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Rough sets and fuzzy sets - some remarks on interrelations. (English) Zbl 0664.04010

This short paper refers to two remarks given by Z. Pawlak [ibid. 17, 99-102 (1985; Zbl 0588.04004)] and disputes them. Any rough set can be expressed by means of a membership function \(U\to \{0, 0.5, 1\}\). We show that this representation can be extended to union and intersection.

MSC:

03E99 Set theory
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
03E72 Theory of fuzzy sets, etc.

Citations:

Zbl 0588.04004
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Full Text: DOI

References:

[1] Pawlak, Z., Rough sets, (Report No. 431 (1981), Polish Academy of Sciences, Institute of Computer Science) · Zbl 0604.90084
[2] Pawlak, Z., Rough sets, Internat. J. Inform. Comput. Sci., 11, 5, 341-356 (1982) · Zbl 0501.68053
[3] Pawlak, Z., Rough sets and fuzzy sets, Fuzzy Sets and Systems, 17, 99-102 (1985) · Zbl 0588.04004
[4] Wygralak, M., Some remarks on rough and fuzzy sets, BUSEFAL, 21, 43-49 (1985) · Zbl 0588.04003
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