Open AccessPreinvexity of $ n $-dimensional fuzzy number-valued functions: characterization, variational inequality and optimization problems
Author(s) -
Zengtai Gong,
AUTHOR_ID,
Han Gao,
Ting Xie,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022340
Subject(s) - mathematics , fuzzy logic , counterexample , characterization (materials science) , combinatorics , discrete mathematics , computer science , materials science , nanotechnology , artificial intelligence
In this paper, the preinvexity of n -dimensional fuzzy number-valued functions are defined and discussed by means of the partial order relation in n -dimensional fuzzy number space which including preinvexity, weak preinvexity, strict preinvexity, weakly strict preinvexity, prequasiinvexity, weak prequasiinvexity, strict prequasiinvexity, weakly strict prequasiinvexity, and so on. In addition, their interrelations of the preinvexity of n -dimensional fuzzy number-valued functions are discussed, and some counterexamples are given. Furthermore, the two-parameter optimization problem, $ n $-dimensional fuzzy variational-like inequality and optimality conditions related to $ n $-dimensional preinvex fuzzy number-valued functions are discussed.