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A note on divisible discrete triangular norms | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 7، دوره 19، شماره 1، فروردین و اردیبهشت 2022، صفحه 73-81 اصل مقاله (163.93 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2022.6552 | ||
| نویسندگان | ||
| F. Kouchakinejad* 1؛ A. Stupnanova2؛ A. Seliga2 | ||
| 1Department of Statistics, Faculty of Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| 2Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinskeho 11, 810 05 Bratislava, Slovakia | ||
| چکیده | ||
| Triangular norms and conorms on [0,1] as well as on finite chains are characterized by 4 independent properties, namely by the associativity, commutativity, monotonicity and neutral element being one of extremal points of the considered domain (top element for t-norms, bottom element for t-conorms). In the case of [0,1]domain, earlier results of Mostert and Shields on I-semigroups can be used to relax the latest three properties significantly, once the continuity of the underlying t-norm or t-conorm is considered. The aim of this short note is to show a similar result for finite chains, we significantly relax 3 basic properties of t-norms and t-conorms (up to the associativity) when the divisibility of a t-norm or of a t-conorm is considered. | ||
| کلیدواژه‌ها | ||
| Discrete I-semigroup؛ divisible t-norm؛ divisible t-conorm؛ finite chain | ||
| مراجع | ||
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[1] E. Asici, R. Mesiar, Alternative approaches to obtain t-norms and t-conorms on bounded lattices, Iranian Journal of Fuzzy Systems, 17(4) (2020), 121-138.
[2] G. D. Çayli, Some methods to obtain t-norms and t-conorms on bounded lattices, Kybernetika, 55(2) (2019), 273-294.
[3] K. Chvalovský, On the independence of axioms in BL and MTL, Fuzzy Sets and Systems, 197 (2012), 123-129.
[4] P. Cintula, Short note: On the redundancy of axiom (A3) in BL and MT L, Soft Computing, 9 (2005), 942, Doi: 10.1007/s00500-004-0445-9.
[5] L. Godo, C. Sierra, A new approach to connective generation in the framework of expert systems using fuzzy logic, In Proceedings of the XVIIIth ISMVL, Palma, (1988), 157-162.
[6] S. Gottwald, Mehrwertige logik, eine einführung in theorie und anwendungen, Akademie-Verlag, Berlin, 1989.
[7] P. Hájek, Basic fuzzy logic and BL-algebras, Soft Computing, 2 (1998), 124-128.
[8] E. P. Klement, R. Mesiar, E. Pap, Triangular norms, In Trends in Logic, 8, Dordrecht, (2000). ISBN: 978- 9048155071.
[9] S. Lehmke, Fun with automated proof search in basic propositional fuzzy logic, In Abstracts of 17th International Conference FSTA, (2004), 78-80.
[10] C. H. Ling, Representation of associative functions, Publicationes Mathematicae Debrecen, 12 (1965), 189-212.
[11] J. Łukasiewicz, On three-valued logic, Ruch Filozoficzny, 5 (1920), 170-171.
[12] J. Łukasiewicz, Philosophical remarks on many-valued systems of propositional logic, In Jan Lukasiewicz Selected Works, (1930), 51-77.
[13] J. Łukasiewicz, A. Tarski, Untersuchungenüber den Aussagenkalkül, Comptes Rendus des Séances de la Sociélé des Scierices et des Lettres des Varsovie Classe III, 23 (1930), 30-50.
[14] G. Mayor, J. Torrens, Triangular norms on discrete settings, In Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, Elsevier Science BV, (2005), 189-230, ISBN 0-444-51814-2.
[15] K. Menger, Statistical metrics, Proceedings of the National Academy of Sciences of the United States of America, 28 (1942), 535-537.
[16] P. S. Mostert, A. L. Shields, On the structure of semigroups on a compact manifold with boundary, Annals of Mathematics, 65 (1957), 117-143.
[17] E. Palmeira, B. Bedregal, R. Mesiar, J. Fernandez, A new way to extend t-norms, t-conorms and negations, Fuzzy Sets and Systems, 240 (2014), 1-21.
[18] J. Pavelka, On fuzzy logic I: Many-valued rules of inference, Mathematical Logic Quarterly, 25 (1979), 45-52.
[19] B. Schweizer, A. Sklar, Espaces métriques aléatories, Comptes Rendus Hebdomadaires des Seances de l’Academie des Sciences, 247 (1958), 2092-2094.
[20] B. Schweizer, A. Sklar, Statistical metric spaces, Pacific Journal of Mathematics, 10 (1960), 313-334.
[21] R. R. Yager, Generalized triangular norm and conorm aggregation operators on ordinal spaces, International Journal of General Systems, 32 (2003), 475-490.
[22] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. | ||
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