A consideration for measure of information based on the dempster‐shafer theory

This paper discusses the measure of information for the event using the probability theory by Dempster and Shafer. By providing various kinds of information to the event containing an ambiguity, the ambiguity is gradually decreased to define the event in a clearer way. The combination rule by Dempster is most suited to represent the combination of information. This paper shows first that several representations can be made for Dempster's combination rule. Then using the upper and lower probabilities defined by the basic probability of the event, the upper and lower information measures are defined, followed by the discussion of their properties. The lower probability of a set (event) is defined as the sum of basic probabilities of all subsets in the set, and the upper probability is defined as the sum of basic probabilities of all sets which contain an element of the set. Thus, the upper and lower information measures can be interpreted as the measures of information concerning the message with ambiguity. Finally, several examples are discussed, determining the information measure for the message containing ambiguity.