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Lattice for Rough Intervals

Year 2013, Volume: 2 Issue: 2, 39 - 46, 01.02.2013

Abstract

This paper deals with the rough interval approach onlattice theory. In the interval-set model, a pair of sets is referredto as the lower and upper bounds which define a family of sets. Asignificant difference between these concepts lies in the definitionand interpretation of their extended set-theoretic operators. Theoperators in the rough-set model are not truth-functional, whilethe operators in the interval-set model are truth-functional. Wehave showed that the collection of all rough intervals in an approximation space forms a distributive lattice. Some important resultsare also proved. Finally, an example is considered to illustratedthe paper

References

  • Z. Bonikowski, A certain conception of the calculus of rough sets, Notre Dame Journal of Formal Logic, 33: 412-421, 1992.
  • M. Chakraborty, M. Banerjee, Logic and algebra of rough sets. In: Rough Sets, Fuzzy Sets and Knowledge Discovery, W.P. Ziarko, Fei., London, Springer-Verlag, 196- 207, 1994.
  • T.Y. Lin, Q. Liu, Rough Approximate Operators.In: Rough Sets, Fuzzy Sets and Knowledge Discovery, W.P. Ziarko, Ed., London, Springer-Verlag, 256-260, 1994. [4] A. Nakamura, On a logic of information for reasoning about knowledge. In: Rough Sets, Fuzzy Sets and Knowledge Discovery, W.P. Ziarko,Ed.,London,Springer- Verlag, 186-195, 1994.
  • C.V. Negoitca, D. A. Ralescu, Applications of Fuzzy Sets to Systems Analysis, Basel: Birkh¨auser Verlag, 1975.
  • E. Orlowska, Rough set semantics for non-classical logics. In: Rough Sets, Fuzzy Sets and Knowledge Discovery, W.P. Ziarko, Fei., London, Springer-Verlag, 143- 148, 1994.
  • Z. Pawlak, Rough Sets, International Journal of Computer and Information Sci- ences, 11: 341-356, 1982.
  • Z. Pawlak, Rough sets: a new approach to vagueness. In: L.A. Zadeh and J. Kacprzyk, Eds, Fuzzy Logic for the Management of Uncertainty, New York, John Wiley and Sons, 105-118, 1992.
  • D. Rana, S.K. Roy, Rough Set Approach on Lattice, Journal of Uncertain Systems, 5(1): 72-80, 2011.
  • Y.Y. Yao, X. Li, Uncertain Reasoning With Interval-Set Algebra. In: Rough Sets, Fuzzy Sets and Knowledge Discovery, W. P. Ziarko. Ed., London, Springer-Verlag, 178-185, 1994.
  • Y.Y. Yao, Probabilistic rough set approximations, International Journal of Approx- imation Reasoning 49:, 255-271, 2008.
  • Y.Y. Yao, Interval Sets and Interval-Set Algebras, Proceedings of the 8th IEEE International Conference on Cognitive Informatics, 307-314, 2009.
Year 2013, Volume: 2 Issue: 2, 39 - 46, 01.02.2013

Abstract

References

  • Z. Bonikowski, A certain conception of the calculus of rough sets, Notre Dame Journal of Formal Logic, 33: 412-421, 1992.
  • M. Chakraborty, M. Banerjee, Logic and algebra of rough sets. In: Rough Sets, Fuzzy Sets and Knowledge Discovery, W.P. Ziarko, Fei., London, Springer-Verlag, 196- 207, 1994.
  • T.Y. Lin, Q. Liu, Rough Approximate Operators.In: Rough Sets, Fuzzy Sets and Knowledge Discovery, W.P. Ziarko, Ed., London, Springer-Verlag, 256-260, 1994. [4] A. Nakamura, On a logic of information for reasoning about knowledge. In: Rough Sets, Fuzzy Sets and Knowledge Discovery, W.P. Ziarko,Ed.,London,Springer- Verlag, 186-195, 1994.
  • C.V. Negoitca, D. A. Ralescu, Applications of Fuzzy Sets to Systems Analysis, Basel: Birkh¨auser Verlag, 1975.
  • E. Orlowska, Rough set semantics for non-classical logics. In: Rough Sets, Fuzzy Sets and Knowledge Discovery, W.P. Ziarko, Fei., London, Springer-Verlag, 143- 148, 1994.
  • Z. Pawlak, Rough Sets, International Journal of Computer and Information Sci- ences, 11: 341-356, 1982.
  • Z. Pawlak, Rough sets: a new approach to vagueness. In: L.A. Zadeh and J. Kacprzyk, Eds, Fuzzy Logic for the Management of Uncertainty, New York, John Wiley and Sons, 105-118, 1992.
  • D. Rana, S.K. Roy, Rough Set Approach on Lattice, Journal of Uncertain Systems, 5(1): 72-80, 2011.
  • Y.Y. Yao, X. Li, Uncertain Reasoning With Interval-Set Algebra. In: Rough Sets, Fuzzy Sets and Knowledge Discovery, W. P. Ziarko. Ed., London, Springer-Verlag, 178-185, 1994.
  • Y.Y. Yao, Probabilistic rough set approximations, International Journal of Approx- imation Reasoning 49:, 255-271, 2008.
  • Y.Y. Yao, Interval Sets and Interval-Set Algebras, Proceedings of the 8th IEEE International Conference on Cognitive Informatics, 307-314, 2009.
There are 11 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Dipankar Rana This is me

Sankar Kumar Roya This is me

Publication Date February 1, 2013
Published in Issue Year 2013 Volume: 2 Issue: 2

Cite

APA Rana, D., & Roya, S. K. (2013). Lattice for Rough Intervals. Journal of New Results in Science, 2(2), 39-46.
AMA Rana D, Roya SK. Lattice for Rough Intervals. JNRS. February 2013;2(2):39-46.
Chicago Rana, Dipankar, and Sankar Kumar Roya. “Lattice for Rough Intervals”. Journal of New Results in Science 2, no. 2 (February 2013): 39-46.
EndNote Rana D, Roya SK (February 1, 2013) Lattice for Rough Intervals. Journal of New Results in Science 2 2 39–46.
IEEE D. Rana and S. K. Roya, “Lattice for Rough Intervals”, JNRS, vol. 2, no. 2, pp. 39–46, 2013.
ISNAD Rana, Dipankar - Roya, Sankar Kumar. “Lattice for Rough Intervals”. Journal of New Results in Science 2/2 (February 2013), 39-46.
JAMA Rana D, Roya SK. Lattice for Rough Intervals. JNRS. 2013;2:39–46.
MLA Rana, Dipankar and Sankar Kumar Roya. “Lattice for Rough Intervals”. Journal of New Results in Science, vol. 2, no. 2, 2013, pp. 39-46.
Vancouver Rana D, Roya SK. Lattice for Rough Intervals. JNRS. 2013;2(2):39-46.


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