- Full text PDF available (30)
In the present paper we introduce and study a generalization of the Hukuhara di¤er-ence and also generalizations of the Hukuhara di¤erentiability to the case of interval valued functions. We consider several possible de…nitions for the derivative of an interval valued function and we study connections between them and their properties. Using these concepts… (More)
In the present paper, using novel generalizations of the Hukuhara di¤erence for fuzzy sets, we introduce and study new generalized di¤erentiability concepts for fuzzy valued functions. Several properties of the new concepts are investigated and they are compared to similar fuzzy di¤erentiabilities …nding connections between them. Characterization and… (More)
We suggest the use of piecewise monotonic interpolations to approximate and represent a fuzzy number (or interval) and to derive a procedure to control the absolute error associated to the arithmetic operations (+, −, ·, :) between fuzzy numbers, in order to reduce the distance between the true result of the operation and its approximation. The monotonic… (More)
We present several models to obtain simple parametric representations of the fuzzy numbers or intervals, based on the use of piecewise monotonic functions of different forms. The representations have the advantage of allowing flexible and easy to control shapes of the fuzzy numbers (we use the standard-cuts setting, but also the membership functions are… (More)
Our paper "Generalized Hukuhara Di¤erentiability of Interval-valued Functions and Interval Di¤erential Equations", appeared in Nonlinear Analysis 71 (2009), contains some imprecisions. In this note we correct them and give few new results on the topic.
The fuzzy transform setting (F-transform), as a tool for general continuous approximation of functions, is proposed to approximate the solution of ordinary, interval or fuzzy (levelwise) differential equations; in particular, one of the basic properties of inverse F-transform allows a good approximation of the solution x(t), starting with the uniform… (More)
The phenomenon of synchronization of a two-dimensional discrete dynamical system is studied for the model of an economic duopoly game, whose time evolution is obtained by the iteration of a noninvertible map of the plane. In the case of identical players the map has a symmetry property that implies the invariance of the diagonal x 1 x 2 , so that… (More)