Relative sets and rough sets

Amin Mousavi; Parviz Jabedar-Maralani

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 3, page 637-653
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Mousavi, Amin, and Jabedar-Maralani, Parviz. "Relative sets and rough sets." International Journal of Applied Mathematics and Computer Science 11.3 (2001): 637-653. <http://eudml.org/doc/207524>.

@article{Mousavi2001,
abstract = {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.},
author = {Mousavi, Amin, Jabedar-Maralani, Parviz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {interval sets; multi-valued logic; knowledge representation; rough sets; set theory; data analysis; Belnap's four-valued logic; relative sets; approximation space; communication among agents},
language = {eng},
number = {3},
pages = {637-653},
title = {Relative sets and rough sets},
url = {http://eudml.org/doc/207524},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Mousavi, Amin
AU - Jabedar-Maralani, Parviz
TI - Relative sets and rough sets
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 3
SP - 637
EP - 653
AB - 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.
LA - eng
KW - interval sets; multi-valued logic; knowledge representation; rough sets; set theory; data analysis; Belnap's four-valued logic; relative sets; approximation space; communication among agents
UR - http://eudml.org/doc/207524
ER -

References

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  1. Arieli O. and Avron A. (1998): The value of the four values. - Artif.Intell., Vol.102, pp.97-141. Zbl0928.03025
  2. Belnap N.D. (1977a): How a computer should think, In: Contemporary Aspects of Philosophy (G. Ryle, Ed.). - Oriel Press, pp.30-56. 
  3. 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. 
  4. Fitting M.C. (1989): Bilattices and the theory of truth. - J. Phil. Logic, Vol.18, pp.225-256. Zbl0678.03028
  5. Fitting M.C. (1990): Bilattices in logic programming. - Proc. 20-th Int. Symp. Multiple-Valued Logic, IEEE Press, pp.238-246. 
  6. Ginsberg M.L. (1986): Multi-valued logic. - Proc. 5-th Nat. Conf. Artificial Intelligence AAAI-86, Morgan Kaufman Publishers, pp.243-247. 
  7. Ginsberg M. L. (1988): A uniform approach to reasoning in artificial intelligence. - Comp. Intell., Vol.4, pp.265-316. 
  8. Lin S.Y.T. and Lin Y.F. (1981): Set Theory with Applications. - Mariner Publishing Company. 
  9. 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). 
  10. 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). 
  11. Pawlak Z. (1982): Rough sets. - Int. J. Inf. Comp. Sci., Vol.11, No.341, pp.145-172. 
  12. Pawlak Z. (1991): Rough Sets: Theoretical Aspects of Reasoning About Data. - Boston: Kluwer. Zbl0758.68054
  13. Pawlak Z. (1996): Why rough sets?. - Proc. IEEE Int. Conf. Fuzzy Systems, New Orleans, La., USA, pp.738-743. 
  14. Pawlak Z. (1997): Vagueness-A rough set view, In: Structures in Logic and Computer Science. - Springer, pp.106-117. 
  15. Pawlak Z. (1998a): Reasoning about data-A rough set perspective, In: Rough Sets and Current Trends in Computing. - Springer, pp.25-34. 
  16. Pawlak Z. (1998b): Granularity of knowledge, indiscernibility and rough sets. - Proc. 1998 IEEE Int. Conf. Computational Intelligence, Vol.1, pp.106-110. 
  17. Rodrigues O. et al. (1998): A translation method for Belnap's logic. - Imperial College Res. Rep. DoC No.987, London. 
  18. Schoter A. (1996): Evidential bilattice logic and lexical inference. - J. Logic. Lang. Inform., Vol.5, pp.65-101. Zbl0851.03008
  19. Yao Y.Y. (1993): Interval-set algebra for qualitative knowledge representation. - Proc. 5-th Int. Conf. Computing and Information, pp.370-375. 
  20. Yao Y.Y. (1996a): Two views of the theory of rough sets in finite universes. - Int. J. Approx. Reason., Vol.15, pp.291-317. Zbl0935.03063
  21. Yao Y. Y. (1996b): Stratified rough sets and granular computing. - Proc. 18-th Int. Conf. North American Fuzzy Information, pp.800-804. 

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