Displaying similar documents to “Fuzzy sets as set classes.”

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.

Measures of fuzziness and operations with fuzzy sets.

Siegfried Gottwald, Ernest Czogala, Witold Pedrycz (1982)

Stochastica

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We discuss the effects that the usual set theoretic and arithmetic operations with fuzzy sets and fuzzy numbers have with respect to the energies and entropies of the fuzzy sets connected and of the resulting fuzzy sets, and we also compare the entropies and energies of the results of several of those operations.

Classification of the regular De Morgan algebras of fuzzy sets.

Francesc Esteva, Núria Piera (1984)

Stochastica

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A characterization of regular lattices of fuzzy sets and their isomorphisms is given in Part I. A characterization of involutions on regular lattices of fuzzy sets and the isomorphisms of De Morgan algebras of fuzzy sets is given in Part II. Finally all classes of De Morgan algebras of fuzzy sets with respect to isomorphisms are completely described.

On some isomorphisms of De Morgan algebras of fuzzy sets.

Francesc Esteva (1983)

Stochastica

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In this paper the classes of De Morgan algebras (P(X),∩,U,n) are studied. With respect to isomorphisms of such algebras, being P(X) the fuzzy sets on a universe X taking values in [0,1], U and ∩ the usual union and intersection given by max and min operations and n a proper complement.

Measures of fuzziness based on t-norms.

Ronald R. Yager (1982)

Stochastica

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We use the concept of t-norms and conorms to develop a pseudo metric and we then use this pseudo metric to define a class of measures of fuzziness associated with a fuzzy set. We investigate the properties of this class of measures of fuzziness.

A theorem on implication functions defined from triangular norms.

Didier Dubois, Henri Prade (1984)

Stochastica

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Several transformation which enable implication functions in multivalued logics to be generated from conjunctions have been proposed in the literature. It is proved that for a rather general class of conjunctions modeled by triangular norms, the generation process is closed, thus shedding some light on the relationships between seemingly independent classes of implication functions.