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Discussion on Optimality Conditions of Fuzzy Optimal Control Problems

In this study, a novel methodology for detecting fuzzy optimal solutions of fuzzy optimal control problems governed by fuzzy differential equations is presented. For this purpose, first the concept of optimal solution is proposed by considering a partial ordering on fuzzy numbers space which is based on a new parametric representation for α-level set of fuzzy numbers. Using this partial ordering and parametric representation, the discussed fuzzy optimal control problems are reduced to general optimal control problems in parametric form. Then by Pontryagin’s principle, a candidate for the solution of the original problem is derived. The procedure of extracting candidate solution is illustrated for two experimental problems, which improve the recent results of Refs. 10 and 17.