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

Hu Zhao; Li-Yan Jia; Gui-Xiu Chen

Displaying similar documents to “Convex $(L,M)$-fuzzy remote neighborhood operators”

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...

$L$ -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...

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...

Minimizing and maximizing a linear objective function under a fuzzy $max - *$ relational equation and an inequality constraint

Zofia Matusiewicz (2022)

Kybernetika

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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...

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...

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.

Yager’s classes of fuzzy implications: some properties and intersections

Michał Baczyński, Balasubramaniam Jayaram (2007)

Kybernetika

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Recently, Yager in the article “On some new classes of implication operators and their role in approximate reasoning” [Yager2004] has introduced two new classes of fuzzy implications called the $f$ -generated and $g$ -generated implications. Along similar lines, one of us has proposed another class of fuzzy implications called the $h$ -generated implications. In this article we discuss in detail some properties of the above mentioned classes of fuzzy implications and we describe their relationships...

$R_{0}$ and $R_{1}$ axioms in fuzzy topology

Z. Petrićević (1989)

Matematički Vesnik

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Hydrological applications of a model-based approach to fuzzy set membership functions

Chleboun, Jan, Runcziková, Judita

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Since the common approach to defining membership functions of fuzzy numbers is rather subjective, another, more objective method is proposed. It is applicable in situations where two models, say $M_{1}$ and $M_{2}$ , share the same uncertain input parameter $p$ . Model $M_{1}$ is used to assess the fuzziness of $p$ , whereas the goal is to assess the fuzziness of the $p$ -dependent output of model $M_{2}$ . Simple examples are presented to illustrate the proposed approach.