Rough prime ideals and rough fuzzy prime ideals in semigroups. (English) Zbl 1088.20041

Summary: We introduce the notions of rough prime ideals and rough fuzzy prime ideals in a semigroup, and give some properties of such ideals. Also, we discuss the relations between the upper [lower] rough prime ideals and the upper [lower] approximations of their homomorphic images.


20N25 Fuzzy groups
20M12 Ideal theory for semigroups
20E36 Automorphisms of infinite groups
Full Text: DOI


[1] Zhang, W.; Wu, W., Theory and method of roughness, (2001), Science Press Beijing
[2] Sheng, D., Abstract algebra, (2001), Science Press Beijing
[3] Ma, J., Fuzzy algebra, (1989), Xueyuan Press Beijing
[4] Pawlak, Z., Rough sets, Int. J. comput. inform. sci., 11, 341-356, (1982) · Zbl 0501.68053
[5] Banerjee, M., Roughness of a fuzzy set, Inform. sci., 93, 235-246, (1996) · Zbl 0879.04004
[6] Kuroki, N., Rough ideals in semigroups, Inform. sci., 100, 139-163, (1997) · Zbl 0916.20046
[7] Biswas, R.; Nanda, S., Rough groups and rough subgroups, Bull. Polish acad. sci. math, 42, 251-254, (1994) · Zbl 0834.68102
[8] Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, Int. J. general syst., 17, 2-3, 191-209, (1990) · Zbl 0715.04006
[9] Dubois, D.; Prade, H., Twofold fuzzy sets and rough sets—some issues in knowledge representation, Fuzzy sets syst., 23, 3-18, (1987) · Zbl 0633.68099
[10] Bonikowaski, Z., Algebraic structures of rough sets, (), 242-247
[11] Iwinski, T., Algebraic approach to rough sets, Bull. Polish acad. sci. math., 35, 673-683, (1987) · Zbl 0639.68125
[12] Pomykala, J.; Pomykala, J.A., The stone algebra of rough sets, Bull. Polish acad. sci. math., 36, 495-508, (1998) · Zbl 0786.04008
[13] Davvaz, B., Roughness in rings, Inform. sci., 164, 147-163, (2004) · Zbl 1072.16042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.