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A propositional logic PRL for rough sets was proposed in [1]. In this paper, we initially introduce the concepts of rough (upper, lower) truth degrees on the set of formulas in PRL. Then, by grading the rough equality relations, we propose the concepts of rough (upper, lower) similarity degree. Finally, three different pseudo-metrics on the set of rough formulas are obtained, and thus an approximate reasoning mechanism is established.
Wydawca
Czasopismo
Rocznik
Tom
Strony
223--239
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
Bibliografia
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- [2] Pawlak, Z.: Rough sets. International Journal of Computer and InformationSciences 11(5): 341-356, 1982.
- [3] Pawlak, Z.: Rough sets−T heoretical aspects of reasoning about data. Knowledge academic publishers, 1991.
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- [6] Grzymala-Busse, J.: Mining numerical data- A rough set approach. Transactions on Rough Sets, XI 5946: 1-13, 2010.
- [7] Pawlak, Z.: Rough logic. Bull. Polish Acad. Sc. (Tech. Sc.), 35: 253-258, 1987.
- [8] Orlowska, E.: Kripke semantics for knowledge representation logics. Studia Logica, XLIX: 255-272, 1990.
- [9] Vakarelov, D.: A modal logic for similarity relations in Pawlak knowledge representaion systems. Fundamenta Informaticae, 15: 61-79, 1991.
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- [11] Duentsch, I.: A logic for rough sets. T heoretical Computer Science, 179: 427-436, 1997.
- [12] Chakrabotry,M.: Rough consequence. Bull. Polish Acad. Sc.(Math.), 41(4): 299-304, 1993.
- [13] Dai, J.: Logic for rough sets with rough double stone algebraic semantics. Lecture Notes in Computer Science, 3641: 141-148, 2005.
- [14] Banerjee, M.: Logic for rough truth. Fundamenta Informaticae, 71(2-3): 139-151, 2006.
- [15] Pagliani, P., Chakraborty,M. A geometry of approximation. Rough set theory : logic, algebra and topology of conceptual patterns. Springer, 2008.
- [16] Banerjee, M.: Propositional logic from rough set theory. Transactions on Rough Sets, VI: 1-25, 2007.
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- [19] Pavelka, J.: On fuzzy logic I, II, III, Zeitschr. Math. Logik Grund. d. Math. 25: 45-72, 119-134, 447-464, 1979.
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- [26] Chakraborty,M., Banerjee, M.: Rough consequence. Bull. Polish Acad., 41(4): 299-304, 1993.
- [27] Chakraborty,M.: Graded consequence: further studies. Journal of Applied Nonclassical Logic, 5:227-237, 1994.
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Bibliografia
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bwmeta1.element.baztech-article-BUS8-0021-0005