Soft set relations and functions. (English) Zbl 1205.03060

Summary: The traditional soft set is a mapping from a parameter to the crisp subset of universe. Molodtsov introduced the theory of soft sets as a generalized tool for modeling complex systems involving uncertain or not clearly defined objects. In this paper the concepts of soft set relations are introduced as a sub soft set of the Cartesian product of the soft sets and many related concepts such as equivalent soft set relation, partition, composition, function etc. are discussed.


03E72 Theory of fuzzy sets, etc.
Full Text: DOI


[1] Maji, P.K.; Roy, A.R., An application of soft sets in a decision making problem, Computers and mathematics with applications, 44, 1077-1083, (2002) · Zbl 1044.90042
[2] Molodtsov, D., Soft set theory—first results, Computers and mathematics with applications, 37, 19-31, (1999) · Zbl 0936.03049
[3] Maji, P.K.; Biswas, R.; Roy, A.R., Soft set theory, Computers and mathematics with applications, 45, 555-562, (2003) · Zbl 1032.03525
[4] Chen, D.; Tsang, E.C.C.; Yeung, D.S.; Wang, X., The parameterization reduction of soft sets and its applications, Computers and mathematics with applications, 49, 757-763, (2005) · Zbl 1074.03510
[5] Bozena Kostek, Soft set approach to the subjective assessment of sound quality, in: IEEE Conferences, vol. 1, 1998, pp. 669-674.
[6] Mushrif, Milind M.; Sengupta, S.; Ray, A.K., Texture classification using a novel, soft set theory based classification algorithm, (2006), Springer Berlin, Heidelberg, pp. 246-254
[7] Yang, Xidei; Yu, Dongjun; Yang, Jingyu; Wu, Chen, Generalization of soft set theory: from crisp to fuzzy case, (), 345-354 · Zbl 1127.03331
[8] Athar Kharal, B. Ahmad, Mappings on fuzzy soft classes, Advances in Fuzzy Systems, 2009, 6. Article ID 407890. · Zbl 1211.54013
[9] Aktas, H.; Çagman, N., Soft sets and soft groups, Information sciences, 177, 2726-2735, (2007) · Zbl 1119.03050
[10] Feng, Feng; Jun, Young Bae; Zhao, Xianzhong, Soft semirings, Computers and mathematics with applications, 56, 2621-2628, (2008) · Zbl 1165.16307
[11] Aygunoglu, Abdulkadir; Aygun, Halis, Introduction to fuzzy soft groups, Computers and mathematics with applications, 58, 1279-1286, (2009) · Zbl 1189.20068
[12] Jun, Y.B., Soft BCK/BCI-algebras, Computers and mathematics with applications, 56, 1408-1413, (2008) · Zbl 1155.06301
[13] Jun, Y.B.; Park, C.H., Applications of soft sets in ideal theory of BCK/BCI-algebras, Information sciences, 178, 2466-2475, (2008) · Zbl 1184.06014
[14] Hrbacek, Karel; Jech, Thomas, Introduction to set theory, (1984), Marcel Dekker Inc. · Zbl 0555.03016
[15] Patrick, Suppes, Axiomatic set theory, (1960), D. Van Nostrand Company Inc. · Zbl 0091.05102
[16] Halmos, Paul R., Naïve set theory, (1960), D. Van Nostrand Company Inc. · Zbl 0087.04403
[17] Daowu Pei, Duoqian Miao, From soft sets to information systems, in: Granular Computing, IEEE International Conference, vol. 2, 2005, pp. 617-621.
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.