Optimization of fuzzy-valued functions using Zadeh's extension principle

摘要

This paper proposes a fuzzy optimization problem whose objective function is Zadeh's extension of a function with respect to a parameter and the independent variable. Making use of a partial order relation, the extension of a function mapping each parameter to the corresponding local minimizing point is proven to provide the local smallest fuzzy value for the extended function. Deploying the usual order relation in the literature, the same point is proven to provide the minimal value for the function. Examples illustrate the results. (C) 2020 Elsevier B.V. All rights reserved.