In this paper we characterize hyper MV -algebras in which 0 or1 are scalar elements . We prove that any nite hyper MV -algebra that 0is a scaler element in it, is an MV -algebra. Finally we characterize hyperMV -algebras of order 2 and order 3.

We generalize the notion of an MV-algebra in the context of residuated lattices to include noncommutative and unbounded structures. We investigate a number of their properties and prove that they can be obtained from lattice-ordered groups via a truncation construction that generalizes the Chang–Mundici Γ functor. This correspondence extends to a categorical equivalence that generalizes the one...

In his classical paper 1 , Chang invented the notion of MV-algebra in order to provide an algebraic proof of the completeness theorem of infinite valued Lukasiewicz propositional calculus. Recently, the algebraic theory of MV-algebras is intensively studied, see 2–5 . The notion of derivation, introduced from the analytic theory, is helpful to the research of structure and property in algebraic...

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MV-pairs and states – p. 1/2

Similarities are an extension of equivalence relations to a fuzzy context. In this paper we introduce the class of similarity MV-algebras obtained as a generalization of the variety of MValgebras by adding a binary operator playing the role of similarity. We further introduce the similarity Łukasiewicz logic and we prove a completeness theorem.

An MV-pair is a pair (B, G) where B is a Boolean algebra and G is a subgroup of the automorphism group of B satisfying certain conditions. Let ∼G be the equivalence relation on B naturally associated with G. We prove that for every MV-pair (B, G), the effect algebra B/ ∼G is an MV-effect algebra. Moreover, for every MV-effect algebra M there is an MV-pair (B, G) such that M is isomorphic to B/ ∼G.