Solutions to fuzzy variational problems: necessary and sufficient conditions
by Mohammad Heidari; Mohadeseh Ramezanzadeh; Akbar Hashemi Borzabadi; Omid Solaymani Fard
International Journal of Modelling, Identification and Control (IJMIC), Vol. 28, No. 2, 2017

Abstract: The aim of this study is to investigate the necessary and sufficient conditions for fuzzy variational problems. To this purpose, based on a parametric representation for the α-level set of a fuzzy valued function, the fuzzy variational problems are converted to general variational problems in a parametric form. The Euler-Lagrange equations as necessary optimality conditions are derived, and then the solutions of these equations lead to the construction of the α-level sets of fuzzy extremal solutions for the original problems. Moreover, a sufficient condition under an appropriate convexity assumption is discussed for fuzzy variational problems. Using an example, the effectiveness of the proposed technique is discussed by comparing with the results of the given approaches in Fard et al. (2014) and Farhadinia (2011).

Online publication date: Fri, 18-Aug-2017

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