A novel fuzzy soft set approach in decision making based on grey relational analysis and Dempster–Shafer theory of evidence

• We introduce a novel fuzzy soft set approach in decision making based on grey relational analysis and D–S theory of evidence (see Section 4).
• We give an application for medical diagnosis (see Section 6).
• We propose an illustrative example (see Example 5.1).

This paper proposes a novel fuzzy soft set approach in decision making based on grey relational analysis and Dempster–Shafer theory of evidence. First, the uncertain degrees of various parameters are determined via grey relational analysis, which is applied to calculate the grey mean relational degree. Second, suitable mass functions of different independent alternatives with different parameters are given according to the uncertain degree. Third, to aggregate the alternatives into a collective alternative, Dempster's rule of evidence combination is applied. Finally, the alternatives are ranked and the best alternatives are obtained. The effectiveness and feasibility of this approach are demonstrated by comparing with the mean potentiality approach because the measure of performance of this approach is the same as the mean potentiality approach's, the belief measure of the whole uncertainty falls from 0.4723 to 0.0782 (resp. 0.3821 to 0.0069) in the example of Section 5 (resp. Section 6).

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