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Multiplication, distributivity and fuzzy-integral. II

Wolfgang Sander, Jens Siedekum (2005)

Kybernetika

Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms (which are...

Multiplication, distributivity and fuzzy-integral. III

Wolfgang Sander, Jens Siedekum (2005)

Kybernetika

Based on the results of generalized additions, multiplications and differences proven in Part I and II of this paper a framework for a general integral is presented. Moreover it is shown that many results of the literature are contained as special cases in our results.

Multiresolution analysis and Radon measures on a locally compact Abelian group

Félix Galindo, Javier Sanz (2001)

Czechoslovak Mathematical Journal

A multiresolution analysis is defined in a class of locally compact abelian groups G . It is shown that the spaces of integrable functions p ( G ) and the complex Radon measures M ( G ) admit a simple characterization in terms of this multiresolution analysis.

Multivalued fractals in b-metric spaces

Monica Boriceanu, Marius Bota, Adrian Petruşel (2010)

Open Mathematics

Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems theory in several topics of applied sciences. It is known that examples of fractals and multivalued fractals are coming from fixed point theory for single-valued and multivalued operators, via the so-called fractal and multi-fractal...

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