Preinvexity of $ n $-dimensional fuzzy number-valued functions: characterization, variational inequality and optimization problems

Zengtai Gong; Han Gao; Ting Xie; Zengtai Gong; Han Gao; Ting Xie

doi:10.3934/math.2022340

AIMS Mathematics

2022, Volume 7, Issue 4: 6099-6127. doi: 10.3934/math.2022340

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Research article

Preinvexity of $ n $-dimensional fuzzy number-valued functions: characterization, variational inequality and optimization problems

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2.
Group of Mathematics, The Fifth Primary School of Chang'an District, Xi'an 710000, China
3.
College of Social Development and Public Administration, Northwest Normal University, Lanzhou 730070, China

Received: 13 September 2021 Revised: 27 December 2021 Accepted: 11 January 2022 Published: 17 January 2022
MSC : 26E50, 28E10

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.
- fuzzy numbers,
- invex set,
- preinvexity fuzzy number-valued functions
Citation: Zengtai Gong, Han Gao, Ting Xie. Preinvexity of $ n $-dimensional fuzzy number-valued functions: characterization, variational inequality and optimization problems[J]. AIMS Mathematics, 2022, 7(4): 6099-6127. doi: 10.3934/math.2022340

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Abstract

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.

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