$S$-measures, $T$-measures and distinguished classes of fuzzy measures

Peter Struk; Andrea Stupňanová

Displaying similar documents to “ $S$ -measures, $T$ -measures and distinguished classes of fuzzy measures”

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...

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...

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.

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

Z. Petrićević (1989)

Matematički Vesnik

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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...

On the isotropic constant of marginals

Grigoris Paouris (2012)

Studia Mathematica

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We show that if μ₁, ..., μₘ are log-concave subgaussian or supergaussian probability measures in $ℝ^{n_{i}}$ , i ≤ m, then for every F in the Grassmannian $G_{N, n}$ , where N = n₁ + ⋯ + nₘ and n< N, the isotropic constant of the marginal of the product of these measures, $π_{F} (μ ₁ \otimes \dots \otimes μ ₘ)$ , is bounded. This extends known results on bounds of the isotropic constant to a larger class of measures.

On Ordinary and Standard Lebesgue Measures on $ℝ^{\infty}$

Gogi Pantsulaia (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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New concepts of Lebesgue measure on $ℝ^{\infty}$ are proposed and some of their realizations in the ZFC theory are given. Also, it is shown that Baker’s both measures [1], [2], Mankiewicz and Preiss-Tišer generators [6] and the measure of [4] are not α-standard Lebesgue measures on $ℝ^{\infty}$ for α = (1,1,...).

Displaying similar documents to “ S -measures, T -measures and distinguished classes of fuzzy measures”

Displaying similar documents to “ $S$ -measures, $T$ -measures and distinguished classes of fuzzy measures”