A NOTE ON THE CONDITIONAL-PROBABILITY OF FUZZY SUBSETS OF A CONTINUOUS DOMAIN

The notion of a mass assignment corresponding to a discrete fuzzy set is generalised to include all fuzzy sets. The definition is motivated by considering a possible mechanism by which an intelligent agent coul d extend set theoretic operations to fuzzy sets. This same mechanism a lso suggests an alternative definition for the conditional probability of fuzzy sets. It is noted that this definition is probability/possib ility consistent and it is shown that in the case, where the probabili ty distribution on the domain has a density function then the conditio nal probability of f given g can be expressed as the probability of f calculated relative to a conditional density function dependent on g. This result is used to develop an analytical method for calculating co nditional probabilities of fuzzy subsets of the reals, where the membe rship functions of f and g and the density function are continuous pie cewise linear functions. Such a method has applications to the develop ment of a general semantic unification in Fril. (C) 1998 Elsevier Scie nce B.V. All rights reserved.