Abstract
The set (X, J) of fuzzy subsetsf:X→J of a setX can be equipped with a structure of ϑ-valued Łukasiewicz-Moisil algebra, where ϑ is the order type of the totally ordered setJ. Conversely, every Łukasiewicz-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\(\bar \theta \)⩾ϑ. The first result of this paper is a characterization of those ϑ-valued Łukasiewicz-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 ϑ-valued Post algebras with are isomorphic to an algebra of the form (X, J) (Theorem 3 and Proposition 2).
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Rudeanu, S. On Łukasiewicz-Moisil algebras of fuzzy sets. Stud Logica 52, 95–111 (1993). https://doi.org/10.1007/BF01053066
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DOI: https://doi.org/10.1007/BF01053066