The parameterization reduction of soft sets and its applications. (English) Zbl 1074.03510

Summary: We focus our discussion on the parameterization reduction of soft sets and its applications. First we point out that the results of soft set reductions offered by P. K. Maji, A. D. Roy and R. Biswas [ibid. 44, 1077–1083 (2002; Zbl 1044.90042)] are incorrect. We also observe that the algorithms used to first compute the reduct-soft-set and then to compute the choice value to select the optimal objects for the decision problems [loc. cit.] are not reasonable and we illustrate this with an example. Finally, we propose a reasonable definition of parameterization reduction of soft sets and compare it with the concept of attribute reduction in rough set theory. By using this new definition of parameterization reduction, we improve the application of a soft set in a decision making problem found in [loc. cit.].


03E72 Theory of fuzzy sets, etc.
68T37 Reasoning under uncertainty in the context of artificial intelligence
90B50 Management decision making, including multiple objectives


Zbl 1044.90042
Full Text: DOI


[1] Maji, P. K.; Roy, A. R.; Biswas, R., An application of soft sets in a decision making problem, Computers Math. Applic., 44, 8/9, 1077-1083 (2002) · Zbl 1044.90042
[2] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606
[3] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96 (1986) · Zbl 0631.03040
[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)
[6] Pawlak, Z., Rough sets, International Journal of Information and Computer Sciences, 11, 341-356 (1982) · Zbl 0501.68053
[7] Molodstov, D., Soft set theory-first results, Computers Math. Applic., 37, 4/5, 19-31 (1999) · Zbl 0936.03049
[8] Pawlak, Z., Rough Sets: Theoretical Aspects of Reasoning About Data (1991), Kluwer Academic · Zbl 0758.68054
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.