An adjustable approach to fuzzy soft set based decision making.

*(English)*Zbl 1274.03082Summary: Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. Recently, decision making based on (fuzzy) soft sets has found paramount importance. This paper aims to give deeper insights into decision making based on fuzzy soft sets. We discuss the validity of the Roy-Maji method and show its true limitations. We point out that the choice value designed for the crisp case is no longer fit to solve decision making problems involving fuzzy soft sets. By means of level soft sets, we present an adjustable approach to fuzzy soft set based decision making and give some illustrative examples. Moreover, the weighted fuzzy soft set is introduced and its application to decision making is also investigated.

##### Keywords:

soft set; fuzzy soft set; level soft set; threshold; comparison table; choice value; score; decision making
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\textit{F. Feng} et al., J. Comput. Appl. Math. 234, No. 1, 10--20 (2010; Zbl 1274.03082)

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##### References:

[1] | Zadeh, L.A., Fuzzy sets, Inform. 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] | Pawlak, Z., Rough sets, Int. J. of inform. comput. sci., 11, 341-356, (1982) · Zbl 0501.68053 |

[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] | Molodtsov, D., Soft set theory – first results, Comput. math. appl., 37, 19-31, (1999) · Zbl 0936.03049 |

[7] | Molodtsov, D., The theory of soft sets, (2004), URSS Publishers Moscow, (in Russian) |

[8] | Maji, P.K.; Biswas, R.; Roy, A.R., Soft set theory, Comput. math. appl., 45, 555-562, (2003) · Zbl 1032.03525 |

[9] | Maji, P.K.; Biswas, R.; Roy, A.R., Fuzzy soft sets, J. fuzzy math., 9, 3, 589-602, (2001) · Zbl 0995.03040 |

[10] | Aktaş, H.; Çağman, N., Soft sets and soft groups, Inform. sci., 177, 2726-2735, (2007) · Zbl 1119.03050 |

[11] | Jun, Y.B., Soft BCK/BCI-algebras, Comput. math. appl., 56, 1408-1413, (2008) · Zbl 1155.06301 |

[12] | Jun, Y.B.; Park, C.H., Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. sci., 178, 2466-2475, (2008) · Zbl 1184.06014 |

[13] | Feng, F.; Jun, Y.B.; Zhao, X.Z., Soft semirings, Comput. math. appl., 56, 2621-2628, (2008) · Zbl 1165.16307 |

[14] | 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 |

[15] | Pawlak, Z., Rough sets: theoretical aspects of reasoning about data, (1991), Kluwer Academic Boston, MA · Zbl 0758.68054 |

[16] | 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 |

[17] | Roy, A.R.; Maji, P.K., A fuzzy soft set theoretic approach to decision making problems, J. comput. appl. math., 203, 412-418, (2007) · Zbl 1128.90536 |

[18] | Kong, Z.; Gao, L.Q.; Wang, L.F., Comment on a fuzzy soft set theoretic approach to decision making problems, J. comput. appl. math., 223, 540-542, (2009) · Zbl 1159.90421 |

[19] | T.Y. Lin, A set theory for soft computing, a unified view of fuzzy sets via neighbourhoods, in: Proceedings of 1996 IEEE International Conference on Furzy Systems. New Orleans, LA, September 8-11, 1996, pp. 1140-1146 |

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