Displaying similar documents to “On functions that cannot be mv-truth values in algebraic structures.”

The σ-complete MV-algebras which have enough states

Antonio Di Nola, Mirko Navara (2005)

Colloquium Mathematicae

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We characterize Łukasiewicz tribes, i.e., collections of fuzzy sets that are closed under the standard fuzzy complementation and the Łukasiewicz t-norm with countably many arguments. As a tool, we introduce σ-McNaughton functions as the closure of McNaughton functions under countable MV-algebraic operations. We give a measure-theoretical characterization of σ-complete MV-algebras which are isomorphic to Łukasiewicz tribes.

Enriched MV-algebras.

Ulrich Höhle (1995)

Mathware and Soft Computing

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This paper introduces the structure of enriched MV-algebras and studies on this basis various relations between sigma-complete MV-algebras and T-tribes.

Specifying t-norms based on the value of T (1/2, 1/2).

Marcin Detyniecki, Ronald R. Yager, Bernadette Bouchon-Meunier (2000)

Mathware and Soft Computing

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We study here the behavior of the t-norms at the point (1/2, 1/2). We indicate why this point can be considered as significant in the specification of t-norms. Then, we suggest that the image of this point can be used to classify the t-norms. We consider some usual examples. We also study the case of parameterized t-norms. Finally using the results of this study, we propose a uniform method of computing the parameters. This method allows not only having the same parameter-scale for all...

Validation sets in fuzzy logics

Rostislav Horčík, Mirko Navara (2002)

Kybernetika

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The validation set of a formula in a fuzzy logic is the set of all truth values which this formula may achieve. We summarize characterizations of validation sets of S -fuzzy logics and extend them to the case of R -fuzzy logics.

Lattice valued intuitionistic fuzzy sets

Tadeusz Gerstenkorn, Andreja Tepavĉević (2004)

Open Mathematics

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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.

On MPT-implication functions for fuzzy logic.

Enric Trillas, Claudi Alsina, Ana Pradera (2004)

RACSAM

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This paper deals with numerical functions J : [0,1] x [0,1] → [0,1] able to functionally express operators →: [0,1] x [0,1] → [0,1] defined as (μ → σ)(x,y) = J(μ(x),σ(y)), and verifying either Modus Ponens or Modus Tollens, or both. The concrete goal of the paper is to search for continuous t-norms T and strong-negation functions N for which it is either T(a, J(a,b)) ≤ b (Modus Ponens) or T(N(b), J(a,b)) ≤ N(a) (Modus Tollens), or both, for all a,b in [0,1] and a given J. Functions J...