This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to $max-*$ fuzzy relational equations and an inequality constraint, where $*$ is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy $max-*$ relational equation and an inequality constraint,...

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 primary aim of this article is to put forward new classes of uni-nullnorms on certain classes of bounded lattices via closure (interior) operators. Due to the new classes of uninorms combining both a t-norm $T$ and a t-conorm $S$ by various kinds of closure operators or interior operators, the relationships and properties among the same class of uninorms on $L$, we obtain new classes of uni-nullnorms on $L$ via closure (interior) operators. The constructions of uni-nullnorms on some certain classes...

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 article, we deeply reveal the relationship between functions $\theta$ and $\vartheta$ in an overlap function additively generated by an additive generator pair ($\theta$,$\vartheta$), which is used to characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions $\theta$ and $\vartheta$. We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo) automorphism....

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...