Fuzzy preinvexity via ranking value functions with applications to fuzzy optimization problems

Abstract

Abstract In this paper, we aim to establish some important properties about preinvex and quasi preinvex fuzzy mappings based on ranking value function of fuzzy numbers proposed by Syau and Lee. We provide characterizations of preinvex and quasi preinvex fuzzy mappings in terms of ranking values function. Other characterizations of preinvex and quasi preinvex fuzzy mappings in terms of, respectively, the invexity of the epigraph and the lower level of the above two fuzzy mappings are proved. Some further properties for preinvex and quasi preinvex fuzzy mappings are derived. Finally, as applications to fuzzy optimization problems in which the objective fuzzy mappings are either preinvex or quasi preinvex, some optimality properties are shown. The above-mentioned results are proved using ranking value function of fuzzy numbers.