Abstract
Invex monotonicity and pseudoinvex monotonicity of fuzzy mappings are introduced in this paper, and relations are discussed between invex monotonicity (pseudoinvex monotonicity) and invexity (pseudoinvexity) of fuzzy mappings. The existence of a solution to the fuzzy variational-like inequality is discussed, and the existence theorem can be achieved. Furthermore, some extended properties of the fuzzy variational-like inequality are researched. Finally, method of solution is discussed based on genetic algorithm.
Highlights
In [1], Chang and Zadeh introduced the concept of fuzzy mapping
We study invex monotonicity and pseudoinvex monotonicity of fuzzy mappings and discuss relations between invex monotonicity and invexity of fuzzy mappings
A well-known fact in mathematical programming is that the variational inequality problem has a close relationship with the optimization problem
Summary
Invex monotonicity and pseudoinvex monotonicity of fuzzy mappings are introduced in this paper, and relations are discussed between invex monotonicity (pseudoinvex monotonicity) and invexity (pseudoinvexity) of fuzzy mappings. The existence of a solution to the fuzzy variational-like inequality is discussed, and the existence theorem can be achieved. Some extended properties of the fuzzy variational-like inequality are researched. Method of solution is discussed based on genetic algorithm
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