Similarity MV-algebras

• Autorzy: Gerla B. , Leustean I.
• Języki publikacji: EN

Abstrakty

EN

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 MV-algebras by adding a binary operator playing the role of similarity. We further introduce the similarity ukasiewicz logic and we prove a completeness theorem.

Słowa kluczowe

EN

many-valued logics; MV-algebras; similarities

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2006
• Tom: Vol. 69, nr 3
• Strony: 287--300
• Opis fizyczny: bibliogr. 12 poz.

Twórcy

autor

Gerla B.

autor

Leustean I.

• DMI University of Salerno, Via S. Allende, 84081 Baronissi (SA), Italy,

Bibliografia

• [1] M. Baaz, Infinite-valued Gödel logics with 0-1-projections and relativizations, in P. Hájek, Ed., GÖDEL'96-Logical Foundations of Mathematics, Computer Science and Physics, Lectures Notes in Logic 6, SpringerVerlag, Berlin, 23-33, 1996.
• [2] J.L. Castro, F. Klawonn, Similarity in Fuzzy Reasoning, using Fuzzy Logic.Mathware and Soft Computing, 2: 197-228, 1995.
• [3] C.C. Chang, Algebraic analysis of many-valued logics, Trans. Amer. Math. Soc., 88: 467-490,1958.
• [4] R. Cignoli, I.M.L. D'Ottaviano, D. Mundici, Algebraic foundations of many-valued reasoning, Trends in Logic 6, Kluwer, Dordrecht, 2000.
• [5] F. Formato, G. Gerla,M. Sessa, Similarity-based unification, Fundamenta Informaticae, 41: 393-414, 2000.
• [6] G. Georgescu, A. Popescu, Concept lattices and similarity in non-commutative fuzzy logic, Fundamenta Informaticae, 53: 23-54, 2002.
• [7] P. Hajek, On very true, Fuzzy Sets and Systems, 124: 329-333, 2001.
• [8] P. Hájek. Metamathematics of Fuzzy Logic, Kluwer, Dordrecht, 1998.
• [9] D. Mundici, Nonboolean partitions and their logic, Soft Computing, 2:18-22, 1998.
• [10] E. Turunen, Mathematics behind fuzzy logic, Physica-Verlag, Heidelberg, 1999.
• [11] E. Turunen, A Łukasiewicz-style many-valued similarity reasoning. Review. in Beyond Two: Theory and Applications of Multiple Valued Logic, Melvin Fitting and Ewa Orłowska editors, 311-321, 2003.
• [12] L. Zadeh, Similarity relations and fuzzy orderings, Information Sciences, 3: 177-200, 1971.