Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)
Session: S16: Fuzzy Numbers and their Applications
8 articles
Proceedings Article
Approximation of fuzzy numbers by nonlinear Bernstein operators of max-product kind
Lucian Coroianu, Sorin G. Gal, Barnabas Bede
In this paper firstly we extend from [0, 1] to an arbitrary compact interval [a, b], the definition of the nonlinear Bernstein operators of max-product kind, B (M) n (f), n N, by proving that their order of uniform approximation to f is 1(f, 1/
Proceedings Article
Translation invariance and scale invariance of approximations of fuzzy numbers
Adrian Ban, Lucian Coroianu
We give some sufficient conditions such that a crisp, interval, triangular, trapezoidal, parametric approximation of a fuzzy number, with or without additional requirements, to have the properties of invariance to translations or scale invariance.
Proceedings Article
Trapezoidal approximations of fuzzy numbers with restrictions on the support and core
Przemyslaw Grzegorzewski, Karolina Pasternak-Winiarska
Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. New operators that fulfill additional requirements for the core and support of the fuzzy number are suggested. These supplementary conditions guarantee the proper interpretation of the solution...
Proceedings Article
Model Inversion using Extended Gradual Intervals Arithmetic
Reda Boukezzoula, Laurent Foulloy, Sylvie Galichet
Recently, gradual numbers have been introduced as a means of extending standard interval computation methods to fuzzy and gradual intervals. However, it is well known that the practical use of standard interval arithmetic operators, just as their fuzzy extension, gives results more imprecise than necessary....
Proceedings Article
Ranking fuzzy numbers using fuzzy maximizing-minimizing points
S. Salahshour, S. Abbasbandy, T. Allahviranloo
Up to now, several approaches have been proposed for ranking of fuzzy numbers using maximizing set and minimizing sets. Often, the reference points are created by real numbers. In this paper, we proposed new reference points so called fuzzy maximizing-minimizing points. To this purpose, we used the center...
Proceedings Article
Ranking of fuzzy numbers based on alpha-distance
Saeid Khezerloo, Tofigh Allahviranloo, Masoume Khezerloo
This paper presents a new approach to compare fuzzy numbers using -distance. Initially, the metric distance on the interval numbers based on the convex hull of the endpoints is proposed and it is extended to fuzzy numbers. All the properties of the -distance are proved in details. Finally, the ranking...
Proceedings Article
Dynamical properties in the space of fuzzy numbers
Jiri Kupka
This paper is a contribution to the theoretical foundations of the theory of fuzzy dynamical systems. More precisely, we study relations between a given discrete dynamical system on the space X and its fuzzy counterpart - Zadeh's extension defined on the space of fuzzy sets on X. We provide a short discussion...
Proceedings Article
Solution of Fuzzy Differential Equations with generalized differentiability using LU-parametric representation
Barnabas Bede, Luciano Stefanini
fuzzy numbers and fuzzy-valued functions, to obtain valid approximations of fuzzy generalized derivative and to solve fuzzy differential equations. The main result is that a fuzzy differential initial-value problem can be translated into a system of in nitely many ordinary differential equations and,...