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 (H m F-sets), which is a reasonable combination of HFSs with m -polar fuzzy sets ( m F 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 m F 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 H m F-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 H m F positive and negative ideal solutions to this framework. We describe applications of H m F-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.