Symmetric and Right-Hand-Side Hesitant Fuzzy Linear Programming

Fuzzy set theory has been extensively employed in mathematical programming, especially in linear programming problems. As a generalization of fuzzy sets, a hesitant fuzzy set is a very useful tool in places where there are some hesitations in determining the membership of an element to a set. There are few studies on hesitant fuzzy linear programming problems; therefore, in this paper, we have studied such problems. For this purpose, at first, the motivation of this paper is explained; then, types of hesitant fuzzy linear programming models are introduced. Since it is not easy to examine all of the hesitant fuzzy models for the linear programming problems in one paper, we have restricted ourselves to symmetric and right-hand-side hesitant fuzzy linear programming problems with the flexible approach and then proposed two new approaches to solve them. Finally, to illustrate the applicability of the proposed approaches, three examples under hesitant fuzzy information are given.