FUZZY ENTROPY AND CONDITIONING

A new nonprobabilistic entropy measure is introduced in the context of fuzzy sets or messages. Fuzzy units, or fits, replace bits in a new framework of fuzzy information theory. An appropriate measure of entropy of fuzziness of messages is shown to be a simple ratio of distances: the distances between the fuzzy message and its nearest and farthest nonfuzzy neighbors. Fuzzy conditioning is examined as the degree of subsethood (submessagehood) of one fuzzy set of message in another. This quantity is shown to behave as a conditional probability in many contexts. A theory of subsets is presented and shown to solve one of the major problems with Bayes-theorem learning and its variants - the problem of requiring that the space of alternatives be partitioned into disjoint exhaustive hypothesis.