Optimal decision of multi-inconsistent information systems based on information fusion

Abstract

This paper discusses the fusion of multi-inconsistent decision information systems. First, basic definitions and properties of rough sets, belief and plausibility functions are reviewed. Then, conditional mass function, conditional belief function and conditional plausibility function based on the decision set are defined. We then study the optimal decision of a test set and the reduction of an inconsistent decision information system based on the conditional mass function. Meanwhile, conditional mass function, conditional belief function and conditional plausibility function based on the conditional attribute set are also discussed and we define an uncertainty degree of an inconsistent information system based on the quasi-probability measure. Further, we study fusion method of inconsistent decision information systems using conditional mass functions based on a decision set. Finally, we define a conditional uncertainty measure and give a method to obtain the optimal decision and the confidence level.