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1 Bulletin of the Polish Academy of Sciences. Technical Sciences

1 2002

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Cantorian Sets, Fuzzy Sets, Rough Sets and Fregean Sets

Apostoli P., Kanda A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2002

Vol. 50, Nr 3

247--276

Fuzzy set theory [101] and rough set theory [68] deal with the concept of vagueness in the setting of set theory in seemingly different ways. The connection between these two theories of vague sets has been studied in [71], [94], [99], [100], where the probabilistic membership function of fuzzy set theory is derived within approximation spaces. This note initiates the study how "vague power sets" and "vague Cartesian products" may be constructed from given vague sets, in the settings of both fuzzy and rough sets. The introduction of vague sets by the principle of comprehension is also studied in both fuzzy and rough set theory. A marked difference between these two vague set theories with respect to these set constructions is revealed.