A similarity-based three-way multiattribute decision model under constrained Pythagorean fuzzy environment

A variety of fuzzy sets, especially Pythagorean fuzzy sets (PFSs), are commonly utilized to describe the ambiguity of information in three-way decision (3WD) models. PFSs can handle fuzzy information well but ignore the description of stochastic information. To address this issue, in this paper, we attempt to construct a novel three-way multiattribute decision model by combining 3WD with constrained Pythagorean fuzzy sets (CPFSs) which can measure the reliability of PFSs. Firstly, we introduce the concept of constrained Pythagorean fuzzy information systems (CPFISs). Comprehensive positive and negative similarities of objects are given in a CPFIS by introducing normalization, score function, comparison rules, and positive and negative ideal solutions. Secondly, by comprehensive positive and negative similarities, novel formulas for calculating comprehensive relative utility function values are obtained and an objective method for estimating conditional probabilities is presented in the absence of decision attributes. Based on the above knowledge, we establish a similarity -based three-way multiattribute decision model in a CPFIS. Furthermore, we conduct a case analysis of appendicitis to realize the application of our proposed model and several comparative analyses to demonstrate the effectiveness and superiority of our model. Finally, the good performance of the new model is verified through experimental analyses.