Jun, Young Bae; Song, Seok Zun Generalized fuzzy interior ideals in semigroups. (English) Zbl 1102.20058 Inf. Sci. 176, No. 20, 3079-3093 (2006). Summary: Using the idea of quasi-coincidence of a fuzzy point with a fuzzy set, the concept of an \((\alpha,\beta)\)-fuzzy interior ideal, which is a generalization of a fuzzy interior ideal, in a semigroup is introduced, and related properties are investigated. Cited in 1 ReviewCited in 48 Documents MSC: 20N25 Fuzzy groups 20M12 Ideal theory for semigroups 03E72 Theory of fuzzy sets, etc. Keywords:fuzzy sets; quasi-coincidences; fuzzy interior ideals; semigroups; fuzzy points PDFBibTeX XMLCite \textit{Y. B. Jun} and \textit{S. Z. Song}, Inf. Sci. 176, No. 20, 3079--3093 (2006; Zbl 1102.20058) Full Text: DOI References: [1] Bhakat, S. K.; Das, P., On the definition of a fuzzy subgroup, Fuzzy Sets Syst., 51, 235-241 (1992) · Zbl 0786.20047 [2] Bhakat, S. K.; Das, P., (∈, ∈∨q)-fuzzy subgroup, Fuzzy Sets Syst., 80, 359-368 (1996) · Zbl 0870.20055 [3] Hong, S. M.; Jun, Y. B.; Meng, J., Fuzzy interior ideals in semigroups, Indian J. Pure Appl. Math., 26, 9, 859-863 (1995) · Zbl 0834.20074 [4] Hwang, S. C.; Kim, H. S., Fuzzy semigroup of a semigroup, Int. Math. J., 4, 2, 191-196 (2003) · Zbl 1177.20080 [5] Kuroki, N., On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets Syst., 5, 203-215 (1981) · Zbl 0452.20060 [6] Kuroki, N., Fuzzy semiprime ideals in semigroups, Fuzzy Sets Syst., 8, 71-79 (1982) · Zbl 0488.20049 [7] Murali, V., Fuzzy points of equivalent fuzzy subsets, Inform. Sci., 158, 277-288 (2004) · Zbl 1041.03039 [8] Pu, P. M.; Liu, Y. M., Fuzzy topology I, neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76, 571-599 (1980) · Zbl 0447.54006 [9] Yuan, X.; Zhang, C.; Ren, Y., Generalized fuzzy groups and many-valued implications, Fuzzy Sets Syst., 138, 205-211 (2003) · Zbl 1024.20048 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.