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In this work we study optimization problems where both objective and constraints are given by fuzzy functions. In order to solve them, we first prove that such problems are equivalent to fuzzy optimization problems where the constraints are non-fuzzy (crisp) functions. Besides we prove a new and appropriate Karush-Kuhn-Tucker type necessary optimality condition based on the gH-differentiability and...
In this article we deal with the algebra of generalized Hukuhara differentiable fuzzy functions (gH-differentiable fuzzy functions, for short). We show that the sum and the gH-difference of two gH-differentiable fuzzy functions are not necessarily gH-differentiable. Then we give conditions on the two fuzzy functions so that the sum and the gH-difference of these to be gH-differentiable. Moreover we...
This article analyzes the quotient space of compact intervals of ℝ with respect to the family of symmetric intervals. We analyze some algebraic and topological properties of this quotient space. Since the space of compact intervals can be embed on this quotient space, we introduce a concept of differentiability for interval-valued functions and then, we make a comparison with other concepts of differentiability...
Let I = [a, b] a real compact interval and ƒ ∶ I → I a continuous function. Define Kc([a, b]) the class of all non empty compact subinterval of [a, b] and let ƒ̄c the natural extension of ƒ to Kc([a, b]), that is to say, ƒ̄c(J) = ƒ(J) for all J ∈ Kc([a, b]). Also, let Fc([a, b]) the class of all fuzzy-intervals with support contained in [a, b] and consider ƒ̂c the Zadeh's extension of ƒ to Fc([a,...
The present article presents new Ostrowski type inequalities for generalized Hukuhara differentible fuzzy-valued functions. As a consequence of this inequalities we present an error estimation to Riemann-type quadrature rule for fuzzy-valued functions.
In this paper we consider optimization problems with fuzzy-valued objective function. For this class of fuzzy optimization problems we obtain Karush-Kuhn-Tucker type optimality conditions considering the concept of strongly generalized differentiable fuzzy-valued functions.
In this article we show the importance of the class of fuzzy differential equations where the right hand side of the equation is a fuzzy function generated by applying Zadeh's extension principle. Through concrete examples, we show that fuzzy functions obtained by applying Zadeh's extension principle are more appropriate than fuzzy functions obtained by using the usual fuzzy interval arithmetic (R...
In this article we present different approaches to the difference of two intervals and its application to differentiability of interval-valued functions. Also, we show the relationship between some definitions of derivative for interval-valued functions.
In this paper we present an approximation for a compact fuzzy set by a sequence of Lipschitz fuzzy sets. For this, given a compact fuzzy set, we construct a sequence of Lipschitz fuzzy sets using the sup-min-convolution which converge in D-metric to the compact fuzzy set original. The results obtained in this paper are a generalization of previous result obtained by the authors.
Let (X, d) be a metric space and f : X rarr X a continuous function. If we consider the space (K(X),H) of all nonempty compact subsets of X endowed with the Hausdorff metric H induced by d, and f macr : K(X) rarr K(X) the natural extension of f to K(X) defined by f(A) = {f(alpha)/alpha isin A}, then the aim of this work is to connect the periodic density of f on X with the periodic density of f restricted...
In this paper we study fuzzy differential equations with generalized derivative. We obtain some properties of the generalized derivative. We discuss the equivalence of the fuzzy Cauchy problem and an Aumann-type integral equation. This study also makes some observations on the existence of solutions.
In this paper we study fuzzy differential equations with generalized derivative. We obtain some properties of the generalized derivative. We discuss the equivalenc of the fuzzy Cauchy problem and an Aumann-type integral equation. This study also makes some observations on the existence of solutions.
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