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Academic literature on the topic 'MV - algebre'

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Published: 10 March 2023

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Journal articles on the topic "MV - algebre"

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Rajabisotudeh, F., and N. Kouhestani. "MV-pseudo metrics on MV-algebras." Annals of the University of Craiova, Mathematics and Computer Science Series 49, no. 1 (June 24, 2022): 35–51. http://dx.doi.org/10.52846/ami.v49i1.1443.

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In this paper, we define the notions of MV-pseudo norm and MV-pseudo metric on MV-algebras and study some of their algebraic properties. The notion of uniform MV-algebra is also introduced and its relationship to MV-pseudo metrics is studied.
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DI NOLA, A., P. FLONDOR, and B. GERLA. "COMPOSITION ON MV-ALGEBRAS." Journal of Algebra and Its Applications 05, no. 04 (August 2006): 417–39. http://dx.doi.org/10.1142/s0219498806001818.

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In this paper we introduce an extension of MV-algebras obtained by adding a binary operation and a constant, with the aim of modelling composition of functions. The variety of Composition MV-algebra (CMV-algebra, for short) is defined and some results regarding ideals and congruences are stated. Further, we define modules over CMV-algebras showing that to any substitution corresponds an endomorphism of modules.
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Heubo-Kwegna, Olivier A., and Jean B. Nganou. "Radically principal MV-algebras." Mathematica Slovaca 73, no. 1 (February 1, 2023): 25–36. http://dx.doi.org/10.1515/ms-2023-0004.

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Abstract An MV-algebra A is radically principal if every prime ideal P of A is radically principal, i.e., there exists a principal ideal I of A such that Rad ( P ) = Rad ( I ) $ \text{Rad}(P)=\text{Rad}(I) $ . We investigate radically principal MV-algebras and provide some characterizations as well as some classes of examples. We prove a Cohen-like theorem, precisely, an MV-algebra is radically principal if and only if every maximal ideal is radically principal. It is also shown that the radically principal hyperarchemedian MV-algebras are the weakly finite ones and the radically principal Boolean algebras are the finite ones. Radically principal MV-algebras are also studied from the perspective of lattice-ordered groups.
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Wang, Jun Tao, Yan Hong She, and Ting Qian. "Study of MV-algebras via derivations." Analele Universitatii "Ovidius" Constanta - Seria Matematica 27, no. 3 (December 1, 2019): 259–78. http://dx.doi.org/10.2478/auom-2019-0044.

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AbstractThe 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. Then, we show that every Boolean algebra (idempotent MV-algebra) is isomorphic to the algebra of all implicative derivations and obtain that a direct product representation of MV-algebra by implicative derivations. Moreover, we prove that regular implicative and difference derivations on MV-algebras are in one to one correspondence and show that the relationship between the regular derivation pair (d, g) and the Galois connection, where d and g are regular difference and implicative derivation on L, respectively. Finally, we obtain that regular difference derivations coincide with direct product decompositions of MV-algebras.
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Meng, Biao Long, and Xiao Long Xin. "A Note of Filters in Effect Algebras." Chinese Journal of Mathematics 2013 (November 10, 2013): 1–4. http://dx.doi.org/10.1155/2013/570496.

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We investigate relations of the two classes of filters in effect algebras (resp., MV-algebras). We prove that a lattice filter in a lattice ordered effect algebra (resp., MV-algebra) does not need to be an effect algebra filter (resp., MV-filter). In general, in MV-algebras, every MV-filter is also a lattice filter. Every lattice filter in a lattice ordered effect algebra is an effect algebra filter if and only if is an orthomodular lattice. Every lattice filter in an MV-algebra is an MV-filter if and only if is a Boolean algebra.
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Alshehri, N. O. "Derivations of MV-Algebras." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–7. http://dx.doi.org/10.1155/2010/312027.

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We introduce the notion of derivation for an MV-algebra and discuss some related properties. Using the notion of an isotone derivation, we give some characterizations of a derivation of an MV-algebra. Moreover, we define an additive derivation of an MV-algebra and investigate some of its properties. Also, we prove that an additive derivation of a linearly ordered MV-algebral is an isotone.
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Borzooei, R. A., Akefe Radfar, and Sogol Niazian. "Relationship Between Hyper MV -algebras and Hyperlattices." Annals of West University of Timisoara - Mathematics and Computer Science 54, no. 2 (December 1, 2016): 75–94. http://dx.doi.org/10.1515/awutm-2016-0016.

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Abstract Sh. Ghorbani, et al. [9], generalized the concept of MV -algebras and defined the notion of hyper MV -algebras. Now, in this paper, we try to prove that any hyper MV -algebra is a hyperlattice. First we prove that any hyper MV -algebra that satisfies the semi negation property is a hyperlattice. Then with a computer program, we show that any hyper MV -algebra of order less than 6, is a hyperlattice. Finally, we claim that this result is correct for any hyper MV -algebra.
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Dvurečenskij, Anatolij. "Pseudo MV-algebras are intervals in ℓ-groups." Journal of the Australian Mathematical Society 72, no. 3 (June 2002): 427–46. http://dx.doi.org/10.1017/s1446788700036806.

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AbstractWe show that any pseudo MV-algebra is isomorphic with an interval Γ(G, u), where G is an ℓ-group not necessarily Abelian with a strong unit u. In addition, we prove that the category of unital ℓ-groups is categorically equivalent with the category of pseudo MV-algebras. Since pseudo MV-algebras are a non-commutative generalization of MV-algebras, our assertions generalize a famous result of Mundici for a representation of MV-algebras by Abelian unital ℓ-groups. Our methods are completely different from those of Mundici. In addition, we show that any Archimedean pseudo MV-algebra is an MV-algebra.
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Chajda, Ivan, and Helmut Länger. "Residuation in non-associative MV-algebras." Mathematica Slovaca 68, no. 6 (December 19, 2018): 1313–20. http://dx.doi.org/10.1515/ms-2017-0181.

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Abstract It is well known that every MV-algebra can be converted into a residuated lattice satisfying divisibility and the double negation law. In a previous paper the first author and J. Kühr introduced the concept of an NMV-algebra which is a non-associative modification of an MV-algebra. The natural question arises if an NMV-algebra can be converted into a residuated structure, too. Contrary to MV-algebras, NMV-algebras are not based on lattices but only on directed posets and the binary operation need not be associative and hence we cannot expect to obtain a residuated lattice but only an essentially weaker structure called a conditionally residuated poset. Considering several additional natural conditions we show that every NMV-algebra can be converted in such a structure. Also conversely, every such structure can be organized into an NMV-algebra. Further, we study an a bit more stronger version of an algebra where the binary operation is even monotone. We show that such an algebra can be organized into a residuated poset and, conversely, every residuated poset can be converted in this structure.
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Belluce, L. P., and A. Di Nola. "Simplicial structures in MV-algebras and logic." Journal of Symbolic Logic 72, no. 2 (June 2007): 584–600. http://dx.doi.org/10.2178/jsl/1185803624.

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Classical logic, as is well known, can be analyzed in a great part by algebraic methods using the Lindenbaum algebra obtained from the formal system. For example the completeness theorem for this logic becomes equivalent to the semisimplicity of the obtained Lindenbaum algebra.Since Chang [4, 5], Łukasiewicz logic has also been analyzed algebraically through the associated Lindenbaum type algebra, that is the algebra of equivalence classes obtained from the relation of provable equivalence. In this case this algebra is an MV-algebra [4]. Once again logical notions have an algebraic counterpart, for example, completeness relates strongly to semisimplicity [4, 5]. However, unlike the classical case where the algebras in question are Boolean and always semisimple, not all MV-algebras are semisimple. This fact, in a sense, enriches the theory of MV-algebras.Now every MV-algebra can be considered a Lindenbaum type algebra, namely an algebra associated to Łukasiewicz logic with additional axioms. Thus we can carry over to any MV-algebra various logical notions such as (in) completeness, consistency, satisfiability, etc.Two important logical notions are those of “formal consequence” and “semantical consequence”. The former just says that a wff α is deducible from a set of wff via the axioms and rules of inference, while the latter just says that every evaluation that “satisfies” all the members of also “satisfies” α.Informally call these relations F, S respectively; consider them as binary relations, Fα and Sα.Now the completeness theorem just states F = S. Thus we can talk about an MV-algebra being “complete” provided the associated relations F, S are equal.
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Dissertations / Theses on the topic "MV - algebre"

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Ferraioli, Anna Rita. "Lukasiewicz logic: algebras and sheaves." Doctoral thesis, Universita degli studi di Salerno, 2011. http://hdl.handle.net/10556/173.

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2009 - 2010
Classical logic arose from the need to study forms and laws of the human reasoning. But soon, it came out the di culties of classical logic to formalize uncertain events and vague concepts, for which it is not possible to assert if a sentence is true or false. In order to overcome these limits, at the beginning of the last century, non classical logics were introduced. In these logic it fails at least one among the basic principles of classical logic. For example, cutting out the principle of truth functionality (the true value of a sentence only depends on the truth values of its component more simpler sentences), we obtain modal logics for which the truth value of a sentence depends on the context where we are. In this case, the context is seen as a possible world of realization. Cutting out the principle of bivalence, we obtain many-valued logics instead. The rst among classical logician not to accept completely the principle of bivalence was Aristotele, who is, however, considered the father of classical logic. Indeed, Aristotele presented again the problem of futuri contingenti1 introduced by Diodorus Cronus as exception to the principle of bivalence (see Chapter 9 in his De Intepretatione). The \futuri contingenti" are sentences talking about future events for which it is not possible to say if they are true or false. However, Aristotele didn't make up a system of many-valued logic able to overcome classical logic's limits. [edited by author]
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Russo, Anna Carla. "MV-algebras, grothendieck toposes and applications." Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC029.

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Dans le cadre de la théorie des topos, nous généralisons deux équivalences classiques qui s'inscrivent dans le domaine des MV-algèbres: l'équivalence de Mundici entre la catégorie des MV-algèbres et celle des groupes abéliennes réticulés (1-groupes) avec unité forte et l'équivalence de Di Nola-Lettieri entre la catégorie des MV-algèbres parfaites et celle des 1-groupes. Ces généralisations produisent deux équivalences de Morita; l'une entre la théorie MV des MV-algèbres et la théorie Lu des 1-groupes avec unité forte et l'autre entre la théorie P des MV-algèbres parfaites et la théorie L des 1-groupes. Les deux équivalences de Morita nous permet d'appliquer la technique 'topos comme ponts' pour transférer des propriétés et des résultats d'une théorie à l'autre, en obtenant des nouvelles connaissances sur ces théories. Parmi elles, nous mentionnons une correspondance biunivoque entre les extensions géométriques de MV et celles de Lu, une forme de complétude et de compacité de la théorie infinitaire Lu, trois niveaux différents de bi-interprétabilitité entre la théorie P et la théorie L et un théorème de représentation pour les objets finiment présentables de la variété de Chang comme produits finis de MV-algèbres parfaites. Nous montrons ensuite que l'équivalence de Morita, résultant de l'équivalence de Di Nola-Lettieri, est seulement l'une de la classe des équivalences de Morita que nous établissons entre les théories des MV-algèbres locales dam des variétés propres des MV-algèbres et les appropriées extensions de la théorie des 1-groupes. En outre, nous généralisons dans ce cadre les résultats de représentation obtenus dans le cas de la variété de Chang
In the thesis we generalize to a topos-theoretic setting two classical equivalences arising in the field of MV-algebras: Mundici's equivalence between the category of MV-algebras and the that of lattice-ordered abelian groups (1-groups, for short) with strong unit and Di Nola-Lettieri's equivalence between the category of perfect MV-algebras and that of 1-groups. These generalizations yield respectively a Morita-equivalence between the theory MV of MV-algebras and the theory Lu of 1-groups with strong unit and one between the theory P of perfect MV-algebras and the theory L of 1-groups. These Morita-equivalences allow us to apply the `bridge technique' whence to transfer properties and results from one theory to the other, obtaining new insights on the theories which are not visible by using classical techniques. Among these results, we mention a bijective correspondence between the geometric extensions of the theory MV and those of the theory Lu, a form of completeness and compactness for the infinitary theory Lu, three different levels of bi-interpretabilitity between the theory P and the theory L and a representation theorem for the finitely presentable objects of Chang's variety as finite products of perfect MV-algebras. We then show that the Morita-equivalence arising from Di Nola-Lettieri's equivalence is just one of a whole class of Morita¬equivalences that we establish between theories of local MV-algebras in proper varieties of MV-algebras and appropriate extensions of the theory of 1-groups. Furthermore, we generalize to this setting the representation results obtained in the case of Chang's variety
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Russo, Anna Carla. "MV-algebras, Grothendieck toposes and applications." Doctoral thesis, Universita degli studi di Salerno, 2016. http://hdl.handle.net/10556/2308.

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2014 - 2015
This thesis is a contribution to the research program ‘toposes as bridges’ introduced in [12], which aims at developing the unifying potential of the notion of Grothendieck topos as a means for relating different mathematical theories to each other through topos-theoretic invariants. The general methodology outlined therein is applied here to study already existing categorical equivalences of particular interest arising in the field of many-valued logics and also to produce new ones. The original content of the disseration is contained in [22], [21] and [23]... [edited by Author]
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Lu, Weiyun. "Topics in Many-valued and Quantum Algebraic Logic." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35173.

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Introduced by C.C. Chang in the 1950s, MV algebras are to many-valued (Łukasiewicz) logics what boolean algebras are to two-valued logic. More recently, effect algebras were introduced by physicists to describe quantum logic. In this thesis, we begin by investigating how these two structures, introduced decades apart for wildly different reasons, are intimately related in a mathematically precise way. We survey some connections between MV/effect algebras and more traditional algebraic structures. Then, we look at the categorical structure of effect algebras in depth, and in particular see how the partiality of their operations cause things to be vastly more complicated than their totally defined classical analogues. In the final chapter, we discuss coordinatization of MV algebras and prove some new theorems and construct some new concrete examples, connecting these structures up (requiring a detour through effect algebras!) to boolean inverse semigroups.
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LEDDA, ANTONIO. "Logical and algebraic structures from Quantum Computation." Doctoral thesis, Università degli Studi di Cagliari, 2008. http://hdl.handle.net/11584/265966.

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The main motivation for this thesis is given by the open problems regarding the axiomatisation of quantum computational logics. This thesis will be structured as follows: in Chapter 2 we will review some basics of universal algebra and functional analysis. In Chapters 3 through 6 the fundamentals of quantum gate theory will be produced. In Chapter 7 we will introduce quasi-MV algebras, a formal study of a suitable selection of algebraic operations associated with quantum gates. In Chapter 8 quasi-MV algebras will be expanded by a unary operation hereby dubbed square root of the inverse, formalising a quantum gate which allows to induce entanglement states. In Chapter 9 we will investigate some categorial dualities for the classes of algebras introduced in Chapters 7 and 8. In Chapter 10 the discriminator variety of linear Heyting quantum computational structures, an algebraic counterpart of the strong quantum computational logic, will be considered. In Chapter 11, we will list some open problems and, at the same time, draw some tentative conclusions. Lastly, in Chapter 12 we will provide a few examples of the previously investigated structures.
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ABBADINI, MARCO. "ON THE AXIOMATISABILITY OF THE DUAL OF COMPACT ORDERED SPACES." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/812809.

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We prove that the category of Nachbin's compact ordered spaces and order-preserving continuous maps between them is dually equivalent to a variety of algebras, with operations of at most countable arity. Furthermore, we show that the countable bound on the arity is the best possible: the category of compact ordered spaces is not dually equivalent to any variety of finitary algebras. Indeed, the following stronger results hold: the category of compact ordered spaces is not dually equivalent to (i) any finitely accessible category, (ii) any first-order definable class of structures, (iii) any class of finitary algebras closed under products and subalgebras. An explicit equational axiomatisation of the dual of the category of compact ordered spaces is obtained; in fact, we provide a finite one, meaning that our description uses only finitely many function symbols and finitely many equational axioms. In preparation for the latter result, we establish a generalisation of a celebrated theorem by D. Mundici: our result asserts that the category of unital commutative distributive lattice-ordered monoids is equivalent to the category of what we call MV-monoidal algebras. Our proof is independent of Mundici's theorem.
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Books on the topic "MV - algebre"

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Mundici, D. Advanced Łukasiewicz calculus and MV-algebras. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-0840-2.

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service), SpringerLink (Online, ed. Advanced Łukasiewicz calculus and MV-algebras. Dordrecht: Springer Science+Business Media B.V., 2011.

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Mundici, D. Advanced Łukasiewicz calculus and MV-algebras. Springer, 2011.

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Mundici, D. Advanced Łukasiewicz calculus and MV-algebras. Springer, 2013.

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Book chapters on the topic "MV - algebre"

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Cignoli, Roberto L. O., Itala M. L. D’Ottaviano, and Daniele Mundici. "Free MV-algebras." In Algebraic Foundations of Many-Valued Reasoning, 51–76. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9480-6_4.

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Di Nola, Antonio, Revaz Grigolia, and Esko Turunen. "MV-Algebras: Generalities." In Fuzzy Logic of Quasi-Truth: An Algebraic Treatment, 27–32. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30406-9_4.

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Di Nola, Antonio, Revaz Grigolia, and Esko Turunen. "Local MV-Algebras." In Fuzzy Logic of Quasi-Truth: An Algebraic Treatment, 33–36. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30406-9_5.

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Di Nola, Antonio, Revaz Grigolia, and Esko Turunen. "Perfect MV-Algebras." In Fuzzy Logic of Quasi-Truth: An Algebraic Treatment, 37–46. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30406-9_6.

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Belluce, L. P., Antonio Di Nola, and Ada Lettieri. "Symmetric MV-Algebras." In Lecture Notes in Computer Science, 30–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-75939-3_3.

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Dvurečenskij, Anatolij, and Sylvia Pulmannová. "MV-algebras and QMV-algebras." In New Trends in Quantum Structures, 129–89. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-017-2422-7_3.

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Dvurečenskij, Anatolij, and Omid Zahiri. "EMV-Algebras—Extended MV-Algebras." In Trends in Logic, 107–32. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52163-9_7.

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Cignoli, Roberto L. O., Itala M. L. D’Ottaviano, and Daniele Mundici. "Varieties of MV-algebras." In Algebraic Foundations of Many-Valued Reasoning, 157–78. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9480-6_9.

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Riečan, Beloslav, and Tibor Neubrunn. "Probability on MV algebras." In Integral, Measure, and Ordering, 183–212. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8919-2_9.

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Belluce, L. P. "α-Complete MV-Algebras." In Non-Classical Logics and their Applications to Fuzzy Subsets, 7–21. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0215-5_2.

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Conference papers on the topic "MV - algebre"

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Leustean, Ioana. "The Tensor PMV-algebra of an MV-algebra." In 2011 IEEE 41st International Symposium on Multiple-Valued Logic (ISMVL). IEEE, 2011. http://dx.doi.org/10.1109/ismvl.2011.37.

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Bakhshi, Mahmood. "Tense pseudo MV-algebras." In 2015 4th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS). IEEE, 2015. http://dx.doi.org/10.1109/cfis.2015.7391675.

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Di Nola, Antonio, and Giacomo Lenzi. "On semirings and MV-algebras." In 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2017. http://dx.doi.org/10.1109/fuzz-ieee.2017.8015378.

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Cheng, Xiao-Yun, Xiao-Long Xin, and Jun-Tao Wang. "Fuzzy stabilizers in MV-algebras." In 2017 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD). IEEE, 2017. http://dx.doi.org/10.1109/fskd.2017.8392921.

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Di Nola, Antonio, and Ioana Leustean. "Riesz MV-algebras and their logic." In 7th conference of the European Society for Fuzzy Logic and Technology. Paris, France: Atlantis Press, 2011. http://dx.doi.org/10.2991/eusflat.2011.125.

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Liu, Xiujuan, Weifeng Du, Dongfu Fang, and Xiumin Liu. "Soft sets and soft MV-algebras." In 2012 2nd International Conference on Applied Robotics for the Power Industry (CARPI 2012). IEEE, 2012. http://dx.doi.org/10.1109/carpi.2012.6356425.

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GIUNTINI, ROBERTO. "AN INDEPENDENT AXIOMATIZATION OF QUANTUM MV ALGEBRAS." In Historical Analysis and Open Questions. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812793560_0017.

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Zhan, Jianming, and Young Bae Jun. "Generalized Fuzzy Ideals of Pseudo MV-Algebras." In 2010 2nd International Workshop on Intelligent Systems and Applications (ISA). IEEE, 2010. http://dx.doi.org/10.1109/iwisa.2010.5473587.

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Forouzesh, F., and A. Borumand Saeid. "Some results in primary ideals of MV-algebras." In 2014 Iranian Conference on Intelligent Systems (ICIS). IEEE, 2014. http://dx.doi.org/10.1109/iraniancis.2014.6802539.

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Liu, Jianming, and Wenjuan Chen. "A non-commutative generalization of quasi-MV algebras." In 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2016. http://dx.doi.org/10.1109/fuzz-ieee.2016.7737677.

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