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On a new class of distances between fuzzy numbers.

Carlo Bertoluzza, Norberto Corral, Antonia Salas (1995)

Mathware and Soft Computing

In the course of the studies on fuzzy regression analysis, we encountered the problem of introducing a distance between fuzzy numbers, which replaces the classical (x - y)2 on the real line. Our proposal is to compute such a function as a suitable weighted mean of the distances between the α-cuts of the fuzzy numbers. The main difficulty is concerned with the definition of the distance between intervals, since the current definitions present some disadvantages which are undesirable in our context....

On an exponential-type fuzzy difference equation.

Stefanidou, G., Papaschinopoulos, G., Schinas, C.J. (2010)

Advances in Difference Equations [electronic only]

On Aumann's theorem that the circle does not admit a mean

F. Javier Trigos-Arrieta, Marian Turzański (2005)

Acta Universitatis Carolinae. Mathematica et Physica

On granular derivatives and the solution of a granular initial value problem

Ildar Batyrshin (2002)

International Journal of Applied Mathematics and Computer Science

Perceptions about function changes are represented by rules like “If X is SMALL then Y is QUICKLY INCREASING.” The consequent part of a rule describes a granule of directions of the function change when X is increasing on the fuzzy interval given in the antecedent part of the rule. Each rule defines a granular differential and a rule base defines a granular derivative. A reconstruction of a fuzzy function given by the granular derivative and the initial value given by the rule is similar to Euler’s...

On models of long-term behavior of concrete

Chleboun, Jan, Dohnalová, Lenka, Runcziková, Judita (2021)

Programs and Algorithms of Numerical Mathematics

Long-term behavior of concrete is modeled by several widely accepted models, such as B3, fib MC 2010, or ACI 209 whose input parameters and output values are not identical to each other. Moreover, the input and, consequently, the output values are uncertain. In this paper, fuzzy input parameters are considered in uncertainty quantification of each model response and, finally, the sets of responses are analyzed by elementary tools of evidence theory. That is, belief and plausibility functions are...

On some isometric spaces of $C_{0}^{F}, C^{F}$ and $ℓ_{\infty}^{F}$ .

Dutta, Hemen (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

On the existence of a fuzzy integral equation of Urysohn-Volterra type

Mohamed Abdalla Darwish (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We present an existence theorem for integral equations of Urysohn-Volterra type involving fuzzy set valued mappings. A fixed point theorem due to Schauder is the main tool in our analysis.

On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application

Michał Boczek, Marek Kaluszka (2016)

Kybernetika

In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-Hölder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi [11] is not true. Next, we study the Minkowski-Hölder inequality for the lower Sugeno integral and the...

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