Enhancing multiple attribute group decision making flexibility based on information fusion technique and hesitant Pythagorean fuzzy sets

Abstract

Abstract The aim of this paper is to develop some novel hesitant Pythagorean fuzzy sets (HPFSs) based methods in enhancing fuzzy related problems flexibility. In view of the effectiveness of hesitant fuzzy sets (HFSs) for expressing the hesitant situation, and the powerfulness of Pythagorean fuzzy sets (PFSs) in handling vagueness and uncertainty, we combine the best aspects of HFSs and PFSs and consider a new concept called the HPFSs. Firstly, some existing basic properties and operators are extended and improved in detail. For the sake of application, considering the deficiencies of pessimistic-optimistic normalization principles in dealing with hesitant fuzzy related sets, on the basis of lowest common multiple principle in number theory, an improved normalization algorithm is proposed to reserve the fidelity of original information. Then, a flexible and multipurpose generalized distance measure for HPFSs is presented. Further, under the HPFSs environment, a multiple attribute group decision making method based on the extended hesitant Pythagorean fuzzy VIKOR is presented. Three numerical examples, one from the bidirectional approximate reasoning system and other from the medical diagnosis and selection model of health management center, are presented to elaborate on the performance of our approach and compared their results with the several existing approaches results.