensive score of all decision makers for each risk criterion on the agricultural products live-streaming e-commerce platform, and obtain the decision maker weights of the risk criterion, as shown in Table 4.

Table 4

Decision maker weights for risk criteria

	Q ₁	Q ₂	Q ₃	Q ₄
H ₁	0.23	0.20	0.24	0.24
H ₂	0.21	0.20	0.29	0.22
H ₃	0.32	0.35	0.27	0.24
H ₄	0.23	0.25	0.20	0.31

The third step is to use Equation (5), the risk criterion’s weight vector of the agricultural products live-streaming e-commerce platform and the decision maker weights of the risk criterion to assemble the individual risk assessment matrix given by the decision maker to obtain a comprehensive risk assessment matrix, as shown in Table 5 shown.

Table 5

Comprehensive risk assessment matrix

	Q ₁	Q ₂	Q ₃	Q ₄
I ₁	([0.45,0.62], [0.17,0.32])	([0.52,0.70], [0.13,0.23])	([0.43,0.55], [0.15,0.34])	([0.39,0.56], [0.20,0.35])
I ₂	([0.41,0.58], [0.12,0.27])	([0.46,0.65], [0.12,0.26])	([0.38,0.56], [0.15,0.37])	([0.43,0.59], [0.27,0.42])
I ₃	([0.41,0.60], [0.17,0.35])	([0.30,0.48], [0.33,0.48])	([0.57,0.73], [0.14,0.24])	([0.38,0.54], [0.27,0.42])
I ₄	([0.45,0.51], [0.22,0.34])	([0.45,0.55], [0.18,0.32])	([0.47,0.58], [0.12,0.30])	([0.45,0.65], [0.17,0.29])
I ₅	([0.36,0.53], [0.34,0.47])	([0.49,0.68], [0.14,0.26])	([0.34,0.50], [0.23,0.39])	([0.63,0.77], [0.12,0.22])

The fourth step is to rank the risks of the alternative agricultural products live-streaming e-commerce platforms. Equation (6) is used to determine the positive ideal point $r_{t}^{+}$ and negative ideal point $r_{t}^{-}$ of the risk criterion of the alternative agricultural products live-streaming e-commerce platform. The results are shown in Table 6.

Table 6

Positive ideal point and negative ideal point of risk criterion

	Q ₁	Q ₂	Q ₃	Q ₄
$r_{t}^{+}$	([0.45,0.62], [0.12,0.27])	([0.52,0.70], [0.13,0.23])	([0.57,0.73], [0.12,0.24])	([0.63,0.77], [0.12,0.22])
$r_{t}^{-}$	([0.36,0.51], [0.34,0.47])	([0.30,0.48], [0.33,0.48])	([0.34,0.50], [0.23,0.39])	([0.38,0.54], [0.27,0.42])

In this example, the decision making using a negotiated consensus-based decision-making mechanism, namely ɛ = 0.5.

Use Equation (7) to calculate the group utility value S_l and obtain S₁ = 0.50, S₂ = 0.56, S₃ = 0.60, S₄ = 0.47, S₅ = 0.51; use Equation (8) to calculate the individual regret value R_l and obtain R₁ = 0.32, R₂ = 0.35, R₃ = 040, R₄ = 0.20, R₅ = 0.30; use Equation (9) to calculate the compromise value Q_l to obtain Q₁ = 0.87, Q₂ = 0.92, Q₃ = 023, Q₄ = 0, Q₅ = 0.57.

Sort each scheme according to S_l from small to large to get S⁽¹ = I₄S⁽² = I₁S⁽³ = I₅S⁽⁴ = I₂S⁽⁵ = I₃; sort each scheme according to R_l from small to large, get R⁽¹ = I₄R⁽² = I₅R⁽³ = I₁, R⁽⁴ = I₂R⁽⁵ = I₃; sort each scheme according to Q_l from small to large, get Q⁽¹ = I₄Q⁽² = I₃Q⁽³ = I₅Q⁽⁴ = I₁Q⁽⁵ = I₂.

Since Q⁽¹ = I₄Q⁽² = I₃, $Q_{3} - Q_{4} = 0.23 > \frac{1}{5}$ , that is, the difference between the second-ranked agricultural products live-streaming e-commerce platform I₃ and the first-ranked agricultural products live-streaming e-commerce platform I₄ in compromise value is greater than the reciprocal of the number of alternative agricultural products live-streaming e-commerce platforms, and the condition 1 is satisfied; Q⁽¹⁾ = S⁽¹ = R¹ = I₄, that is, the group utility value and individual regret value of the agricultural products live-streaming e-commerce platform I₄ ranked first in the compromise value also ranked first, satisfying condition 2. The compromised agricultural products live-streaming e-commerce platform is I₄, that is Pinduoduo.

Therefore, in this case, Pinduoduo is the platform with the lowest comprehensive risk among the alternative agricultural products live-streaming e-commerce platforms. As one of the largest agricultural product retail platforms in China, Pinduoduo has focused on the sinking market since its inception and has a deep connection with agriculture and rural areas [46, 47]. In terms of information security, Pinduoduo attaches great importance to the information security of users and uses secure technical means to strengthen the protection of information and improve the confidentiality of information. In terms of live-streaming technology, Pinduoduo has developed a lot of fission-style gameplay, such as red envelope fission, fan group fission, etc. Through word-of-mouth communication, the spread rate is higher than traditional situational marketing promotion and Baidu search promotion, which makes Pinduoduo live-streaming a huge development prospect. In terms of cold chain logistics, Pinduoduo realizes that the supply chain of agricultural products is a shortcoming that restricts the growth of agricultural products in China. Therefore, Pinduoduo is relying on digitalization to continue to invest heavily in the construction of cold storage, fresh cold chain logistics systems, and other infrastructure, establish a supply chain system suitable for fresh agricultural products, improve circulation efficiency and reduce losses. It is precisely because of the outstanding performance of Pinduoduo in the above risk management and controls that it can stand out among the many agricultural products live-streaming e-commerce platforms in this case, and become an important platform to be chosen for live-streaming e-commerce sales of Horned Pepper [48, 49].

5.2 Comparative analysis

The proposed risk evaluation method of agricultural products live-streaming e-commerce platforms based on interval-valued intuitionistic fuzzy MCGDM determines the decision-maker weight for risk criteria according to their expertise, and ranks the risk of the alternative agricultural products live-streaming e-commerce platforms using the VIKOR method. This section compares the method in this paper with other interval-valued intuitionistic fuzzy MCGDM risk evaluation methods, as shown in Table 7.

Table 7
Comparison of the method in this paper with other risk evaluation methods based on interval intuitionistic fuzzy MCGDM

Literature Whether to determine the weight of decision makers for the criteria The adopted alternative ranking method

Literature[32] No TOPSIS

Literature[33] No TODIM (an acronym in Portuguese for Interactive and Multicriteria Decision Making)

Literature[34] No Combined method of TOPSIS and vector projection

Literature[35] No Linear weighting method

the method in this paper Yes VIKOR

Literature	Whether to determine the weight of decision makers for the criteria	The adopted alternative ranking method
Literature[32]	No	TOPSIS
Literature[33]	No	TODIM (an acronym in Portuguese for Interactive and Multicriteria Decision Making)
Literature[34]	No	Combined method of TOPSIS and vector projection
Literature[35]	No	Linear weighting method
the method in this paper	Yes	VIKOR

The literature [32 –34], and [35] assume that there is no difference in decision-maker weights for different criteria, i.e., decision-makers are given the same weight for different criteria. However, in realistic scenarios, due to the difference in professional background, knowledge level, and personal ability, there are always criteria that decision makers are good at evaluating, and a larger weight should be assigned to decision makers for such criteria; on the contrary, a smaller weight should be assigned to criteria that decision makers are not good at. Therefore, this paper proposes a method for determining decision-maker weights for criteria based on the expertise of decision-makers, which can assign different weights to decision-makers for different criteria.

Although the solution ranking methods used in the literature [32 –34], and [35] have their own advantages, the VIKOR method used in this paper is more applicable to the context of this study, which can consider group utility values and individual regret values, and provide a variety of compromise solutions for agricultural merchants by changing the decision mechanism coefficients, thus satisfying the different decision-making habits of decision makers and providing more comprehensive decision making suggestions for agricultural merchants.

However, the method proposed in this paper also has some shortcomings. First, compared with the methods for determining decision-maker weights proposed in the literature [32 –34], and [35], the method for determining decision-maker weights for criteria proposed in this paper requires decision makers to score each other’s expertise, which is more subjective and will affect the scientificity of decision making to some extent. In addition, the alternative ranking method used in this paper has certain contextual limitations, and the method becomes less applicable when the context changes, for example, TODIM is more applicable when the psychological factors of decision-makers need to be considered.

6 Conclusions

With the continuous advancement of the rural revitalization strategy and the rapid development of live-streaming e-commerce, agricultural products live-streaming e-commerce platforms have shown a strong momentum of development. Choosing a live-streaming e-commerce platform to settle in is the first step for agricultural products to start the live-streaming e-commerce business. Different live-streaming e-commerce platforms will bring different risks and challenges to agricultural product merchants, such as imperfect information security strategies, irregular digital management, backward live-streaming technology, irregular cold chain logistics, etc. Therefore, when agricultural products merchants choose a live-streaming e-commerce platform to settle in, they must first conduct a comprehensive evaluation of the risks of the platforms, to determine the platform with the lowest comprehensive risk.

Considering the complexity of the risks of the agricultural products live-streaming e-commerce platforms, the ambiguity of the risk evaluation environment, and the fact that decision-makers are affected by their knowledge structure, knowledge level, and emotional factors, it is difficult to give accurate evaluation information. This paper proposes the improved interval-valued intuitionistic fuzzy MCGDM method to evaluate the risk of agricultural products live-streaming e-commerce platforms. The traditional interval-valued intuitionistic fuzzy MCGDM method does not take into account the difference in the professionalism of decision-makers. It is unreasonable and unrealistic to assign the same weight to decision-makers for different criteria. Therefore, this paper proposes an improved interval-valued intuitionistic fuzzy MCGDM method that considers the professionalism of decision-makers to evaluate the risk of agricultural products live-streaming e-commerce platforms. This method determines the decision maker’s weight for the risk criterion according to the professional degree of the decision maker in the risk criterion. If the decision maker is highly specialized in a certain risk criterion, the decision maker will be given a larger weight for the risk criterion. If the decision maker is weakly specialized in a certain risk criterion, the decision maker will be given a smaller weight for the risk criterion. At the same time, the method adopts the VIKOR method to rank the alternative agricultural products live-streaming e-commerce platform. The VIKOR method provides a variety of compromise solutions for agricultural product merchants by changing the decision-making mechanism coefficient, which is more in line with the decision-making habits of decision-makers. The research in this paper provides a new way to solve the risk assessment problem of agricultural products live-streaming e-commerce platforms in reality. It can help agricultural merchants identify the live-streaming e-commerce platform with the least overall risk while also urging the live-streaming e-commerce platform to reduce its own risk, thus promoting the agricultural products live-streaming e-commerce industry to achieve sustainable development and helping to realize rural revitalization. In addition, this study can also contribute to the development and enrichment of theoretical research results of agricultural products live-streaming e-commerce platforms.

There are also some limitations in this study. For example, this paper considers the four main risk criteria of agricultural products live-streaming e-commerce platforms. In reality, other factors affect the risk of agricultural products live-streaming e-commerce platforms. In their upcoming work, the study team will broaden the criteria for risk in live-streaming e-commerce for agricultural products and investigate and include other aspects that affect those risks in the model for more in-depth analysis. At the same time, the method of determining decision-maker weight for the criteria mainly relies on subjective scoring among decision-makers, and future research may consider adding more objective criteria for scoring when determining decision-maker weight for the criteria. Finally, regarding the ranking method of alternatives, the VIKOR used in this paper has some contextual limitations, and future studies could use methods with broader contextual applicability.

Funding

This work was supported by the Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN202200808).

References

Luo

Z.D.

and Xiang

J.Y.

, New rural development and rural revitalization path in the era of mobile internet, City Planning Review 43(10) (2019), 29–36.

Guo

Q.Z.

, The development motivation, present situation and trend of live-streaming e-commerce in China, News and Writing (08) (2020), 84–91.

, Luo

and Pu

, Information acquisition from data-driven analytics: A perspective of blockchain service in a duopoly market, Computers & Industrial Engineering (2023), 108994.

, Cao

and Zhao

Y.J.

, Business model innovation of retail enterprises in the era of “new retail”, Enterprise Economy (04) (2020), 37–45.

Zeng

Y.W.

, Ma

C.J.

, Li

L.L.

, et al., Live streaming e-commerce and the value recreation of agricultural marketing from rural to areas: mechanism and implementation paths, Issues in Agricultural Economy (02) (2022), 108–117.

Liu

, Yan

Z.H.

and Sun

, Pricing strategies under the framework of “Hardware Product+Software Service” ——Taking iOS and Android for Examples, Chinese Journal of Management Science 29(09) (2021), 144–155.

Batlles-delaFuente

, Abad-Segura

, González-Zamar

M.D.

, et al., An evolutionary approach on the framework of circular economy applied to agriculture, Agronomy 12(3) (2022), 620.

, Shi

and Chen

, Platform encroachment with price matching: introducing a self-constructing online platform into the sea-cargo market, Computers & Industrial Engineering 156 (2021), 107266.

Xie

, Wang

, Yang

, et al., crowdsourcing: a combined MCDM approach; crowdsourcing: a combined MCDM approach, International Journal of Intelligent Computing and Cybernetics 15(2) (2021), 198–223.

10.

Zhen

and Cheng

, Analysis the development and security policy of third-party online payment platform[C], 2010 3rd International Conference on Computer Science and Information Technology, IEEE 3 (2010), 43–47.

11.

, Shi

and Chen

, Agency encroachment and information sharing: cooperation and competition in freight forwarding market, Maritime Policy & Management 50(3) (2023), 321–334.

12.

Harish

A.R.

, Liu

X.L.

, Zhong

R.Y.

, et al., Log-flock: A blockchain-enabled platform for digital asset valuation and risk assessment in E-commerce logistics financing, Computers & Industrial Engineering 151 (2021), 107001.

13.

C.M.

, Jiang

J.D.

and Zhang

L.B.

, Template-based product information model of small agricultural machinery, Computer Integrated Manufacturing Systems (06) (2008), 1101–1105+1147.

14.

, Limitations and optimization of network platform participating in content governance, Research on Rule of Law (06) (2021), 93–99.

15.

Xia

Y.K.

, Deng

Y.D.

, Pang

, et al., Fresh food vehicle routing problem with split deliveries and customer classification, Computer Integrated Manufacturing Systems 27(04) (2021), 1238–1248.

16.

Zhao

, Cao

B.M.

and Dou

J.P.

, Multi-objective optimal design of agri-food supply chain network based on swarm intelligence, Computer Integrated Manufacturing Systems 21(09) (2015), 2515–2527.

17.

Zan

M.Y.

and Wang

Z.B.

, E-commerce live streaming of agricultural products: a new mode of Poverty Alleviation, Issues in Agricultural Economy (11) (2020), 77–86.

18.

Ren

, Research on the live-streaming operation strategy of agricultural products e-commerce[C], Journal of Physics: Conference Series, IOP Publishing 1992(4) (2021), 042–054.

19.

Wang

and Fang

, Research on the supply chain problems and optimization of live streaming e-commerce, Frontiers in Business, Economics and Management 2(3) (2021), 100–104.

20.

Liu

, The logic, Practical problems and countermeasures of agricultural product supply chain integration from the perspective of live streaming e-commerce, Journal of Commercial Economics (24) (2021), 4.

21.

Yuan

Y.Y.

and Zhang

W.M.

, The dilemma and its solution of rural livestreaming marketing from the perspective of social capital, China Business and Market 35(10) (2021), 74–81.

22.

Cetinkaya

, Özkan

, Özceylan

, et al., An eco-friendly evaluation for locating wheat processing plants: an integrated approach based on interval type-2 fuzzy AHP and COPRAS, Soft Computing 26(9) (2022), 4081–4102.

23.

Yang

, Liang

X.D.

, Li

L.X.

, et al., Risk management and assessment for customer collaborative products innovation realization, Computer Integrated Manufacturing Systems 16(05) (2010), 1020–1025.

24.

Jokar

, Aminnejad

and Lork

, Assessing and prioritizing risks in Public-Private Partnership (PPP) projects using the integration of fuzzy multi-criteria decision-making methods, Operations Research Perspectives 8 (2021), 100190.

25.

Mousavi

S.M.

and Gitinavard

, An extended multi-criteria group decision approach for selection of outsourcing services activities for information technology under risks, International Journal of Applied Decision Sciences 12(3) (2019), 227–241.

26.

Darko

A.P.

and Liang

, Some q-rung orthopair fuzzy hamacher aggregation operators and their application to multiple criteria group decision making with modified EDAS method, Engineering Applications of Artificial Intelligence 87 (2020), 103259.

27.

Chen

S.M.

, Yang

M.W.

, Lee

L.W.

, et al., Fuzzy multiple criteria group decision-making based on ranking interval type-2 fuzzy sets, Expert Systems with Applications An International Journal 39(5) (2012), 5295–5308.

28.

Haiyun

, Zhixiong

, Yüksel

, et al., Analysis of the innovation strategies for green supply chain management in the energy industry using the QFD-based hybrid interval valued intuitionistic fuzzy decision approach, Renewable and Sustainable Energy Reviews 143 (2021), 110844.

29.

Kamal

and Shyi

M.C.

, Multiple criteria group decision making based on advanced linguistic intuitionistic fuzzy weighted averaging aggregation operator of linguistic intuitionistic fuzzy numbers, Information Sciences 587 (2022), 813–824.

30.

Rahman

, Abdullah

, Ali

, et al., Pythagorean fuzzy ordered weighted averaging aggregation operator and their application to multiple criteria group decision-making, EURO Journal on Decision Processes 8(1) (2020), 61–77.

31.

Zhao

, Qin

S.S.

, Xie

J.H.

, et al., Interval-valued intuitionistic fuzzy multi-attribute group decision making considering risk preference of decision maker, Operations Research and Management Science 27(01) (2018), 7–16.

32.

M.X.

, Ming

S.C.

, Yu

J.L.

, et al., A choquet integral based interval type-2 trapezoidal fuzzy multiple criteria group decision making for sustainable supplier selection, Computers & Industrial Engineering 165 (2022), 107935.

33.

You

, Liu

and Sun

, A multi-criteria group decision making method considering both the correlation coefficient and hesitancy degrees under interval-valued intuitionistic fuzzy environment, Applied Soft Computing 104 (2021), 107187.

34.

Huang

L.C.

, Liu

C.W.

, Wu

F.F.

, et al., An improved TOPSIS method based on vertical projection distance of connection vector, Systems Engineering 37(06) (2019), 119–129.

35.

Wang

H.D.

, He

S.F.

, Pan

X.H.

, et al., A new VIKOR method for multi-attribute group decision-making based on game theory weight integration model, Statistics & Decision 35(15) (2019), 39–43.

36.

Peng

, Liu

X.H.

and Sun

J.B.

, Interval-valued intuitionistic fuzzy multi-attribute group decision making approach based on the hesitancy degrees and correlation coefficient, Chinese Journal of Management Science 29(08) (2021), 229–240.

37.

Fang

, Han

and Wen

C.H.

, Probabilistic hesitant fuzzy multi-attribute group decision-making based on new distance measure, Control and Decision 37(03) (2022), 729–736.

38.

Zhang

J.F.

, Zhou

L.G.

and Jin

Z.Q.

, An approach to performance evaluation based on the pythagorean hesitant fuzzy entropy and cross entropy, Journal of Systems Science and Mathematical Sciences 41(02) (2021), 436–448.

39.

P.T.

, Wang

S.Y.

, Li

W.W.

, et al., Expert weighting method based on prior information and one-dimensional data clustering, Operations Research and Management Science 31(03) (2022), 31–37.

40.

Atanassov

, Intuitionistic fuzzy sets, International Journal Bioautomation 20(1) (2016), 1–6.

41.

Atanassov

K.T.

, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets And Systems 64(2) (1994), 159–174.

42.

Z.S.

, Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control and Decision (02) (2007), 215–219.

43.

Hutton

R.J.B.

and Klein

, Expert decision making, Systems Engineering: The Journal of The International Council on Systems Engineering 2(1) (1999), 32–45.

44.

Levy

, Agrawal

, Satyanarayan

, et al., Assessing the impact of automated suggestions on decision making: Domain experts mediate model errors but take less initiative[C], Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems (2021), 1–13.

45.

Zhang

and Wang

, The service quality evaluation of agricultural e-commerce based on interval-valued intuitionistic fuzzy GRA method, Journal of Mathematics (2022), 1–10.

46.

, Xu

, Li

, et al., A Supply Chain Member Selection Method Considering Green Innovation Capability in a Hesitant Fuzzy Environment, Axioms 12(2) (2023), 188.

47.

Chen

, Su

, Wu

, et al., Optimal production and subsidy rate considering dynamic consumer green perception under different government subsidy orientations, Computers & Industrial Engineering 168 (2022), 108073.

48.

Puska

and Stojanović

, Fuzzy multi-criteria analyses on green supplier selection in an agri-food company, Journal of Intelligent Management Decision 1(1) (2022), 2–16.

49.

Sharmaa

, Jain

and Pajni

N.S.

, Risk Identification Techniques in Retail Industry: A case study of Tesco Plc, Journal of Corporate Governance, Insurance, and Risk Management 9 (2022), 201–214.