In this paper we shall describe a very natural extension of MV-algebras, the divisible MV-algebras (DMV). Such algebraic structures will be used to give a formal description of rules of fuzzy control.

Weak pseudo BL-algebras (WPBL-algebras) are non-commutative fuzzy structures which arise from pseudot-norms (i.e. the non-commutative versions of triangular norms). In this paper, we study the pairs of weak negations on WPBL-algebras, extending the case of weak negations on Esteva–Godo MTL-algebras. A geometrical characterization of the pairs of weak negations in bounded chains is provided. Our...

In this paper, we study the generalized derivation of a Lie sub-algebra algebra polynomial vector fields on $\mathbb{R}^n$ where $n\geq1$, containing all constant and Euler field, under some conditions sub-algebra.

We prove that on the finitely generated free MV-algebras the only automorphism-invariant truth averaging process that detects pseudotrue propositions is the integral with respect to Lebesgue measure.

We introduce the tense LMn-algebras and the tense MV algebras as algebraic structures for some tense many-valued logics. A representation theorem for tense LMn-algebras is proved and the polynomially equivalence between tense LM3-algebras (resp. tense LM4-algebras) and tense MV3-algebras (resp. tense MV4-algebras) is established. We study the pairs of dually-conjugated operations on MV -algebra...

This work presents measurements of the electrical resistivity srd, Seebeck coefficient, and thermal conductivity skd of icosahedral Al70Pd22.5sRe1−xMnxd7.5 quasicrystals from 10 to 300 K. A series of quasicrystals was prepared with x=0, 0.1, 0.2, 0.3, 0.5, 0.6, 0.8, and 1.0 to systematically study the effect of substitution. The electrical resistivity increases as the temperature decreases, sug...

Quasi-MV algebras are generalisations of MV algebras arising in quantum computational logic. Although a reasonably complete description of the lattice of subvarieties of quasi-MV algebras has already been provided, the problem of extending this description to the setting of quasivarieties has so far remained open. Given its apparent logical repercussions, we tackle the issue in the present pape...

The algebraic theory of quasi-MV algebras, generalizations of MV algebras arising in quantum computation, is by now rather well-developed. Although it is possible to define several interesting logics from these structures, so far this aspect has not been investigated. The present article aims at filling this gap.

In this paper we prove algebraic equivalents of the conservative extension theorems of Lukasiewicz propositional logic to rational Pavelka propositional logic. The results concerns the conservative extension and the very conservative extension of MV-algebras to Pavelka algebras.

By studying two unsharp quantum structures, namely extended lattice ordered effect algebras and lattice ordered QMV algebras, we obtain some characteristic theorems of MV algebras. We go on to discuss automata theory based on these two unsharp quantum structures. In particular, we prove that an extended lattice ordered effect algebra (or a lattice ordered QMV algebra) is an MV algebra if and on...