Heterogeneous multi-attribute nonadditivity fusion for behavioral three-way decisions in interval type-2 fuzzy environment

Abstract

Uncertainty and complexity can cause an increasingly risk impact on our decision-making processes. Different from two-way decisions, three-way decisions can effectively reduce the decision risk by adopting a new delayed decision. However, when different decision makers face the decision risks, they may have different behaviors and attitudes in the actual decision-making process. Considering this phenomenon, we introduce prospect theory into three-way decisions and propose behavioral three-way decisions under interval type-2 fuzzy environment. In this scenario, we utilize prospect theory to describe decision makers’ risk attitude. In this paper, we firstly construct the relative loss function and relative benefit function that learn from single interval type-2 fuzzy attribute information with attribute aspiration in advance and then establish behavioral three-way decisions based on Bayesian decision procedure. In this case, we discuss five cases of the attribute aspirations, respectively. Subsequently, we apply behavioral three-way decisions model into multi-attribute decision-making (MADM) problem. In order to deal with interactions between attributes under interval type-2 fuzzy environment, a nonadditivity fusion of heterogeneous multi-attribute behavioral three-way decisions is constructed with 2-additive Choquet integral (TAC). The nonadditivity fusion of heterogeneous multi-attribute behavioral three-way decisions can process the decision information more comprehensively and take into account the decision makers’ attitudes towards risks. Finally, a decision-making problem of distinctive street identification of Chengdu is used to prove the validity of our method.