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.
Highlights
In many real-world problems, examples contain some uncertain information, with examples including new stock, emergencies, military experiments, etc
A fuzzy number is a kind of special fuzzy set and its operation was a key factor in processing fuzzy information
Let us recall that the fuzzy variational inequality problem is to find x ∈ S ⊂ Rn satisfying ( x − x )T F ( x, ξ ) ≥ 0 ∀ x ∈ S, a.s
Summary
School of Mathematics and Information Science, Ningxia Collaborative Innovation Center of Scientific Department of Healthcare Administration and Medical Informatics, and Research Center of Nonlinear Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 807, Taiwan
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