The Sugeno Integral and Its Applications of Nonadditive Set Functions Based on Sigma-Lambda Rules

Sugeno integral is used as an aggregation tool in information fusion which could be regarded as the inverse problem of information fusion as well as in nonlinear multi-regressions and nonlinear classification. Introducing more types of nonlinear integrals with provide more choices for various of objectives and components in these problems. However, when sample space is huge, regarding needs the information contribution to obtain is very difficult, this paper has carried on the discussion on this. In this paper, first we introduce a kind of nonadditive measure based on sigma-lambda rules and its calculate of the defect of additivity are given. Then based on this, we could calculate contributions of their joint attributes by means of sigma-lambda rules based on the contributions of individual attributes. Finally, the lower integral and upper Sugeno integral of the nonadditive set functions based on sigma-lambda rules are defined and calculated by the integer program problems.