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Abstrakty
In this paper we present some fuzzy modal operators and show their two possible applications. These operators are fuzzy generalizations of modal operators well-known in modal logics. We present an application of some compositions of these operators in approximations of fuzzy sets. In particular, it is shown how skills of candidates can be matched for selecting research projects. The underlying idea is based on the observation that fuzzy sets approximations can be viewed as intuitionistic fuzzy sets introduced by Atanassov. Distances between intuitionistic fuzzy sets, proposed by Szmidt and Kacprzyk, support the reasoning process. Also, we point out how modal operators are useful for representing linguistic hedges, that is terms like “very”, “definitely”, “rather”, or “more or less”.
Rocznik
Tom
Strony
10--20
Opis fizyczny
Bibliogr. 33 poz., rys.
Twórcy
autor
- Warsaw University of Technology, Faculty of Mathematics and Information Science, Koszykowa 75, 00-662 Warsaw, Poland
Bibliografia
- [1] K. Atanassov, “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, vol. 20, no. 1, 1986, 87–96, DOI: 10.1016/S0165-0114(86)80034-3.
- [2] K. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, Physica–Verlag, 1999, DOI: 10.1007/978-3-7908-1870-3.
- [3] M. Baczyń ski and B. Jayaram, Fuzzy Implications, Studies in Fuzziness and Soft Computing, Springer-Verlag Berlin Heidelberg, 2008, DOI: 10.1007/978-3-540-69082-5.
- [4] M. De Cock and E. E. Kerre, “Fuzzy modifiers based on fuzzy relations”, Information Sciences, vol. 160, 2004, 173–199, DOI: 10.1016/j.ins.2003.09.002.
- [5] M. De Cock, A. M. Radzikowska, and E. E. Kerre. “Modelling Linguistic Modifiers using Fuzzy Rough Structures”. In: Proceedings of 8th International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems IPMU, June 2000, Madrid, Spain, 1381–1388. Consejo Superior de Investigaciones Cientificas, 2000. ISBN 84-95479-02-8.
- [6] M. De Cock, A. M. Radzikowska, and E. E. Kerre. “A Fuzzy-Rough Approach to the Representation of Linguistic Hedges”. In: B. Bouchon-Meunier, J. Gutierrez-Rios, L. Magdalena, and R. R. Yager, eds., Technologies of Constructing Intelligent Systems, volume 2, 33–43. Physica-Verlag, Heidelberg, New York, 2002. DOI: 10.1007/978-3-7908-1797-3_3.
- [7] S. Demri and E. Orłowska, Incomplete Information: Structure, Inference, Complexity, EATCS Monographs in Theoretical Computer Science, Springer Berlin, Heidelberg, 2002, Hardcover ISBN: 978-3-540-41904-4.
- [8] I. Düntsch and G. Gediga. “Modal-Style Operators in Qualitative Data Analysis”. In: Proceedings of the 2002 IEEE International Conference on Data Mining ICDM’2002, 155–162. IEEE Computer Society Press, 2002. DOI:10.1109/ICDM.2002.1183898.
- [9] I. Düntsch and G. Gediga, “Skill set analysis in knowledge structures”, British Journal of Mathematical and Statistical Psychology, vol. 55, 2002, 361–384, DOI: 10.1348/000711002760554516.
- [10] G. Gargov, S. Passy, and T. Tinchev. “Modal Environment for Boolean Speculations”. In: D. Skordev, ed., Mathematical Logic and Applications, 253–263. Plenum Press, New York, 1987. DOI: 10.1007/978-1-4613-0897-3_17.
- [11] V. Goranko, “Modal Definability in Enriched Languages”, Notre dame Journal of formal Logic, vol. 31, no. 1, 1990, 81–105, DOI: 10.1305/ndjfl/1093635335.
- [12] I. L. Humberstone, “Inaccessible worlds”, Notre Dame Journal of Formal Logic, vol. 24, 1983, 346–352, DOI: 10.1305/ndjfl/1093870378.
- [13] E. P. Klement, R. Mesiar, and E. Pap, Triangular norms, Springer Netherlands, 2000, DOI: 10.1007/978-94-015-9540-7.
- [14] E. Orłowska, Incomplete Information: Rough Set Analysis, Studies in Fuzziness and Soft Computing, Physica Verlag, 1998, DOI: 10.1007/978-3- 7908-1888-8.
- [15] E. Orłowska, A. M. Radzikowska, and I. Rewitzky, Dualities for Structures of Applied Logics, volume 56 of Mathematical Logic and Foundations, College Publications, 2015, ISBN: 978-84890-181-0.
- [16] Z. Pawlak, “Rough Sets”, International Journal of Computer and Information Sciences, vol. 11, no. 5, 1982, 341–356, DOI: 10.1007/BF01001956.
- [17] Z. Pawlak, Rough Sets - Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, 1991, DOI: 10.1007/978-94-011-3534-4.
- [18] A. M. Radzikowska. “Fuzzy Modal-like Approximation Operations Based on Residuated Lattices”. In: Proceedings of the 11th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU, July 2-7, 2006, Paris, France, 444–451.EDK - Editions Médicales et Scientifiques, 2006.
- [19] A. M. Radzikowska, “Fuzzy Modal-like Approximation Operators Based on Double Residuated Lattices”, Journal of Applied Non–Classical Logics, vol. 16, no. 3-4, 2006, 485–506, DOI: 10.3166/jancl.16.485-506.
- [20] A. M. Radzikowska, “Duality via Truth for Information Algebras Based on De Morgan Lattices”, Fundamenta Informaticae, vol. 144, no. 1, 2016, 45–72, DOI: 10.3233/FI-2016-1323.
- [21] A. M. Radzikowska, “A Fuzzy Relation-based Approximation Techniques in Supporting Medical Diagnosis”, Journal of Automation, Mobile Robotics & Intelligent Systems, vol. 11, no. 1, 2017, 20–27, DOI: 10.14313/JAMRIS_1-2017/2.
- [22] A. M. Radzikowska and E. E. Kerre, “A comparative study of fuzy rough sets”, Fuzzy Sets and Systems, vol. 126, 2002, 137–155, DOI: 10.1016/S0165-0114(01)00032-X.
- [23] A. M. Radzikowska and E. E. Kerre. “A Fuzzy Generalization of Information Relations”. In: E. Orłowska and M. Fitting, eds., Beyond Two: Theory and Applications of Multiple-Valued Logics, volume 114 of Studies in Fuzziness and Soft Computing, 287–312. Physica-Verlag Heidelberg, 2002. DOI: 10.1007/978-3-7908-1769-0.
- [24] A. M. Radzikowska and E. E. Kerre. “Fuzzy Rough Sets Based on Residuated Lattices”. In: J. F. Peters, A. Skowron, D. Dubois, J. W. GrzymałaBusse, M. Inuiguchi, and L. Polkowski, eds., Transactions on Rough Sets II: Rough Sets and Fuzzy Sets, volume 3135 of Lecture Notes in Computer Science, 278–296. Springer-Verlag Berlin Heidelberg, 2004. DOI: 10.1007/978-3-540- 27778-1_14.
- [25] A. M. Radzikowska and E. E. Kerre. “On L-Fuzzy Rough Sets”. In: L. Rutkowski, J. H. Siekmann, R. Tadeusiewicz, and L. A. Zadeh, eds., Artificial Intelligence and Soft Computing - ICAISC 2004. Proceedings of the 7th International Conference, Zakopane, Poland, June 7-11, 2004, volume 3070 of Lecture Notes in Artificial Intelligence, 526–531. Springer Berlin Heidelberg, 2004. DOI: 10.1007/978-3-540-24844-6_78.
- [26] A. M. Radzikowska and E. E. Kerre. “An Algebraic Approach to Fuzzy Modalities”. In: O. Hryniewicz, J. Kacprzyk, and D. Kuchta, eds., Issues in Soft Computing - Decisions and Operation Research, 71–86. Akademicka Oficyna Wydawnicza EXIT, Warsaw, Poland, 2005. ISBN: 83-87674-98-2.
- [27] A. M. Radzikowska and E. E. Kerre. “Algebraic Characterisations of Some Fuzzy Information Relations”. In: O. Hryniewicz, J. Kacprzyk, and D. Kuchta, eds., Soft Computing: Foundations and Theoretical Aspects, 71–86. Akademicka Oficyna Wydawnicza EXIT, Warsaw, 2005. ISBN: 83-87674-97-4.
- [28] A. M. Radzikowska and E. E. Kerre, “Characterisations of main classes of fuzzy relations using fuzzy modal operators”, Fuzzy Sets and Systems, vol. 152, no. 2, 2005, 223–247, DOI: 10.1016/j.fss.2004.09.005.
- [29] A. M. Radzikowska and E. E. Kerre. “Fuzzy Information Relations and Operators: An Algebraic Approach Based on Residuated Lattices”. In: H. de Swart, E. Orłowska, G. Schmidt, and M. Roubens, eds., Theory and Applications of Relational Structures as Knowledge Instruments II, number 4342 in Lecture Notes in Artificial Intelligence, 162–184. Springer-Verlag, 2006. DOI: 10.1007/11964810_8.
- [30] E. Szmidt and J. Kacprzyk, “Distances between intuitionistic fuzzy sets”, Fuzzy Sets and Systems, vol. 114, no. 3, 2000, 505–518, DOI: 10.1016/S0165-0114(98)00244-9.
- [31] R. Wille. “Restructuring lattice theory: An approach based on hierarchies of concepts”. In: I. Rival, ed., Ordered sets, volume 83 of NATO Advanced Studies Institute, 445–470. Springer Netherlands, 1982. DOI: 0.1007/978-94-009-7798-3_15.
- [32] L. A. Zadeh, “Fuzzy sets”, Information and Control, vol. 8, 1965, 338–353, DOI: 10.1016/S0019-9958(65)90241-X.
- [33] L. A. Zadeh, “A Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges”, Journal of Cybernetics, vol. 2:3, 1972, 4–34, DOI: 10.1080/01969727208542910.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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