On łukasiewicz-moisil algebras of fuzzy sets

Studia Logica 52 (1):95 - 111 (1993)
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Abstract

The set (X, J) of fuzzy subsetsf:XJ of a setX can be equipped with a structure of -valued ukasiewicz-Moisil algebra, where is the order type of the totally ordered setJ. Conversely, every ukasiewicz-Moisil algebra — and in particular every Post algebra — is isomorphic to a subalgebra of an algebra of the form (X, J), whereJ has an order type . The first result of this paper is a characterization of those -valued ukasiewicz-Moisil algebras which are isomorphic to an algebra of the form (X, J) (Theorem 1). Then we prove that (X, J) is a Post algebra if and only if the setJ is dually well-ordered (Theorem 2) and we give a characterization of those -valued Post algebras with are isomorphic to an algebra of the form (X, J) (Theorem 3 and Proposition 2).

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References found in this work

Fuzzy Sets.Lofti A. Zadeh - 1965 - Information and Control 8 (1):338--53.
Boolean Algebras.Roman Sikorski - 1966 - Journal of Symbolic Logic 31 (2):251-253.
Essais Sur les Logiques Non Chrysippiennes.Grigore C. Moisil - 1972 - Éditions de l'Académie Socialiste de Roumanie.

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