Re-Examination of the Relationship between Fuzzy Set Theory and Probability Theory.

摘要

Recently, a manner of articles have appeared in newspapers and popular magazines and journals emphasizing a dichotomy in regard to fuzzy sets: the great potential benefit of using an intuitively appealing and simple approach to modeling uncertainties and its almost universal rejection or avoidance by orthodox scientists in the United States trained in probability theory. Thus, once more, it is of some interest to attempt to determine dispassionately what relations, if any, exist between fuzzy sets and probabilities. Previously, Goodman et al. were the first to point out that rather basic connections do indeed exist between fuzzy set theory and probability theory via random sets and their one point coverage functions. (See, e.g. Goodman, Some new results concerning random sets and fuzzy sets, info. Sci.34, 1984 or Goodman Nguyen, Uncertainty Models for Knowledge-Based Systems (monograph), North-Holland Co., Amsterdam, 1985.) But relatively few individuals have utilized these connections (Dubois Prade on occasion and Oblow emphasizing full random set representations through his hybrid O-Theory), mainly due to the foreboding complex structure of random sets - as compared to the relatively simple form of random variables or random vectors. Even the relatively recent contributions of Lindley, Klir, and others in comparing the roles and game theoretic admissibility properties of fuzzy sets and probabilities do not address the deeper relations between the two areas.