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

Zofia Matusiewicz

Displaying similar documents to “Minimizing and maximizing a linear objective function under a fuzzy $max - *$ relational equation and an inequality constraint”

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.

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...

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...

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

Z. Petrićević (1989)

Matematički Vesnik

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Optimization problem under two-sided (max, +)/(min, +) inequality constraints

Karel Zimmermann (2020)

Applications of Mathematics

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$(max, +)$ -linear functions are functions which can be expressed as the maximum of a finite number of linear functions of one variable having the form $f (x_{1}, \dots, x_{h}) = {max}_{j} (a_{j} + x_{j})$ , where $a_{j}$ , $j = 1, \dots, h$ , are real numbers. Similarly $(min, +)$ -linear functions are defined. We will consider optimization problems in which the set of feasible solutions is the solution set of a finite inequality system, where the inequalities have $(max, +)$ -linear functions of variables $x$ on one side and $(min, +)$ -linear functions of variables $y$ on the other side....

Cauchy-like functional equation based on a class of uninorms

Feng Qin (2015)

Kybernetika

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Commuting is an important property in any two-step information merging procedure where the results should not depend on the order in which the single steps are performed. In the case of bisymmetric aggregation operators with the neutral elements, Saminger, Mesiar and Dubois, already reduced characterization of commuting $n$ -ary operators to resolving the unary distributive functional equations. And then the full characterizations of these equations are obtained under the assumption that...

Controllable and tolerable generalized eigenvectors of interval max-plus matrices

Matej Gazda, Ján Plavka (2021)

Kybernetika

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By max-plus algebra we mean the set of reals $ℝ$ equipped with the operations $a \oplus b = max {a, b}$ and $a \otimes b = a + b$ for $a, b \in ℝ .$ A vector $x$ is said to be a generalized eigenvector of max-plus matrices $A, B \in ℝ (m, n)$ if $A \otimes x = λ \otimes B \otimes x$ for some $λ \in ℝ$ . The investigation of properties of generalized eigenvectors is important for the applications. The values of vector or matrix inputs in practice are usually not exact numbers and they can be rather considered as values in some intervals. In this paper the properties of matrices and vectors with inexact (interval)...

Conditional distributivity of overlap functions over uninorms with continuous underlying operators

Hui Liu, Wenle Li (2024)

Kybernetika

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The investigations of conditional distributivity are encouraged by distributive logical connectives and their generalizations used in fuzzy set theory and were brought into focus by Klement in the closing session of Linzs 2000. This paper is mainly devoted to characterizing all pairs $(O, F)$ of aggregation functions that are satisfying conditional distributivity laws, where $O$ is an overlap function, and $F$ is a continuous t-conorm or a uninorm with continuous underlying operators.

On the $T$ -conditionality of $T$ -power based implications

Zuming Peng (2022)

Kybernetika

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It is well known that, in forward inference in fuzzy logic, the generalized modus ponens is guaranteed by a functional inequality called the law of $T$ -conditionality. In this paper, the $T$ -conditionality for $T$ -power based implications is deeply studied and the concise necessary and sufficient conditions for a power based implication $I^{T}$ being $T$ -conditional are obtained. Moreover, the sufficient conditions under which a power based implication $I^{T}$ is $T^{*}$ -conditional are discussed, this discussions...

Saddle point criteria for second order $η$ -approximated vector optimization problems

Anurag Jayswal, Shalini Jha, Sarita Choudhury (2016)

Kybernetika

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The purpose of this paper is to apply second order $η$ -approximation method introduced to optimization theory by Antczak [2] to obtain a new second order $η$ -saddle point criteria for vector optimization problems involving second order invex functions. Therefore, a second order $η$ -saddle point and the second order $η$ -Lagrange function are defined for the second order $η$ -approximated vector optimization problem constructed in this approach. Then, the equivalence between an (weak) efficient solution...

Displaying similar documents to “Minimizing and maximizing a linear objective function under a fuzzy max - * relational equation and an inequality constraint”

Displaying similar documents to “Minimizing and maximizing a linear objective function under a fuzzy $max - *$ relational equation and an inequality constraint”