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A characterization of uninorms on bounded lattices via closure and interior operators

Gül Deniz Çayli (2023)

Kybernetika

Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms.

A new definition of the fuzzy set

Andrzej Piegat (2005)

International Journal of Applied Mathematics and Computer Science

The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic.

Aggregation of fuzzy vector spaces

Carlos Bejines (2023)

Kybernetika

This paper contributes to the ongoing investigation of aggregating algebraic structures, with a particular focus on the aggregation of fuzzy vector spaces. The article is structured into three distinct parts, each addressing a specific aspect of the aggregation process. The first part of the paper explores the self-aggregation of fuzzy vector subspaces. It delves into the intricacies of combining and consolidating fuzzy vector subspaces to obtain a coherent and comprehensive outcome. The second...

An ε-insensitive approach to fuzzy clustering

Jacek Łęski (2001)

International Journal of Applied Mathematics and Computer Science

Fuzzy clustering can be helpful in finding natural vague boundaries in data. The fuzzy c-means method is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantages of this method is its sensitivity to the presence of noise and outliers in the data. The present paper introduces a new ε-insensitive Fuzzy C-Means (εFCM) clustering algorithm. As a special case, this algorithm includes the well-known Fuzzy C-Medians method (FCMED)....

Combination of t-norms and their conorms

Karel Zimmermann (2023)

Kybernetika

Non-negative linear combinations of t min -norms and their conorms are used to formulate some decision making problems using systems of max-separable equations and inequalities and optimization problems under constraints described by such systems. The systems have the left hand sides equal to the maximum of increasing functions of one variable and on the right hand sides are constants. Properties of the systems are studied as well as optimization problems with constraints given by the systems and appropriate...

Distributivity of strong implications over conjunctive and disjunctive uninorms

Daniel Ruiz-Aguilera, Joan Torrens (2006)

Kybernetika

This paper deals with implications defined from disjunctive uninorms U by the expression I ( x , y ) = U ( N ( x ) , y ) where N is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a t -norm or a t -conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works when the implications...

Entropies of vague information sources

Milan Mareš (2011)

Kybernetika

The information-theoretical entropy is an effective measure of uncertainty connected with an information source. Its transfer from the classical probabilistic information theory models to the fuzzy set theoretical environment is desirable and significant attempts were realized in the existing literature. Nevertheless, there are some open topics for analysis in the suggested models of fuzzy entropy - the main of them regard the formal aspects of the fundamental concepts. Namely their rather additive...

Entropy of T -sums and T -products of L - R fuzzy numbers

Anna Kolesárová, Doretta Vivona (2001)

Kybernetika

In the paper the entropy of L – R fuzzy numbers is studied. It is shown that for a given norm function, the computation of the entropy of L – R fuzzy numbers reduces to using a simple formula which depends only on the spreads and shape functions of incoming numbers. In detail the entropy of T M –sums and T M –products of L – R fuzzy numbers is investigated. It is shown that the resulting entropy can be computed only by means of the entropy of incoming fuzzy numbers or by means of their parameters without the...

Exponential entropy on intuitionistic fuzzy sets

Rajkumar Verma, Bhu Dev Sharma (2013)

Kybernetika

In the present paper, based on the concept of fuzzy entropy, an exponential intuitionistic fuzzy entropy measure is proposed in the setting of Atanassov's intuitionistic fuzzy set theory. This measure is a generalized version of exponential fuzzy entropy proposed by Pal and Pal. A connection between exponential fuzzy entropy and exponential intuitionistic fuzzy entropy is also established. Some interesting properties of this measure are analyzed. Finally, a numerical example is given to show that...

Fundamentals of a mathematical theory of fuzzy sets

Jindřich Spal (1982)

Aplikace matematiky

Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.

Fuzzy Mathematical Programming approach for Solving Fuzzy Linear Fractional Programming Problem

Chinnadurai Veeramani, Muthukumar Sumathi (2014)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper, a solution procedure is proposed to solve fuzzy linear fractional programming (FLFP) problem where cost of the objective function, the resources and the technological coefficients are triangular fuzzy numbers. Here, the FLFP problem is transformed into an equivalent deterministic multi-objective linear fractional programming (MOLFP) problem. By using Fuzzy Mathematical programming approach transformed MOLFP problem is reduced single objective linear programming (LP) problem. The proposed...

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