Generalized Ordered Propositions Fusion Based on Belief Entropy

A set of ordered propositions describe the different intensities of a characteristic of an object, the intensities increase or decrease gradually. A basic support function is a set of truth-values of ordered propositions, it includes the determinate part and indeterminate part. The indeterminate part of a basic support function indicates uncertainty about all ordered propositions. In this paper, we propose generalized ordered propositions by extending the basic support function for power set of ordered propositions. We also present the entropy which is a measure of uncertainty of a basic support function based on belief entropy. The fusion method of generalized ordered proposition also be presented. The generalized ordered propositions will be degenerated as the classical ordered propositions in that when the truth-values of non-single subsets of ordered propositions are zero. Some numerical examples are used to illustrate the efficiency of generalized ordered propositions and their fusion.

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