Marko Antonio Rojas-Medar

Embedding of level-continuous fuzzy sets on Banach spaces☆

In this paper we present an extension of the Minkowski embedding theorem, showing the existence of an isometric embedding between the class Fc(X) of compact-convex and level-continuous fuzzy sets on a real separable Banach space X and C([0,1]×B(X∗)), the Banach space of real continuous functions defined on the cartesian product between [0,1] and the unit ball B(X∗) in the dual space X∗. Also, by using this embedding, we give some applications to the characterization of relatively compact subsets of Fc(X). In particular, an Ascoli–Arzela type theorem is proved and applied to solving the Cauchy problem x(t)=f(t,x(t)), x(t0)=x0 on Fc(X).

Magneto-micropolar fluid motion: global existence of strong solutions

By using the spectral Galerkin method, we prove a result on global existence in time of strong solutions for the motion of magneto-micropolar fluid without assuming that the external forces decay with time. We also derive uniform in time estimates of the solution that are useful for obtaining error bounds for the approximate solutions.

A generalization of the Minkowski embedding theorem and applications

Abstract Puri and Ralescu (1985) gave, recently, an extension of the Minkowski Embedding Theorem for the class ELn of fuzzy sets u on Rn with the level application α → Lαu Lipschitzian on the C([0, 1] x Sn−1) space. In this work we extend the above result to the class ECn of level-continuous applications. Moreover, we prove that ECn is a complete metric space with E L n /nb E C n and E L n = E C n To prove the last result, we use the multivalued Bernstein polynomials and the Vitalis approximation theorem for multifunction. Also, we deduce some properties in the setting of fuzzy random variable (multivalued).

On the equivalence of convergences of fuzzy sets

Abstract The aim of this paper is to compare D, H and L-convergences with the variational covergence. Our analysis, which is carried out in ®″, is made through the introduction of the space ϵc″ of compact fuzzy sets u on ®″, for which the level function α ∃ [0, 1] → L, μ ∃ Π K (ϵ″) is continuous. We prove that in this space all the above notions of convergence are equivalent.

The extension principle and a decomposition of fuzzy sets

We give an algorithm to decompose a fuzzy interval u. Using this decomposition and the multilinearization of a univariate function f, we obtain an approximation of the fuzzy interval , where is obtained from f by applying the extension principle. We provide approximation bounds. Some numeric illustration is provided.

On the level-continuity of fuzzy integrals

In this paper we define the level-convergence of measurable functions on a fuzzy measure space, by using the closure operator in the Moore sense. We study some of the properties of this convergence and give conditions for the continuity of the fuzzy integral in relation to the level-convergence.

Optimality conditions for Pareto nonsmooth nonconvex programming in Banach spaces

In this paper, we consider a vector optimization problem where all functions involved are defined on Banach spaces. We obtain necessary and sufficient criteria for optimality in the form of Karush–Kuhn–Tucker conditions. We also introduce a nonsmooth dual problem and provide duality theorems.

On the approximate controllability of Stackelberg-Nash strategies for Stokes equations

Abstract. We study a Stackelberg strategy subject to the evolutionary Stokes equations, considering a Nash multi-objective equilibrium (not necessarily cooperative) for the “follower players” (as they are called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following three main results: the existence and uniqueness of the Nash equilibrium and its characterization, the approximate controllability of the Stokes system with respect to the leader control and the associate Nash equilibrium, and the existence and uniqueness of the Stackelberg-Nash problem and its characterization.

Fuzzy quasilinear spaces and applications

We introduce the concept of fuzzy quasilinear space and fuzzy quasilinear operator. Moreover we state some properties and give results which extend to the fuzzy context some results of linear functional analysis.

Nonsmooth continuous-time optimization problems: necessary conditions☆

Abstract We consider Lipschitz continuous-time nonlinear optimization problems and provide first-order necessary optimality conditions of both Fritz John and Karush-Kuhn-Tucker types.