Non-Additive Probability Measures with Interval Density Functions

Abstract

Probability measures are well-defined measures which have additivity. However, it is slightly tight because of its condition of additivity. The substitute measures are proposed such as fuzzy measures which do not satisfy additivity. The only belief function involves a density function among them. In this paper, we propose two density functions by extending values of conventional density function to interval values, which do not satiafy additivity, and define a combination rule, a conditional probability and a expected value and then we clarify the properties of the proposed measure.