Credibility of a Combined Result of Mutually Dependent Observations with Uncertainty and Contradiction

Abstract

A method is proposed and discussed to evaluate credibility of a combined result of plural observations with uncertainty and contradiction for the cases of positive dependence, negative dependence and independence among the observations. In this paper credibility of an observation is described by 4-tuple grades, I.e., grades of truth, contradiction, uncertainty and false in the observation. These grades are determined in the same manner as membership functions are determined based on a concept of ground set. Then the credibility of plural observations is evaluated by the combination of fuzzy set products, where the fuzzy sets are characterized by the above mentioned grades, and the set products are determined using general probabilistic set operations. Credibilities for a pair of observations and repeated plural observations are derived and their properties are discussed.