linear fractional programming problem in hesitant fuzzy environment

In recent years, the hesitant fuzzy set as a proper generalization of the fuzzy set theory, which can imply in situations that the decision maker hesitates in determining the membership of parameters, has been introduced. several applications of such sets have been revealed in the multi-criteria decision-making, graph theory and clustering methods, but there is little research on hesitant fuzzy programming problems and solving process for them in the literature. however, recently some research has been carried out in the field of linear programming under hesitant fuzzy information. however, less research can be found that has developed this perspective in nonlinear mode and especially for linear fractional programming under hesitant fuzzy data. hence, our main focus is to propose the modeling of the linear fractional programming problem with hesitant fuzzy parameters along with the introduction of a method to solve this type of structure. for this aim, two kinds of linear fractional programming with hesitancy in different values are introduced. then, a novel method is suggested to determine the optimal solutions for them. some numerical examples show the reliability and validity of the models.