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Rough sets. (English) Zbl 0501.68053
Summary: We investigate in this paper approximate operations on sets, approximate equality of sets, and approximate inclusion of sets. The presented approach may be considered as an alternative to fuzzy set theory and tolerance theory. Some applications are outlined.

68T05 Learning and adaptive systems in artificial intelligence
68T10 Pattern recognition, speech recognition
03E99 Set theory
68T37 Reasoning under uncertainty in the context of artificial intelligence
62H30 Classification and discrimination; cluster analysis (statistical aspects)
03B52 Fuzzy logic; logic of vagueness
Full Text: DOI
[1] E. Konrad, E. Or?owska, and Z. Pawlak,An approximate concept learning (Berlin, Bericht, 1981), pp. 81?87.
[2] W. Marek and Z. Pawlak, ?Rough sets and information systems,?ICS PAS Reports (441) (1981). · Zbl 0546.68088
[3] R. Michalski, ?S., Pattern Recognition as Role-Guided Inductive Interference,?IEEE Transaction on Pattern Analysis and Machine Intelligence 2:179?187 (1971).
[4] E. Or?owska, ?Semantics of vague concepts, Application of rough sets,?ICS PAS Reports (469) (1982).
[5] E. Or?owska, ?Logic of vague concepts, Application of rough sets,?ICS PAS Reports (474) (1982).
[6] E. Or?owska and Z. Pawlak, ?Measurement and observability, Application of rough sets,? (to appear).
[7] Z. Pawlak, ?Rough sets,?ICS PAS Reports (431) (1981). · Zbl 0516.04001
[8] Z. Pawlak, ?Rough relations,?ICS PAS Reports (435) (1981).
[9] Z. Pawlak, ?Rough functions,?ICS PAS Reports (167) (1981). · Zbl 0516.04001
[10] Z. Pawlak, ?Information systems, theoretical foundations,?Information systems 6 (3):205?218 (1981). · Zbl 0462.68078 · doi:10.1016/0306-4379(81)90023-5
[11] Z. Pawlak, ?Rough sets, Algebraic and topological approach,?ICS PAS Reports (482) (1982).
[12] A. Robinson,Non-standard analysis (North-Holland Publishing Company, Amsterdam, 1966). · Zbl 0151.00803
[13] L. A. Zadah, ?Fuzzy sets,?Information and Control 8:338?353 (1965). · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[14] E. O. Zeeman, ?The Topology of the Brain and Visual Perception,? inTopology of 3-Manifolds and related topics, M. K. Fort, ed. (Englewood Cliffs, N.Y., 1962). · Zbl 1246.92006
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