A three-way decision approach with prospect-regret theory via fuzzy set pair dominance degrees for incomplete information systems

Abstract

The generalized three-way decision (G3WD) theory is featured by a trisecting-acting-outcome paradigm. Experiments in psychology and economics have indicated that risky decision-making problems should take into account the psychological characteristic of agents. Moreover, the loss of information acts as a serious challenge in G3WD. Thus, exploring valid G3WD approaches that consider the mental state of decision-makers in incomplete information systems (IISs) is imperative. This paper explores a new three-way decision (3WD) approach that combines the prospect theory with the regret theory for IISs with the support of fuzzy set pair dominance degrees. First, the notion of fuzzy set pair dominance degrees to process evaluation information in IISs is put forward. Then, an approach that obtains objective reference points and determines the weighting function in the prospect theory is given by combining 3WD with the behavioral decision theory. In light of the prospect theory, a prospect value function is obtained, which is introduced into the regret theory to obtain two utility perception functions. As a consequence, a G3WD approach based on fuzzy set pair dominance degrees and the behavioral decision theory is constructed for IISs. By using two medical cases in the KEEL and UCI datasets, the superiority, effectiveness and stability of the constructed approach are verified via corresponding comparative and experimental analyses.