Introducing hesitant fuzzy equations and determining market equilibrium price

A vast majority of research has been performed in the field of hesitant fuzzy sets (HFSs), involving the introduction of some properties, operations, relations and modifications of such sets or considering the application of HFSs in MCDM (multicriteria decision making). On the other hand, no research has been performed in the field of fully hesitant fuzzy equations. Therefore, in this paper, fully hesitant fuzzy equations and dual hesitant fuzzy equations are introduced. First, a method is proposed to solve one-element hesitant fuzzy equations. Then, the proposed method is extended to solve n-element hesitant fuzzy equations effectively. Moreover, to show the applicability of the proposed method, it is used to solve a real world problem. Thus, the proposed method is applied to determine market equilibrium price. Also, some other numerical examples are presented to better show the performance of the proposed method.