On the Newton method for solving fuzzy optimization problems

In this article we consider optimization problems where the objectives are fuzzy functions (fuzzy-valued functions). For this class of fuzzy optimization problems we discuss the Newton method to find a non-dominated solution. For this purpose, we use the generalized Hukuhara differentiability notion, which is the most general concept of existing differentiability for fuzzy functions. This work improves and correct the Newton Method previously proposed in the literature.Fondo Nacional de Desarrollo Científico y Tecnológico (Chile)Ministerio de Ciencia y TecnologíaConselho Nacional de Desenvolvimento Científico e Tecnológico (Brasil)Centro de Pesquisa em Matemática Aplicada à Indústria (Fundação de Amparo à Pesquisa do Estado de São Paulo

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Applied Mathematics', ISSN: 0377-0427. Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication 20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515

Some remarks on optimality conditions for fuzzy optimization problems

In this article we present a new concept of stationary point for gH-differentiable fuzzy functions which generalize previous concepts that exist in the literature. Also, we give a concept of generalized convexity for gH-differentiable fuzzy functions more useful than level-wise generalized convexity (generalized convexity of the endpoint functions). Then we give optimatily conditions for fuzzy optimization problems.En este artículo presentamos un nuevo concepto de punto estacionario para funciones difusas gHdiferenciables que generalizan los conceptos previos que existen en la literatura. También damos un concepto de convexidad generalizada para funciones difusas gH-diferenciables más útil que los basados en las funciones extremos. A partir de esos conceptos, damos condiciones de optimalidad para problemas de optimización difusos.Fondo Nacional de Desarrollo Científico y Tecnológico (Chile)Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo Regiona

Necessary and sufficient conditions for interval-valued differentiability

This paper presents necessary and sufficient conditions for generalized Hukuhara differentiability of interval-valued functions and counterexamples of some equivalences previously presented in the literature, for which important results are based on. Moreover, applications of interval generalized Hukuhara differentiability are presented