Relative sets and rough sets

• Autorzy: Amin Mousavi , Parviz Jabedar-Maralani
• Języki publikacji: EN

Abstrakty

EN

In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap's four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Like truth-values of Belnap's logic, relative sets have two orderings; one is an order of inclusion and the other is an order of knowledge or information. By defining a rough set as a pair of definable sets, an integrated approach to relative sets and rough sets is obtained. With this definition, we are able to define an approximation of a rough set in an approximation space, and so we can obtain sequential approximations of a set, which is a good model of communication among agents.

Słowa kluczowe

EN

interval sets; multi-valued logic; knowledge representation; rough sets; set theory; data analysis

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: 11
• Numer: 3
• Strony: 637-653

Daty

wydano

2001

otrzymano

2001-03-01

poprawiono

2001-06-01

Twórcy

autor

Amin Mousavi

• Department of Electrical and Computer Engineering, University of Tehran, P.O. Box 14395/515, Tehran, Iran

autor

Parviz Jabedar-Maralani

• Department of Electrical and Computer Engineering, University of Tehran, P.O. Box 14395/515, Tehran, Iran

Bibliografia

• Arieli O. and Avron A. (1998): The value of the four values. - Artif.Intell., Vol.102, pp.97-141.
• Belnap N.D. (1977a): How a computer should think, In: Contemporary Aspects of Philosophy (G. Ryle, Ed.). - Oriel Press, pp.30-56.
• Belnap N.D. (1977b): A useful four-valued logic, In: Modern Uses of Multiple-Valued Logic (J.M. Dunn and G. Epstein, Eds.). - D. Reidel, pp.8-37.
• Fitting M.C. (1989): Bilattices and the theory of truth. - J. Phil. Logic, Vol.18, pp.225-256.
• Fitting M.C. (1990): Bilattices in logic programming. - Proc. 20-th Int. Symp. Multiple-Valued Logic, IEEE Press, pp.238-246.
• Ginsberg M.L. (1986): Multi-valued logic. - Proc. 5-th Nat. Conf. Artificial Intelligence AAAI-86, Morgan Kaufman Publishers, pp.243-247.
• Ginsberg M. L. (1988): A uniform approach to reasoning in artificial intelligence. - Comp. Intell., Vol.4, pp.265-316.
• Lin S.Y.T. and Lin Y.F. (1981): Set Theory with Applications. - Mariner Publishing Company.
• Mousavi A. and Jabedar-Maralani P. (1999): A new approach to Belnap's four-valued logic: Relative truth-value and relative set. - Proc. 7-th Iranian Conf. Electrical Engineering, Tehran, Iran, pp.25-32 (in Persian).
• Mousavi A. and Jabedar-Maralani P. (2000): An integrated approach to relative sets and rough sets: A method for combining information tables. - Proc. 8-th Iranian Conf. Electrical Engineering, Isfahan, Iran, Vol.1, pp.237-244 (in Persian).
• Pawlak Z. (1982): Rough sets. - Int. J. Inf. Comp. Sci., Vol.11, No.341, pp.145-172.
• Pawlak Z. (1991): Rough Sets: Theoretical Aspects of Reasoning About Data. - Boston: Kluwer.
• Pawlak Z. (1996): Why rough sets?. - Proc. IEEE Int. Conf. Fuzzy Systems, New Orleans, La., USA, pp.738-743.
• Pawlak Z. (1997): Vagueness-A rough set view, In: Structures in Logic and Computer Science. - Springer, pp.106-117.
• Pawlak Z. (1998a): Reasoning about data-A rough set perspective, In: Rough Sets and Current Trends in Computing. - Springer, pp.25-34.
• Pawlak Z. (1998b): Granularity of knowledge, indiscernibility and rough sets. - Proc. 1998 IEEE Int. Conf. Computational Intelligence, Vol.1, pp.106-110.
• Rodrigues O. et al. (1998): A translation method for Belnap's logic. - Imperial College Res. Rep. DoC No.987, London.
• Schoter A. (1996): Evidential bilattice logic and lexical inference. - J. Logic. Lang. Inform., Vol.5, pp.65-101.
• Yao Y.Y. (1993): Interval-set algebra for qualitative knowledge representation. - Proc. 5-th Int. Conf. Computing and Information, pp.370-375.
• Yao Y.Y. (1996a): Two views of the theory of rough sets in finite universes. - Int. J. Approx. Reason., Vol.15, pp.291-317.
• Yao Y. Y. (1996b): Stratified rough sets and granular computing. - Proc. 18-th Int. Conf. North American Fuzzy Information, pp.800-804.