The lower and upper approximations in a fuzzy group. (English) Zbl 0878.20050

Summary: We introduce the notion of a rough subgroup with respect to a normal subgroup of a group, and give some properties of the lower and the upper approximations in a group. We also discuss a rough subgroup with respect to a \(t\)-level subset of a fuzzy normal subgroup.


20N25 Fuzzy groups
20E07 Subgroup theorems; subgroup growth
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[1] Biswas, R.; Nanda, S., Rough groups and rough subgroups, Bull. Polish Acad. Math., 42, 251-254 (1994) · Zbl 0834.68102
[2] Bonikowaski, Z., Algebraic structures of rough sets, (Ziarko, W. P., Rough Sets, Fuzzy Sets and Knowledge Discovery (1995), Springer-Verlag: Springer-Verlag Berlin), 242-247
[3] Iwinski, T., Algebraic approach to rough sets, Bull. Polish Acad. Sci. Math., 35, 673-683 (1987) · Zbl 0639.68125
[4] Kuroki, N., Fuzzy congruences and fuzzy normal subgroups, Inform. Sci., 60, 247-259 (1992) · Zbl 0747.20038
[5] Pawlak, Z., Rough sets, Int. J. Inf. Comp. Sci., 11, 341-356 (1982) · Zbl 0501.68053
[6] Pawlak, Z., Rough Sets Theoretical Aspects of Reasoning about Data (1991), Kluwer Academic: Kluwer Academic Norwell, MA · Zbl 0758.68054
[7] Pomykala, J.; Pomykala, J. A., The stone algebra of rough sets, Bull. Polish Acad. Sci. Math., 36, 495-508 (1988) · Zbl 0786.04008
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