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Intuitionistic fuzzy relations (Part II). Effect of Atanassov's operators on the properties of the intuitionistic fuzzy relations.

Pedro J. Burrillo, Humberto Bustince (1995)

Mathware and Soft Computing

In this paper we study the effect of Atanassov's operator on the properties of properties reflexive, symmetric, antisymmetric, perfect antisymmetric and transitive intuitionistic fuzzy relations. We finish the paper analysing the partial enclosure of the intuitionistic fuzzy relations and its effect on the conservation of the transitive property through Atanassov's operator.

Involutions in fuzzy set theory.

Sergei V. Ovchinnikov (1980)

Stochastica

All possible involutions in fuzzy set theory are completely described. Any involution is a composition of a symmetry on a universe of fuzzy sets and an involution on a truth set.

Juegos no cooperativos con preferencias difusas.

Juan Tejada Cazorla (1988)

Trabajos de Investigación Operativa

El objetivo de este trabajo es el estudio de los juegos no cooperativos en los que los jugadores expresan sus preferencias sobre las consecuencias que se derivan de sus acciones mediante relaciones binarias difusas. El concepto de solución que se maneja es el de estrategias en equilibrio. La existencia de tales estrategias queda probada en el caso de que los jugadores definan sus preferencias sobre las consecuencias aleatorias mediante la extensión lineal introducida en Montero-Tejada (1986a).

Lattice valued algebras.

Antonio Di Nola, Giangiacomo Gerla (1987)

Stochastica

In this paper we propose a general approach to the theory of fuzzy algebras, while the early existing papers deal with a particular type of fuzzy structures as fuzzy groups, fuzzy ideals, fuzzy vector spaces and so on.

Lattice valued intuitionistic fuzzy sets

Tadeusz Gerstenkorn, Andreja Tepavĉević (2004)

Open Mathematics

In this paper a new definition of a lattice valued intuitionistic fuzzy set (LIFS) is introduced, in an attempt to overcome the disadvantages of earlier definitions. Some properties of this kind of fuzzy sets and their basic operations are given. The theorem of synthesis is proved: For every two families of subsets of a set satisfying certain conditions, there is an lattice valued intuitionistic fuzzy set for which these are families of level sets.

Left and right semi-uninorms on a complete lattice

Yong Su, Zhudeng Wang, Keming Tang (2013)

Kybernetika

Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary...

m * -fuzzy basically disconnected spaces in smooth fuzzy topological spaces

B. Amudhambigai, Mallasamudram Kuppusamy Uma, Elango Roja (2013)

Mathematica Bohemica

In this paper, the concepts of m * r -fuzzy g ˜ -open F σ sets and m * -fuzzy basically disconnected spaces are introduced in the sense of Šostak and Ramadan. Some interesting properties and characterizations are studied. Tietze extension theorem for m * -fuzzy basically disconnected spaces is discussed.

Many-dimensional observables on Łukasiewicz tribe: constructions, conditioning and conditional independence

Tomáš Kroupa (2005)

Kybernetika

Probability on collections of fuzzy sets can be developed as a generalization of the classical probability on σ -algebras of sets. A Łukasiewicz tribe is a collection of fuzzy sets which is closed under the standard fuzzy complementation and under the pointwise application of the Łukasiewicz t-norm to countably many fuzzy sets. An observable is a fuzzy set-valued mapping defined on a σ -algebra of sets and satisfying some additional properties; formally, the role of an observable is in a sense analogous...

Mathematical aspects of the theory of measures of fuzziness.

Doretta Vivona (1996)

Mathware and Soft Computing

After recalling the axiomatic concept of fuzziness measure, we define some fuzziness measures through Sugeno's and Choquet's integral. In particular, for the so-called homogeneous fuzziness measures we prove two representation theorems by means of the above integrals.

Medidas de nitidez para conjuntos difusos.

Leandro Pardo Llorente (1983)

Trabajos de Estadística e Investigación Operativa

En este trabajo se realiza un estudio de Medidas de Nitidez para conjuntos difusos. Se comienza dando los conceptos de Medida Puntual de Nitidez o Auto-nitidez puntual y Medida de Nitidez para conjunto difuso, pasando a continuación a dar dos teoremas de construcción de Medidas de Nitidez y uno de caracterización para aquellas medidas que sean valoraciones en el retículo Ln(X).

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

Zofia Matusiewicz (2022)

Kybernetika

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 inequality constraint,...

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