Transactions on Rough Sets II: Rough Sets and Fuzzy Sets

ISBN-13: 9783540239901 / Angielski / Miękka / 2004 / 363 str.

III James F. Peters; Andrzej Skowron; Didier DuBois

Opis

This collection of articles is devoted to fuzzy as well as rough set theories. Both theoriesarebasedonrigorousideas, methodsandtechniquesinlogic, mathem- ics, and computer science for treating problems for which approximate solutions are possible only, due to their inherent ambiguity, vagueness, incompleteness, etc. Vast areas of decision making, data mining, knowledge discovery in data, approximatereasoning, etc., aresuccessfully exploredusing methods workedout within fuzzy and rough paradigms. By the very nature of fuzzy and rough paradigms, outlined above, they are related to distinct logical schemes: it is well-known that rough sets are related to modal logicsS5andS4(Orl owska, E., Modal logics in the theory of infor- tion systems, Z. Math. Logik Grund. Math. 30, 1984, pp. 213 ?.; Vakarelov, D., Modal logics for knowledgerepresentationsystems, LNCS 363,1989, pp. 257?.) and to ?nitely-valued logics (Pagliani, P., Rough set theory and logic-algebraic structures. In Incomplete Information: Rough Set Analysis, Orlo wska, E., ed., Physica/Springer, 1998, pp. 109 ?.; Polkowski, L. A note on 3-valued rough logic accepting decision rules, Fundamenta Informaticae 61, to appear). Fuzzy sets are related to in?nitely-valued logics (fuzzy membership to degree r? 0,1]expressingtruthdegreer)(Goguen, J.A., Thelogicofinexactconcepts, Synthese18/19,1968 9, pp.325?.;Pavelka, J., OnfuzzylogicI, II, III, Z. Math. Logik Grund. Math. 25, 1979, pp. 45 ?., pp. 119 ?., pp. 454 ?.; Dubois, D., Prade, H., Possibility Theory, Plenum Press, 1988; Haj ek, P., Metamathematics of Fuzzy Logic, Kluwer

Spis treści

Feature Selection with Rough Sets for Web Page Classification.- On Learning Similarity Relations in Fuzzy Case-Based Reasoning.- Incremental versus Non-incremental Rule Induction for Multicriteria Classification.- Three Strategies to Rule Induction from Data with Numerical Attributes.- Fuzzy Transforms.- Possible Equivalence Relations and Their Application to Hypothesis Generation in Non-deterministic Information Systems.- Applications of Fuzzy Logic Functions to Knowledge Discovery in Databases.- Fuzzy Integral Based Fuzzy Switching Functions.- First Steps towards Computably-Infinite Information Systems.- Data Structure and Operations for Fuzzy Multisets.- A Non-controversial Definition of Fuzzy Sets.- Algebraic Structures for Rough Sets.- Rough Mereology as a Link between Rough and Fuzzy Set Theories. A Survey.- Fuzzy Rough Sets Based on Residuated Lattices.- Semantics of Fuzzy Sets in Rough Set Theory.- A New Proposal for Fuzzy Rough Approximations and Gradual Decision Rule Representation.- Emergent Rough Set Data Analysis.