ABSTRACT
The concepts of fuzzy mappings and fuzzy models play an important role in several areas of modern research such as finance (Verdegay [278]; Buckley [30]; Fedrizzi et al. [79]), networking and transportation (Jimnez and Verdegay [120] and Moreno et al. [208]), interest rate forecasting (Maciel et al. [174]), and ecological models (Mouton et al. [209]). The concept of fuzzy mapping has been introduced by Chang and Zadeh [42]. Nanda and Kar [212] introduced the concept of convex fuzzy mapping and established that fuzzy mapping is convex if and only if its epigraph is convex. Since then, generalized convexity of fuzzy mapping has been extensively studied. Syau [265] introduced the concepts of pseudoconvexity, invexity, and pseudoinvexity for fuzzy mappings of one variable by using the notion of differentiability and the results proposed by Goestschel and Voxman [93]. Panigrahi [218] employed Buckley-Feuring’s [31] approach for fuzzy differentiations to extend and generalize these notions to fuzzy mappings of several variables. Wu and Xu [286] introduced the concept of fuzzy pseudoconvex, fuzzy invex, fuzzy pseudoinvex, and fuzzy preinvex mappings from Rn to the set of fuzzy numbers by employing the concept of differentiability of fuzzy mappings defined by Wang and Wu [279]. Moreover, Mishra et al. [204] introduced the concept of pseudolinear fuzzy mappings by relaxing the definition of pseudoconvex fuzzy mappings. The concept of η-pseudolinear fuzzy mappings is also introduced by relaxing the definition of pseudoinvex fuzzy mappings. By means of the basic properties of pseudolinear fuzzy mappings, the solution set of a pseudolinear fuzzy program is characterized. Then, characterizations of the solution set of an η-pseudolinear program are also derived.
