Optimality conditions for fuzzy constrained programming problems

Triangular Norm based Invex Fuzzy Sets

“…In resent years, convex functions and invex functions have been generalized to fuzzy case by many scholars , for example, authors in [1], [2], [4], [6], [10][11][12][13], [17], [18], [20], [26] have studied generalized convex fuzzy mapping According to these results, fuzzy convex functions and fuzzy invex functions are :…”

Study on Generalized Directional Differentiability Problems of Fuzzy Mappings

“…Meanwhile, they put forward a new and feasible method for studying the differentiability of fuzzy mappings and its application. Since then, many scholars have studied the gH-differentiability and application of fuzzy mappings, and obtained a series of valuable results [3][4][5][6][7][8][9][10][11].…”

“…In reference [13] and [14], we discussed respectively the differentiability (Hdifferentiability) and application in fuzzy programming for fuzzy mappings and the gH-directional differentiability of interval-valued mappings and so on, in the meantime, some important conclusions are obtained. On this basis, in the first section of this article, the concepts of gH-differentiability, gH-derivative, gH-partial derivative of fuzzy mappings and the concept and related properties of gH-differentiability of interval-valued mappings are given in references [3,10,14]. In Section 2, the problem of gH-directional differentiability of fuzzy mappings is discussed.…”

“…In Section 2, the problem of gH-directional differentiability of fuzzy mappings is discussed. Using the concept of gH-directional differentiability and related properties of interval-valued mappings [14], the relevant properties of gH-directional differentiability fuzzy mappings are given; And gH-directional derivative are used to characterize gH-derivative [3], gH-partial derivative [10] and gH-gradient [10].…”

Integrated Planning for Regional Electric Power System Management with Risk Measure and Carbon Emission Constraints: A Case Study of the Xinjiang Uygur Autonomous Region, China

“…Büyüközkan and Güleryüz established an evaluation model to select the most appropriate renewable energy resources in Turkey [23]. Osuna-Gómez et al solved optimization problems where both the objective and constraints are given by fuzzy functions [24].…”