Soft set theory. (English) Zbl 1032.03525

Summary: The authors study the theory of soft sets initiated by Molodtsov. The authors define equality of two soft sets, subsets and supersets of a soft set, the complement of a soft set, the null soft set, and the absolute soft set, along with some examples. Soft binary operations like AND, OR and also the operations of union and intersection are defined. De Morgan’s laws and a number of results are verified in soft set theory.


03E72 Theory of fuzzy sets, etc.
68T37 Reasoning under uncertainty in the context of artificial intelligence
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[1] Zadeh, L. A., Fuzzy sets, Infor. and Control, 8, 338-353 (1965) · Zbl 0139.24606
[2] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96 (1986) · Zbl 0631.03040
[3] Atanassov, K., Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64, 159-174 (1994) · Zbl 0844.04001
[4] Gau, W. L.; Buehrer, D. J., Vague sets, IEEE Trans. System Man Cybernet, 23, 2, 610-614 (1993) · Zbl 0782.04008
[5] Gorzalzany, M. B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems, 21, 1-17 (1987) · Zbl 0635.68103
[6] Pawlak, Z., Rough sets, International Journal of Information and Computer Sciences, 11, 341-356 (1982) · Zbl 0501.68053
[7] Molodtsov, D., Soft set theory—First results, Computers Math. Applic., 37, 4/5, 19-31 (1999) · Zbl 0936.03049
[8] Pawlak, Z., Hard set and soft sets, ICS Research Report, Institute of Computer Science (1994), Poland
[9] Zimmerman, H. J., Fuzzy Set Theory and Its Applications (1996), Kluwer Academic: Kluwer Academic Boston, MA · Zbl 0845.04006
[10] Prade, H.; Dubois, D., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: Academic Press London · Zbl 0444.94049
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