Tri-reference point method for [formula omitted]-rung orthopair fuzzy multiple attribute decision making by considering the interaction of attributes with Bayesian network

Abstract

As an irrational behavior theory, the tri-reference point (TRP) method proposed by combining multiple reference points and practical scenarios can consider more complex and realistic scenarios. In order to explore the application of TRP under q-rung orthopair fuzzy (q-ROF) environment, we construct a new TRP model and solve the multi-attribute decision making (MADM) problem with Bayesian network (BN). More specifically, considering that BN can automatically learn the relationship of attributes from both the direction of influence and the degree of interaction, we firstly introduce the BN into q-ROF environment to depict the interaction between attributes in a MADM. BN can deduce posterior probability according to the prior knowledge, so it can calculate the probabilities of attributes for a MADM problem under q-ROF environment. Based on their probabilities, we further propose an improved Borda score method to calculate the attributes weights. Then, inspired by prospect theory, we develop a new TRP model by utilizing the double-S shape of TRP. Meanwhile, a novel comparison method for two q-rung orthopair fuzzy numbers (q-ROFNs) is presented which combines possibility degree method and score function. Finally, we give an example of land investment project selection of rural cooperative to elaborate and verify our proposed method.