Jun, Young Bae; Park, Chul Hwan Applications of soft sets in ideal theory of BCK/BCI-algebras. (English) Zbl 1184.06014 Inf. Sci. 178, No. 11, 2466-2475 (2008). Summary: The notions of soft ideals and idealistic soft BCK/BCI-algebras are introduced, and several examples are given. Relations between soft BCK/BCI-algebras and idealistic soft BCK/BCI-algebras are provided. The intersection, union, “AND” operation, and “OR” operation of soft ideals and idealistic soft BCK/BCI-algebras are established. Cited in 117 Documents MSC: 06F35 BCK-algebras, BCI-algebras Keywords:soft set; soft BCK/BCI-algebra; soft ideal PDF BibTeX XML Cite \textit{Y. B. Jun} and \textit{C. H. Park}, Inf. Sci. 178, No. 11, 2466--2475 (2008; Zbl 1184.06014) Full Text: DOI References: [1] Aktaş, H.; Çağman, N., Soft sets and soft groups, Inform. Sci., 177, 2726-2735 (2007) · Zbl 1119.03050 [2] Chaudhry, M. A., Weakly positive implicative and weakly implicative BCI-algebras, Math. Jpn., 35, 141-151 (1990) · Zbl 0702.06014 [3] Chen, D.; Tsang, E. C.C.; Yeung, D. S.; Wang, X., The parametrization reduction of soft sets and its applications, Comput. Math. Appl., 49, 757-763 (2005) · Zbl 1074.03510 [4] Davvaz, B.; Dudek, W. A.; Jun, Y. B., Intuitionistic fuzzy \(H_v\)-submodules, Inform. Sci., 176, 285-300 (2006) · Zbl 1090.16028 [5] Dudek, W. A.; Davvaz, B.; Jun, Y. B., On intuitionistic fuzzy sub-hyperquasigroups of hyperquasigroups, Inform. Sci., 170, 251-262 (2005) · Zbl 1072.20088 [7] Jun, Y. B.; Öztürk, M. A.; Park, C. H., Intuitionistic nil radicals of intuitionistic fuzzy ideals and Euclidean intuitionistic fuzzy ideals in rings, Inform. Sci., 177, 4662-4677 (2007) · Zbl 1129.16041 [8] Jun, Y. B.; Shim, W. H., Fuzzy strong implicative hyper BCK-ideals of hyper BCK-algebras, Inform. Sci., 170, 351-361 (2005) · Zbl 1071.06012 [9] Jun, Y. B.; Song, S. Z., Generalized fuzzy interior ideals in semigroups, Inform. Sci., 176, 3079-3093 (2006) · Zbl 1102.20058 [10] Jun, Y. B.; Xu, Y.; Ma, J., Redefined fuzzy implicative filters, Inform. Sci., 177, 1422-1429 (2007) · Zbl 1111.03325 [11] Jun, Y. B.; Xu, Y.; Zhang, X. H., Fuzzy filters of MTL-algebras, Inform. Sci., 175, 120-138 (2005) · Zbl 1077.03044 [12] Maji, P. K.; Biswas, R.; Roy, A. R., Soft set theory, Comput. Math. Appl., 45, 555-562 (2003) · Zbl 1032.03525 [13] Maji, P. K.; Roy, A. R.; Biswas, R., An application of soft sets in a decision making problem, Comput. Math. Appl., 44, 1077-1083 (2002) · Zbl 1044.90042 [14] Molodtsov, D., Soft set theory – first results, Comput. Math. Appl., 37, 19-31 (1999) · Zbl 0936.03049 [15] Meng, J.; Jun, Y. B., BCK-algebras (1994), Kyungmoon Sa Co., Seoul · Zbl 0814.06012 [16] Pawlak, Z.; Skowron, A., Rudiments of rough sets, Inform. Sci., 177, 3-27 (2007) · Zbl 1142.68549 [17] Pawlak, Z.; Skowron, A., Rough sets: Some extensions, Inform. Sci., 177, 28-40 (2007) · Zbl 1142.68550 [18] Pawlak, Z.; Skowron, A., Rough sets and Boolean reasoning, Inform. Sci., 177, 41-73 (2007) · Zbl 1142.68551 [19] Rosenfeld, A., Fuzzy groups, J. Math. Anal. Appl., 35, 512-517 (1971) · Zbl 0194.05501 [20] Zadeh, L. A., From circuit theory to system theory, Proc. Inst. Radio Eng., 50, 856-865 (1962) [21] Zadeh, L. A., Fuzzy sets, Inform. Control, 8, 338-353 (1965) · Zbl 0139.24606 [22] Zadeh, L. A., Toward a generalized theory of uncertainty (GTU) - an outline, Inform. Sci., 172, 1-40 (2005) · Zbl 1074.94021 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.