Novel TOPSIS method for group decision-making based on hesitant m-polar fuzzy model

Hesitant fuzzy sets (HFSs) present a general structure to express the uncertain concepts and data that have been served as in most of the generalizations of fuzzy sets. In this research article, we introduce a novel hybrid model called hesitant m-polar fuzzy sets (HmF-sets), which is a reasonable combination of HFSs with m-polar fuzzy sets (mF sets). It is the generalization of the concept HFSs, in which the membership degrees of an element of given set deals the m different numeric and fuzzy values that enables to deal the hesitancy of multipolar information. Hesitancy integrates the conformity for the analysis of given data, and an mF format concedes to severalize the sources of multi-polar information. We highlight and explore some useful properties, construct fundamental operations and investigate comparison laws of HmF-sets. Moreover, we develop the hesitant m-polar fuzzy TOPSIS approach for multi-criteria group decision-making (MCGDM), which is the natural extension of TOPSIS method and used to rank and choose the best alternative under HmF positive and negative ideal solutions to this framework. We describe applications of HmF-sets in group decision-making and apply our proposed method in real life examples to show its efficiency. Finally, we develop an algorithm that implements our decision-making procedure by using computer programming.