Transactions on Rough Sets II : Rough Sets and Fuzzy Sets

James F. Peters

ISBN 10: 3540239901 / ISBN 13: 9783540239901

Published by Springer, Springer Spektrum, 2004

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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, 1998).

Seller Inventory # 9783540239901

Bibliographic Details

• Title: Transactions on Rough Sets II : Rough Sets and Fuzzy Sets
• Publisher: Springer, Springer Spektrum
• Publication Date: 2004
• Language: English
• ISBN 10: 3540239901
• ISBN 13: 9783540239901
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 21D millimeters 235 millimeters width by 155 millimeters height by 21 millimeters depth
• Weight: 575 grams

About this title

Synopsis

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, 1998).