Results 11 to 20 of about 27,722 (108)
Pseudo MV-algebras and Lexicographic Product [PDF]
Fuzzy Sets and Systems, 2014 We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital $\ell$-group and an $\ell$-group that is not necessary Abelian.
Dvurečenskij, Anatolij
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Kullback–Leibler Divergence and Mutual Information of Partitions in Product MV Algebras [PDF]
Entropy, 2017 The purpose of the paper is to introduce, using the known results concerning the entropy in product MV algebras, the concepts of mutual information and Kullback–Leibler divergence for the case of product MV algebras and examine algebraic properties of ...
Dagmar Markechová, Beloslav Riečan
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Boolean Products of MV-Algebras: Hypernormal MV-Algebras
Journal of Mathematical Analysis and Applications, 1996 Introduced by C. C. Chang in the late fifties as the Lindenbaum algebras of the infinite-valued calculus of Lukasiewicz, MV-algebras have been attracting renewed interest in the last decade, because they form an equational class being naturally equivalent to the category of lattice-ordered abelian groups with strong unit. As a consequence, countable MV-
Cignoli, R., Torrell, A.T.
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Subdirect product decompositions of MV-algebras [PDF]
Czechoslovak Mathematical Journal, 1999 As is known, every \(MV\)-algebra \(A\) can be represented by means of an abelian lattice ordered group \(G\) with a strong order unit \(u\). The author shows that the lattices of congruences of \(A\) and \(G\) are isomorphic and uses this fact to describe the connections between subdirect product decompositions of \(A\) and of \(G\).
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Direct product decomposition of $MV$-algebras [PDF]
Czechoslovak Mathematical Journal, 1994 To each MV-algebra \({\mathcal A}= (A; \oplus, *, \neg, 0,1)\) we can assign a lattice \(L({\mathcal A})= (A; \wedge, \vee)\) by defining, for all \(x,y\in A\), \(x\wedge y= \neg (\neg x\vee \neg y)\) and \(x\vee y= (x* \neg y)\oplus y\). If \({\mathcal A}_ 1\) and \({\mathcal A}_ 2\) are MV-algebras such that the lattices \(L({\mathcal A}_ 1)\) and ...
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Weakly Divisible MV-Algebras and Product
Journal of Mathematical Analysis and Applications, 1999 The authors prove that any weakly divisible \(\sigma\)-complete (and hence divisible) MV-algebra \(M\) is isomorphic, as an MV-algebra, with the set of all continuous fuzzy subsets defined on the set of maximal ideals of \(M\). They use this to define on \(M\) an associative, commutative product with \(1\) as the identity.
Dvurečenskij, Anatolij +1 more
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Study of MV-algebras via derivations
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 The main goal of this paper is to give some representations of MV-algebras in terms of derivations. In this paper, we investigate some properties of implicative and difference derivations and give their characterizations in MV-algebras.
Wang Jun Tao, She Yan Hong, Qian Ting
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Subalgebras, direct products and associated lattices of MV-algebras [PDF]
Glasgow Mathematical Journal, 1992 MV-algebras were introduced by C. C. Chang [3] in 1958 in order to provide an algebraic proof for the completeness theorem of the Lukasiewicz infinite valued propositional logic. In recent years the scope of applications of MV-algebras has been extended to lattice-ordered abelian groups, AF C*-algebras [10] and fuzzy set theory [1].
L. P. Belluce +2 more
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Lukasiewicz logic and Riesz spaces [PDF]
, 2013 We initiate a deep study of {\em Riesz MV-algebras} which are MV-algebras endowed with a scalar multiplication with scalars from $[0,1]$. Extending Mundici's equivalence between MV-algebras and $\ell$-groups, we prove that Riesz MV-algebras are ...
Di Nola, Antonio, Leustean, Ioana
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Stone duality above dimension zero: Axiomatising the algebraic theory of C(X) [PDF]
, 2016 It has been known since the work of Duskin and Pelletier four decades ago that KH^op, the category opposite to compact Hausdorff spaces and continuous maps, is monadic over the category of sets.
Marra, Vincenzo, Reggio, Luca
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