Applications of Fuzzy-Rough Classifications to Logics
From a point of view of handling imperfect knowledge like uncertainty, vagueness, imprecision, etc., a concept of fuzzy-rough classifications is introduced. This is a notion defined as a kind of modification of the rough classifications. Two logics based on the fuzzy-rough classifications are proposed, and various properties are examined as compared with the indiscernibility relations. Also, decision procedures for the proposed logics are given in the tableau style which is useful in automated reasoning.
Unable to display preview. Download preview PDF.
- D. Dubois and H. Prade: Rough fuzzy sets and fuzzy rough sets, Proc. of Internat. Conf. Fuzzy Sets in Informatics, Moscow, ( Sept. 1988 ), 20–23.Google Scholar
- L. Farinas del Cerro and H. Prade: Rough sets, twofold fuzzy sets and modal logics. Fuzziness in indiscemibility and partial information, in: A.Di Nola and A.G. Ventre (ed.), The Math. of Fuzzy Systems, Verlag TÜV Rheinland, Köln, (1986), 103–120.Google Scholar
- L. Farinas del Cerro and Andreas Herzig: A modal analysis of possibility theory, Lecture Notes in Computer Science,(Symbolic and Quantitative Approaches to Uncertainty), 548, 58–62.Google Scholar
- G. Gargov: Two completeness theorems in the logic for data analysis ICS PAS Reports 581 Polish Academy of Sciences(1986) Google Scholar
- M. Krynicki and H-P. Tuschik: An axiomatization of the logic with the rough quantifier J. of Symbolic Logic56, (1991), 608–617 Google Scholar
- A. Nakamura: Topological soft algebra for the S5-modal fuzzy logic Proc. of the 21st ISMVL May 26–29 1991 Victoria80–84 Google Scholar
- A. Nakamura: A logic of imprecise monadic predicates and its relation to the S5-modal fuzzy logic, Lecture Notes in Computer Science,(Symbolic and Quantitative Approaches to Uncertainty), 548, 254–261.Google Scholar
- E. Orlowska: Logic of indiscemibility relation Bulletin of the Polish Academy of Sciences Mathematics(1985), 475–485 Google Scholar
- Z. Pawlak: Rough sets International J. of Information and Computer Sciences 11(1982), 345–356 Google Scholar