The characterization of a measure of information discrepancy

A Function of Degree of Disagreement (FDOD) function has been introduced in the study of information discrepancies among multiple information sources [W. Fang, Mathematical Social Sciences 28 (2) (1994) 85–111; J. Global Optim. 11 (1997) 387–408]. It possesses some peculiar properties and can be applied in some areas, in which the traditional measures of information discrepancy are not valid, for example, in the study of multiple DNA sequence comparison. In this paper, based on the ideas concerned with Shannon entropy and measures of difference, we investigate its characterization. The final results and even intermediate results show a close connection between the FDOD function and Shannon entropy.