A MODIFIED MEASURE FOR FUZZY SUBSETHOOD

Fuzzy conditioning is reconsidered not only by the degree of subsethood, but also by the distance between two fuzzy messages. This quantity is shown to behave like a, conditional probability in many contexts of fuzzy sets. The proposed measure of fuzzy subsethood bears the information of similarity of two fuzzy messages in the n-cube space besides the subsethood. The proposed measure leads to a fuzzy version of Bayesian's theorem. The theory of subsethood is also shown to resolve the shortcoming of the Bayesian's learning, the problem of requiring that the space must be partitioned into disjoint exhaustive hypotheses.