Sets with partial memberships: a rough set view of fuzzy sets
- 27 November 2002
- conference paper
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE) in 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228)
- Vol. 1, 785-790 vol.1
- https://doi.org/10.1109/fuzzy.1998.687590
Abstract
Fuzzy set theory on a universe of granules (crisp sets) are considered. In this setting, the grade of a membership can be interpreted in the most elementary fashion. A grade of 1/2 membership means exactly one half of the granule (in a suitable measure) belongs to the fuzzy set. Based on such views, fuzzy set theoretical operations can be very naturally induced from the classical set theoretical operations; they are called R-operations. Some traditional operations, such as max and min, are R-operations of specific classes of fuzzy sets. The granular view of fuzzy sets provides a new and healthy insight into how fuzzy set theory might be structured.Keywords
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