Interval fuzzy matrix equations

Emília Draženská; Helena Myšková

Displaying similar documents to “Interval fuzzy matrix equations”

Preservation of properties of fuzzy relations during aggregation processes

Józef Drewniak, Urszula Dudziak (2007)

Kybernetika

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Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by $n$ -ary operations is considered. Namely, with the use of fuzzy relations $R_{1}, ..., R_{n}$ and $n$ -argument operation $F$ on the interval $[0, 1]$ , a new fuzzy relation $R_{F} = F (R_{1}, ..., R_{n})$ is created....

Properties of fuzzy relations powers

Józef Drewniak, Barbara Pȩkala (2007)

Kybernetika

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Properties of $sup$ - $*$ compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider $sup$ - $*$ powers of fuzzy relations under diverse assumptions about $*$ operation. At first, we remind fundamental properties of $sup$ - $*$ composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations...

Suzuki type fuzzy $𝒵$ -contractive mappings and fixed points in fuzzy metric spaces

Dhananjay Gopal, Juan Martínez-Moreno (2021)

Kybernetika

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In this paper, we propose the concept of Suzuki type fuzzy $𝒵$ -contractive mappings, which is a generalization of Fuzzy $𝒵$ -contractive mappings initiated in the article [S. Shukla, D. Gopal, W. Sintunavarat, A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Sets and Systems 350 (2018)85-95]. For this type of contractions suitable conditions are framed to ensure the existence of fixed point in $G$ -complete as well as $M$ -complete fuzzy metric spaces. A comprehensive set...

Convex $(L, M)$ -fuzzy remote neighborhood operators

Hu Zhao, Li-Yan Jia, Gui-Xiu Chen (2024)

Kybernetika

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In this paper, two kinds of remote neighborhood operators in $(L, M)$ -fuzzy convex spaces are proposed, which are called convex $(L, M)$ -fuzzy remote neighborhood operators. It is proved that these two kinds of convex $(L, M)$ -fuzzy remote neighborhood operators can be used to characterize $(L, M)$ -fuzzy convex structures. In addition, the lattice structures of two kinds of convex $(L, M)$ -fuzzy remote neighborhood operators are also given.

Extensions of fuzzy connectives on ACDL

Hui Liu, Bin Zhao (2019)

Kybernetika

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The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend...

Fuzzy differential subordinations connected with the linear operator

Sheza M. El-Deeb, Georgia I. Oros (2021)

Mathematica Bohemica

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We obtain several fuzzy differential subordinations by using a linear operator $ℐ_{m, γ}^{n, α} f (z) = z + \sum_{k = 2}^{\infty} {(1 + γ (k - 1))}^{n} m^{α} {(m + k)}^{- α} a_{k} z^{k}$ . Using the linear operator $ℐ_{m, γ}^{n, α},$ we also introduce a class of univalent analytic functions for which we give some properties.

Tolerance problems for generalized eigenvectors of interval fuzzy matrices

Martin Gavalec, Helena Myšková, Ján Plavka, Daniela Ponce (2022)

Kybernetika

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Fuzzy algebra is a special type of algebraic structure in which classical addition and multiplication are replaced by maximum and minimum (denoted $\oplus$ and $\otimes$ , respectively). The eigenproblem is the search for a vector $x$ (an eigenvector) and a constant $λ$ (an eigenvalue) such that $A \otimes x = λ \otimes x$ , where $A$ is a given matrix. This paper investigates a generalization of the eigenproblem in fuzzy algebra. We solve the equation $A \otimes x = λ \otimes B \otimes x$ with given matrices $A, B$ and unknown constant $λ$ and vector $x$ . Generalized eigenvectors...

$L$ -fuzzy ideal degrees in effect algebras

Xiaowei Wei, Fu Gui Shi (2022)

Kybernetika

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In this paper, considering $L$ being a completely distributive lattice, we first introduce the concept of $L$ -fuzzy ideal degrees in an effect algebra $E$ , in symbol $𝔇_{e i}$ . Further, we characterize $L$ -fuzzy ideal degrees by cut sets. Then it is shown that an $L$ -fuzzy subset $A$ in $E$ is an $L$ -fuzzy ideal if and only if $𝔇_{e i} (A) = ⊤,$ which can be seen as a generalization of fuzzy ideals. Later, we discuss the relations between $L$ -fuzzy ideals and cut sets ( $L_{β}$ -nested sets and $L_{α}$ -nested sets). Finally, we obtain that...

Generalized convexities related to aggregation operators of fuzzy sets

Susana Díaz, Esteban Induráin, Vladimír Janiš, Juan Vicente Llinares, Susana Montes (2017)

Kybernetika

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We analyze the existence of fuzzy sets of a universe that are convex with respect to certain particular classes of fusion operators that merge two fuzzy sets. In addition, we study aggregation operators that preserve various classes of generalized convexity on fuzzy sets. We focus our study on fuzzy subsets of the real line, so that given a mapping $F : [0, 1] \times [0, 1] \to [0, 1]$ , a fuzzy subset, say $X$ , of the real line is said to be $F$ -convex if for any $x, y, z \in ℝ$ such that $x \leq y \leq z$ , it holds that $μ_{X} (y) \geq F (μ_{X} (x), μ_{X} (z))$ , where $μ_{X} : ℝ \to [0, 1]$ stands here for the...

A short note on $L_{C B A}$ - fuzzy logic with a non-associative conjunction

Miroslav Kolařík (2016)

Discussiones Mathematicae General Algebra and Applications

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We significantly simplify the axiomatic system $L_{C B A}$ for fuzzy logic with a non-associative conjunction.