A Class of Nonlinear Fuzzy Variational Inequality Problems
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 establishe...
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| Format: | Article |
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MDPI AG
2019-01-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/7/1/54 |
| _version_ | 1811236423919992832 |
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| author | Cunlin Li Zhifu Jia Yeong-Cheng Liou |
| author_facet | Cunlin Li Zhifu Jia Yeong-Cheng Liou |
| author_sort | Cunlin Li |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T12:08:30Z |
| format | Article |
| id | doaj.art-ed5acb39de5e4042a7ad9f662eda0109 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-12T12:08:30Z |
| publishDate | 2019-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ed5acb39de5e4042a7ad9f662eda01092022-12-22T03:33:39ZengMDPI AGMathematics2227-73902019-01-01715410.3390/math7010054math7010054A Class of Nonlinear Fuzzy Variational Inequality ProblemsCunlin Li0Zhifu Jia1Yeong-Cheng Liou2School of Management, Ningxia Key Laboratory of intelligent information and Big Data Processing, North Minzu University, Yinchuan 750021, ChinaSchool of Mathematics and Information Science, Ningxia Collaborative Innovation Center of Scientific Computation and Intelligent Information Processing, North Minzu University, Yinchuan 750021, ChinaDepartment of Healthcare Administration and Medical Informatics, and Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, TaiwanIn 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.http://www.mdpi.com/2227-7390/7/1/54fuzzy variational inequalitiesfuzzy set theoryexpected residual functionsSC1 property of FERM modelcompact approximations |
| spellingShingle | Cunlin Li Zhifu Jia Yeong-Cheng Liou A Class of Nonlinear Fuzzy Variational Inequality Problems Mathematics fuzzy variational inequalities fuzzy set theory expected residual functions SC1 property of FERM model compact approximations |
| title | A Class of Nonlinear Fuzzy Variational Inequality Problems |
| title_full | A Class of Nonlinear Fuzzy Variational Inequality Problems |
| title_fullStr | A Class of Nonlinear Fuzzy Variational Inequality Problems |
| title_full_unstemmed | A Class of Nonlinear Fuzzy Variational Inequality Problems |
| title_short | A Class of Nonlinear Fuzzy Variational Inequality Problems |
| title_sort | class of nonlinear fuzzy variational inequality problems |
| topic | fuzzy variational inequalities fuzzy set theory expected residual functions SC1 property of FERM model compact approximations |
| url | http://www.mdpi.com/2227-7390/7/1/54 |
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