Abstract
A problem of the optimal approximation to a fuzzy tolerance relation is discussed in this paper. Specifically, our aim is to get the optimal fuzzy equivalence relation from a given fuzzy tolerance relation. Firstly, we discuss the relationship between the covering and the partition of a set. Then, we give the concept of distance between coverings (or partitions) and put forward the algorithms to get the optimal partition from a given covering. Main results include: 1) give the sufficient and necessary conditions for the optimal approximation of coverings in union sets; 2) give the necessary condition for absolutely optimal approximation of coverings; 3) based on the optimal approximation of each covering in the covering chain, the optimal fuzzy equivalence relation is obtained from the given fuzzy tolerance relation.
Supported by National Grand Fundamental Research 973 Program of China under Grant # 2007CB311003, supported by National Natural Science Foundation of China under Grant #61073117, supported by Natural Science Foundation of Anhui Province under Grant #11040606M145 and Grant #11040606M133, support by Outstanding Young Talents in Higher Education Institutions of Anhui Province under Grant #2009SQRZ020ZD and Grant #2010SQRL021.
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Zhang, L., Zhang, Yp., Zhao, S. (2011). The Optimal Approximation of Fuzzy Tolerance Relation. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds) Rough Sets and Knowledge Technology. RSKT 2011. Lecture Notes in Computer Science(), vol 6954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24425-4_75
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DOI: https://doi.org/10.1007/978-3-642-24425-4_75
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24424-7
Online ISBN: 978-3-642-24425-4
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