This paper considers compositions of relations based on the notion of the afterset and the foreset, i. e., the subproduct, the superproduct and the square product introduced by Bandler and Kohout with modification proposed by De Baets and Kerre. There are proven all possible mixed pseudo-associativity properties of Bandler – Kohout compositions of relations.

Standard Möbius transform evaluation formula for the Choquet integral is associated with the $\mathrm{𝐦𝐢𝐧}$-aggregation. However, several other aggregation operators replacing $\mathrm{𝐦𝐢𝐧}$ operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method...

En este artículo se considera un programa de Programación Lineal en el que los coeficientes del sistema de inecuaciones lineales, que definen el conjunto de restricciones, están dados de forma imprecisa o vaga. Se supone entonces que tales coeficientes pueden ser definidos mediante números difusos. Se propone un enfoque de resolución basado en las distintas versiones existentes para la comparación de números difusos. Finalmente, se obtienen diferentes modelos auxiliares de Programación Lineal, que...

In this paper, we consider nearness-based convergence in a linear space, where the coordinatewise given nearness relations are aggregated using weighted pseudo-arithmetic and geometric means and using continuous t-norms.

All the negations of PL(X) satisfying the extension principle and the generalized extension principle are fully described through the negation of L. Necessary and sufficient conditions are given for n to be an ortho or u-complementation and for n to satisfy the DeMorgan laws.

The main goal of this paper is to introduce hybrid positive implicative and hybrid implicative (pre)filters of EQ-algebras. In the following, some characterizations of this hybrid (pre)filters are investigated and it is proved that the quotient algebras induced by hybrid positive implicative filters in residuated EQ-algebras are idempotent and residuated EQ-algebra. Moreover, the relationship between hybrid implicative prefilters and hybrid positive implicative prefilters are discussed and it is...

In this work we introduce a nonparametric recursive aggregation process called Multilayer Aggregation (MLA). The name refers to the fact that at each step the results from the previous one are aggregated and thus, before the final result is derived, the initial values are subjected to several layers of aggregation. Most of the conventional aggregation operators, as for instance weighted mean, combine numerical values according to a vector of weights (parameters). Alternatively, the MLA operators...

In this note, we point out that Theorem 3.1 as well as Theorem 3.5 in G. D. Çaylı and F. Karaçal (Kybernetika 53 (2017), 394-417) contains a superfluous condition. We have also generalized them by using closure (interior, resp.) operators.

In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice $L$. We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice $L$, and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm.

Distributivity of fuzzy implications over different fuzzy logic connectives have a very important role to play in efficient inferencing in approximate reasoning, especially in fuzzy control systems (see [9, 15] and [4]). Recently in some considerations connected with these distributivity laws, the following functional equation appeared (see [5]) $$f(min(x+y,a\left)\right)=min\left(f\right(x)+f(y),b),$$ where $a,b>0$ and $f:[0,a]\to [0,b]$ is an unknown function. In this paper we consider in detail a generalized version of this equation, namely the equation $$f\left(m_1(x+y)\right)=m_2(f\left(x\right)+f\left(y\right)),$$ where $m_1,m_2$ are functions...

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....

Once the concept of De Morgan algebra of fuzzy sets on a universe X can be defined, we give a necessary and sufficient condition for a De Morgan algebra to be isomorphic to (represented by) a De Morgan algebra of fuzzy sets.

This paper is devoted to the study of a class of left-continuous uninorms locally internal in the region $A\left(e\right)$ and the residual implications derived from them. It is shown that such uninorm can be represented as an ordinal sum of semigroups in the sense of Clifford. Moreover, the explicit expressions for the residual implication derived from this special class of uninorms are given. A set of axioms is presented that characterizes those binary functions $I:{[0,1]}^2\to [0,1]$ for which a uninorm $U$ of this special class exists...

Uninorms, as binary operations on the unit interval, have been widely applied in information aggregation. The class of almost equitable uninorms appears when the contradictory information is aggregated. It is proved that among various uninorms of which either underlying t-norm or t-conorm is continuous, only the representable uninorms belong to the class of almost equitable uninorms. As a byproduct, a characterization for the class of representable uninorms is obtained.

The asymptotic behaviour of universal fuzzy measures is investigated in the present paper. For each universal fuzzy measure a class of fuzzy measures preserving some natural properties is defined by means of convergence with respect to ultrafilters.