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

Z. Petrićević

Displaying similar documents to “ $R_{0}$ and $R_{1}$ axioms in fuzzy topology”

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

Chleboun, Jan, Runcziková, Judita

Similarity:

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.

$L$ -fuzzy ideal degrees in effect algebras

Xiaowei Wei, Fu Gui Shi (2022)

Kybernetika

Similarity:

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

Similarity:

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...

Tolerance problems for generalized eigenvectors of interval fuzzy matrices

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

Kybernetika

Similarity:

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...

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

Zofia Matusiewicz (2022)

Kybernetika

Similarity:

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...