Displaying similar documents to “On the fundamentals of fuzzy sets.”

Fuzzy relation equation under a class of triangular norms: A survey and new results.

Antonio Di Nola, Witold Pedrycz, Salvatore Sessa, Wang Pei Zhuang (1984)

Stochastica

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By substituting the classical lattice operator min of the unit real interval with a triangular norm of Schweizer and Sklar, the usual fuzzy relational equations theory of Sanchez can be generalized to wider theory of fuzzy equations. Considering a remarkable class of triangular norms, for such type of equations defined on finite sets, we characterize the upper an lower solutions. We also characterize the solutions posessing a minimal fuzziness measure of Yager valued with...

On a representation theorem of De Morgan algebras by fuzzy sets.

Francesc Esteva (1981)

Stochastica

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Once the concept of De Morgan algebra of fuzzy sets on a universe X can be defined, we give a necessary and sufficient condition for a De Morgan algebra to be isomorphic to (represented by) a De Morgan algebra of fuzzy sets.

On fuzzy binary relations.

Sergei V. Ovchinnikov, Teresa Riera Madurell (1983)

Stochastica

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A binary relation language is an important tool of the theory of measurements (see, for example, book [5]). Specifically, the theory of nominal and ordinal scales is based on theories of equivalent relations and weak orderings. These binary relations have a simple structure which can be described as follows (bearing in mind a context of the measurement theory).

Involutions in fuzzy set theory.

Sergei V. Ovchinnikov (1980)

Stochastica

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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.

On the additivity of the cardinalities of fuzzy sets of type II.

Ronald R. Yager (1983)

Stochastica

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In this short note we show that for fuzzy sets of type II the additive rule for cardinalities holds true. The proof of this result requires an application of approximate reasoning as means of inference by use of the entailment principle.

The minimun inaccuracy fuzzy estimation: An extension of the maximum likelihood principle.

Norberto Corral, M.ª Angeles Gil (1984)

Stochastica

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The present paper deals with the extension of the likelihood estimation to the situation where the experimentation does not provide exact information but rather vague information. The extension process tries to achieve three fundamental objectives: the new method must be an extension of the maximum likelihood method, it has to be very simple to apply and it must allow for an interesting interpretation. These objectives are achieved herein by using the following...

A stochastic model of choice.

Sergei V. Ovchinnikov (1985)

Stochastica

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An approach to choice function theory is suggested which is probabilistic and non-deterministic. In the framework of this approach fuzzy choice functions are introduced and a number of necessary and sufficient conditions for a fuzzy choice function to be a fuzzy rational choice function of a certain type are established.