The norms and conorms family tree root is uninorm. It will be shown, that distance based operators satisfy most of properties of generally defined parametrical operators. Based on this theory some new types of fuzzy integrals are introduced theoretically. It can be shown, that the reason used for fuzzy integral introduction is similar to the reasons in decision-making by fuzzy control logic.

Most existing universal approximation results for fuzzy systems are based on the assumption that we use t conorms and t conorms to represent and and or Yager has proposed to use within the fuzzy system modeling paradigm more general operations based on uninorms In this paper we show that the universal approximation property holds for an arbitrary choice of a uninorm

In this paper, we firstly show that the $N$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $N$-dual operation. As a dual result, the $N$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...

This paper is devoted to classify all idempotent uninorms defined on the finite scale Ln = {0, 1, . . . , n}, called discrete idempotent uninorms. It is proved that any discrete idempotent uninorm with neutral element e ∈ Ln is uniquely determined by a decreasing function g : [0, e]→ [e, n] and vice versa. Based on this correspondence, the number of all possible discrete idempotent uninorms on ...

This paper presents a continuation of the study on a mathematical morphology based on left-continuous conjunctive uninorms given in [1]. Experimental results are displayed using the morphological Top-Hat transformation, used to highlight certain components of the image, and on the reduction and elimination of noise using alternate filters that are generated with the operators of opening and clo...

in this paper, we firstly show that the $n$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $n$-dual operation. as a dual result, the $n$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...

In signal processing applications, a key role is played by the Fourier transforms. The mathematical structure underlying Fourier analysis is the linear structure. In the present paper we propose and study a tool designed for nonlinear signal and image processing, that is novel Fourier-like transforms, based on a pair of pseudo-operations consisting of a uninorm and an absorbing norm. We analyse...