In this note we prove that it is impossible to extend the natural equivalence between the category of MV-algebras and the category of Abelian `-groups with strong unit described by C. C. Chang, 1958, and Cignoli & Mundici, 1997, to a natural equivalence between the category of m-zeroids and some category containing the category of Abelian `-groups with strong unit.

We prove that RS-BL-algebras are MV-algebras.

In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a...

BACKGROUND Halothane shortens ventricular action potential duration (APD), as a consequence of its inhibitory effects on a variety of membrane currents, an effect that is greater in sub-endocardial than sub-epicardial myocytes. In hypertrophied ventricle, APD is prolonged as a consequence of electrical remodelling. In this study, we compared the effects of halothane on transmural APD in myocyte...

Coalition games are generalized to semisimple MV-algebras. Coalitions are viewed as [0,1]-valued functions on a set of players, which enables to express a degree of membership of a player in a coalition. Every game is a real-valued mapping on a semisimple MV-algebra. The goal is to recover the so-called core: a set of final distributions of payoffs, which are represented by measures on the MV-a...

Lukasiewicz implication algebras are the {→, 1}-subreducts of MV algebras. They are the algebraic counterpart of SuperLukasiewicz Implicational Logics. We give a description of free Lukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Lukasiewicz implication algebra is isomorphic to ⋃ x∈X [xθ) for a certain congruence θ over the |X|-...

In this paper, by considering the notion of upsets we construct some topologies on BLalgebras. We show that any BL-algebras with respect to these topologies formes semitopological BLalgebra. Then we obtain some of the topological aspects of theses structures such as connectivity and compactness. Moreover, we introduced two kinds of semitopological MV -algebra by using two kinds of definition of...

We define the Lukasiewicz Transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “ Lukasiewicz Transform Based” ( LTB) algorithm for image processing. We also propose a strong extension of such concepts and results in the framework of quantales and quantale modules. 1 The Lukasiewicz transform and its applications Th...

In this paper, we investigate related properties of some particular derivations and give some characterizations of additive derivations in MV-algebras. Then, we obtain that the fixed point set of additive derivations is still an MV-algebra. Also, we study Boolean additive derivations and their adjoint derivations. In particular, we get that the fixed point set of Boolean addition derivations an...

Definition 1. An algebra (A,⊕,∗ , 0) with a binary operation ⊕ : A×A → A and with a unary operation ∗ : A → A and a constant 0, is said to be an MV -algebra iff satisfies the following conditions for all a, b, c ∈ A: (1) (A,⊕, 0) is a commutative monoid; (2) x⊕ 0∗ = 0∗ for every x ∈ A; (3) (x∗)∗ = x for every x ∈ A; (4) (x∗ ⊕ y)∗ ⊕ y = (x⊕ y∗)∗ ⊕ x for every x, y ∈ A. ¿From (4), setting y = 0∗,...