Identification of Fuzzy Sets with a Class of Canonically Induced Random Sets and Some Applications

摘要

Any random subset of a space X clearly determines the membership function of a fuzzy subset through its one point coverages. This paper shows, conversely, that any fuzzy subset A of X can always be identified with, in general, many random subsets S(A) of X with respect to one point coverages. In a related manner, it is shown that any fuzzy set can be uniformly closely approximated with respect to one point coverages by a random set having a finite number of outcomes. Applications of the results to fuzzy attribute reasoning in both military and general contexts are presented, emphasizing the close connection between fuzzy and random confidence sets. Extensions of the above results to non-canonical mappings and multiple point coverage functions are also treated.