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A Class of Nonlinear Fuzzy Variational Inequality Problems

Author

Listed:
  • Cunlin Li

    (School of Management, Ningxia Key Laboratory of intelligent information and Big Data Processing, North Minzu University, Yinchuan 750021, China)

  • Zhifu Jia

    (School of Mathematics and Information Science, Ningxia Collaborative Innovation Center of Scientific Computation and Intelligent Information Processing, North Minzu University, Yinchuan 750021, China)

  • Yeong-Cheng Liou

    (Department of Healthcare Administration and Medical Informatics, and Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan
    Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 807, Taiwan)

Abstract

In this paper, we consider nonlinear variational inequality problems with fuzzy variables. The fuzzy variables were introduced to deal with the variational inequality containing noise for which historical data is not available. The fuzzy expected residual minimization (FERM) problems were established. We discussed the S C 1 property of the FERM model. Furthermore, results of convergence analysis were obtained based on an approximation model of the FERM model. The convergence of global optimal solutions and the convergence of stationary points were analysed.

Suggested Citation

  • Cunlin Li & Zhifu Jia & Yeong-Cheng Liou, 2019. "A Class of Nonlinear Fuzzy Variational Inequality Problems," Mathematics, MDPI, vol. 7(1), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:54-:d:195463
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    References listed on IDEAS

    as
    1. Paolo Cubiotti & Jen-Chih Yao, 1997. "Discontinuous implicit quasi-variational inequalities with applications to fuzzy mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 213-228, June.
    2. Zezhong Wu & Jiuping Xu, 2013. "A Class of Fuzzy Variational Inequality Based on Monotonicity of Fuzzy Mappings," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-17, November.
    3. Hsiao-Fan Wang & Hsueh-Ling Liao, 1998. "Fuzzy resolution on the infeasibility of variational inequality," European Journal of Operational Research, Elsevier, vol. 106(1), pages 198-203, April.
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