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A Class of Fuzzy Variational Inequality Based on Monotonicity of Fuzzy Mappings

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  • Zezhong Wu
  • Jiuping Xu

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.

Suggested Citation

  • Zezhong Wu & Jiuping Xu, 2013. "A Class of Fuzzy Variational Inequality Based on Monotonicity of Fuzzy Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:854751
    DOI: 10.1155/2013/854751
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    References listed on IDEAS

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    1. X. Q. Yang & C. J. Goh, 1997. "On Vector Variational Inequalities: Application to Vector Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 431-443, November.
    2. X. Q. Yang, 1997. "Vector Variational Inequality and Vector Pseudolinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 729-734, December.
    3. K. L. Lin & D. P. Yang & J. C. Yao, 1997. "Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 117-125, January.
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