Approach to interval numbers investment decision-making based on grey incidence coefficients and D-S theory of evidence

This paper focuses mainly on problems of selecting investment cases when attribute values of corresponding alternatives fall into intervals.Ideal attribute interval numbers for benefit type indices and cost type indices are defined respectively.The concept of ideal attribute deviation is also defined in this paper. A matrix of interval numbers is converted into the matrix of measures with ideal attribute deviations by above definitions.Then an uncertain problem is converted into the certain problem which can be addressed relatively easier.A combination of the grey incidence analysis method and the theory of evidence is presented based on the understanding of problems.A novel method extracting the degree of ignorance for information and a new method for basic probability assignment function are constructed to combine distinct pieces of information in accordance with the Dempster combination rule.A conversion relationship between a belief function and a basic probability assignment function is also discussed in this paper.After all required steps completed for information fusion the Dempster combination rule is applied and the optimal investment case is derived in terms of the largest belief function value.A numerical example is utilized to illustrate the method proposed in this paper.The result indicates that a satisfied case can be obtained through applying the method and an obvious decrease can be observed in the uncertainty of decision-making.