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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)
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)
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)
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)