An approach to fuzzy soft sets in decision making based on grey relational analysis and Dempster–Shafer theory of evidence: An application in medical diagnosis

• We propose an approach to fuzzy soft set in decision making based on grey relational analysis and D-S theory of evidence.
• The effectiveness and feasibility of our approach is demonstrated by comparing with the mean potentiality approach and giving an application in medical diagnosis.

ObjectiveThe existing methods of fuzzy soft sets in decision making are mainly based on different kinds of level soft sets, and it is very difficult for decision makers to select a suitable level soft set in most instances. The goal of this paper is to present an approach to fuzzy soft sets in decision making to avoid selecting a suitable level soft set and to apply this approach to solve medical diagnosis problems.MethodsThis approach combines grey relational analysis with the Dempster–Shafer theory of evidence. It first utilizes grey relational analysis to calculate the grey mean relational degree, by which we calculate the uncertain degree of various parameters. Then, on the basis of the uncertain degree, the suitable basic probability assignment function of each independent alternative with each parameter can be obtained. Next, we apply Dempster–Shafer rule of evidence fusion to aggregate these alternatives into a collective alternative, by which these alternatives are ranked and the best alternative is obtained. Finally, we compare this approach with the mean potentiality approach.ResultsThe results demonstrate the effectiveness and feasibility of this approach vis-a-vis the mean potentiality approach, Feng's method, Analytical Hierarchy Process and Naive Bayes’ classification method because the measure of performance of this approach is the same as that of the mean potentiality approach, and the belief measure of the whole uncertainty falls from the initial mean 0.3821 to 0.0069 in an application of medical diagnosis.ConclusionAn approach to fuzzy soft sets in decision making by combining grey relational analysis with Dempster–Shafer theory of evidence is introduced. The advantages of this approach are discussed. A practical application to medical diagnosis problems is given.