Summary
Rough sets were originally defined in the presence of an equivalence relation. This concept is applied to several cases where the equivalence relation, or equivalently, the partition, is replaced with several relations or with a covering. Slowinski and Vanderpooten [1] extended the rough set to a case in which an equivalence relation is replaced with a similarity relation (see also Greco et al. [2]). Yao and Lin [3] and Yao [4, 5] discussed rough sets under various kinds of extended equivalence relations. Bonikowski et al. [6] investigated rough sets under a covering which is an extension of a partition. Inuiguchi and Tanino [7] have also considered rough sets under a similarity relation and a covering. Greco et al. [2] defined rough sets under an ordering relation and showed the importance of their approach in multicriteria decision making problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R. Slowinski, D. Vanderpooten. A generalized definition of rough approximations based on similarity.IEEE Transactions on Data and Knowledge Engineering12(2): 331–336, 2000.
S. Greco, B. Matarazzo, R. Slowinski. The use of rough sets and fuzzy sets in MCDM. In T. Gal, T. J. Stewart, T. Hanne, editorsMulticriteria Decision Making: Advances in MCDM Models Algorithms,Theory and Applications14.1–14.59, Kluwer, Boston, 1999.
Y.Y. Yao, T. Y. Lin. Generalization of rough sets using modal logics.International Journal of Intelligent Automation and Soft Computing2(2): 103–120, 1996.
Y.Y. Yao. Two views of the theory of rough sets in finite universes.International Journal of Approximate Reasoning15: 291–317, 1996.
Y.Y. Yao. Relational interpretations of neighborhood operators and rough set approximation operators.Information Sciences111: 239–259, 1998.
Z. Bonikowski, E. Bryniarski, and U. Wybraniec-Skardowska. Extensions and intensions in the rough set theory.Information Sciences107: 149–167, 1998.
M. Inuiguchi, T. Tanino. On rough sets under generalized equivalence relations. InProceedings of the International Workshop on Rough Sets Theory and Granular Computing(RSTGC 2001), vol. 5(1/2) of theBulletin of International Rough Set Society, 167–171, 2001.
A. Nakamura. Fuzzy rough sets.Notes on Multiple-Valued Logic in Japan9(8): 1–8, 1998.
D. Dubois, H. Prade. Rough fuzzy sets and fuzzy rough sets.International Journal of General Systems17: 191–209, 1990.
D. Dubois, H. Prade. Putting rough sets and fuzzy sets together. In R. Slowinski, editorIntelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory203–232, Kluwer, Dordrecht, 1992.
A.M. Radzikowska, E.E. Kerre. Fuzzy rough sets revisited. InProceedings of the 5th European Conference on Fuzzy Information Technology (EUFIT’99)CD-ROM file cd 1–3–12679p), Verlag Mainz, Aachen, 1999.
L.A. Zadeh. A fuzzy-set theoretic interpretation of linguistic hedges.Journal of Cybernetics2(2): 4–34, 1972.
D. Dubois, H.Prade. Fuzzy sets in approximate reasoning, part 1: Inference with possibility distributions.Fuzzy Sets and Systems40: 143–202, 1991.
.M. Inuiguchi, M. Sakawa. On the closure of generation processes of implication functions from a conjunction function. In T. Yamakawa, G. Matsumoto, editorsMethodologies for the Conception Design and Application of Intelligent Systems: Proceedings of the 4th International Conference on Soft Computing,Vol.1, 327–330, World Scientific, Singapore, 1996.
M. Inuiguchi, Y. Kume. Necessity measures defined by level set inclusions: Nine kinds of necessity measures and their properties.International Journal of General Systems22:245–275,1994.
M. Inuiguchi, T. Tanino. (2000) Necessity measures and parametric inclusion relations of fuzzy sets.Fundamenta Informaticae42(3/4): 279–302, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Inuiguchi, M., Tanino, T. (2004). New Fuzzy Rough Sets Based on Certainty Qualification. In: Pal, S.K., Polkowski, L., Skowron, A. (eds) Rough-Neural Computing. Cognitive Technologies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18859-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-18859-6_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62328-8
Online ISBN: 978-3-642-18859-6
eBook Packages: Springer Book Archive