Research on Hybrid Multi-Attribute Three-Way Group Decision Making Based on Improved VIKOR Model

Abstract

In the era of internet connection and IOT, data-driven decision-making has become a new trend of decision-making and shows the characteristics of multi-granularity. Because three-way decision-making considers the uncertainty of decision-making for complex problems and the cost sensitivity of classification, it is becoming an important branch of modern decision-making. In practice, decision-making problems usually have the characteristics of hybrid multi-attributes, which can be expressed in the forms of real numbers, interval numbers, fuzzy numbers, intuitionistic fuzzy numbers and interval-valued intuitionistic fuzzy numbers (IVIFNs). Since other forms can be regarded as special forms of IVIFNs, transforming all forms into IVIFNs can minimize information distortion and effectively set expert weights and attribute weights. We propose a hybrid multi-attribute three-way group decision-making method and give detailed steps. Firstly, we transform all attribute values of each expert into IVIFNs. Secondly, we determine expert weights based on interval-valued intuitionistic fuzzy entropy and cross-entropy and use interval-valued intuitionistic fuzzy weighted average operator to obtain a group comprehensive evaluation matrix. Thirdly, we determine the weights of each attribute based on interval-valued intuitionistic fuzzy entropy and use the VIKOR method improved by grey correlation analysis to determine the conditional probability. Fourthly, based on the risk loss matrix expressed by IVIFNs, we use the optimization method to determine the decision threshold and give the classification rules of the three-way decisions. Finally, an example verifies the feasibility of the hybrid multi-attribute three-way group decision-making method, which provides a systematic and standard solution for this kind of decision-making problem.

Three-way decisions in generalized intuitionistic fuzzy environments: survey and challenges

“…( 2022a ) IF information system Song et al. ( 2022 ) Hybrid multi-attribute information system Yi et al. ( 2022 ) PF information system Liang et al.…”

“…* The relative loss function is calculated in light of the evaluation value, which reduces the decision risk of subjective loss functions * By converting IF numbers into fuzzy numbers and obtaining the relative loss function, this method focuses on processing fuzzy numbers in the model Song et al. ( 2022 ) * The hybrid multi-attribute environment is more compatible with real-life situations and has greater versatility. * Determining expert weights from the perspectives of IVIF entropy and cross-entropy is a more reasonable and objective approach.…”

“…Song et al. ( 2022 ) used the VIKOR method for grey correlation analysis to confirm the conditional probability in a mixed MAGDM problem. Dai et al ( 2023 ) created a new IF loss function based on IF concepts.…”

“…Song et al. ( 2022 ) studied a hybrid MAGDM method. First, attribute values of different forms were converted into the IVIF number form with minimum information distortion, and then expert weights were computed by using IVIF entropy and cross-entropy to create a group comprehensive evaluation matrix.…”

“…However, when assigning attribute weight, To make accurate evaluations, it is imperative to consider both the attributes’ internal connections and the experts’ level of authority (Song et al. 2022 ). Therefore, in order to obtain reasonable attribute weights, some researchers combine subjective empowerment methods and objective weighting methods to determine attribute weights, and then make up for the shortcomings caused by single empowerment.…”