Title: Solutions to fuzzy variational problems: necessary and sufficient conditions
Authors: Mohammad Heidari; Mohadeseh Ramezanzadeh; Akbar Hashemi Borzabadi; Omid Solaymani Fard
Addresses: School of Mathematics and Computer Science, Damghan University, Damghan, Iran ' School of Mathematics and Computer Science, Damghan University, Damghan, Iran ' School of Mathematics and Computer Science, Damghan University, Damghan, Iran ' School of Mathematics and Computer Science, Damghan University, Damghan, Iran
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).
Keywords: fuzzy valued functions; fuzzy variational problems; fuzzy isoperimetric problems; necessary and sufficient conditions.
DOI: 10.1504/IJMIC.2017.085948
International Journal of Modelling, Identification and Control, 2017 Vol.28 No.2, pp.187 - 198
Received: 18 May 2016
Accepted: 31 Oct 2016
Published online: 18 Aug 2017 *