Proceedings [antikvár]

Toward a Unified Theory of Uncertainty'Lotfi A. ZadehProfessor in the Graduate School and Director, Berkeley initiative in Soft Computing (BISC), Computer Science Division and the Electronics Research Laboratory, Department of EECS, University of California, Berkeley, CA 94720-1776; Telephone: 510-642-4959; Fax: 510-642-1712;E-Mail: [email protected] science, and especially within probability community, it is an almost universally held view that probability theory is the theory of uncertainty, and that no other theory of uncertainty is needed. To quote Professor Dennis Lindley, an eminent probabilist, "The only satisfactory description of uncertainty is probability. By this I mean that every uncertainty statement must be in the form of a probability; that several uncertainties must be combined using the rules of probability; and that the calculus of probabilities is adequate to handle all situations involving uncertainty probability is the only sensible description of uncertainty and is adequate for all problems involving uncertainty. All other methods are inadequate anything that can be done with fuzzy logic, belief functions, upper and lower probabilities, or any other alternative to probability can better be done with probability." (Lindley, 1987) A quick counterpoint. An important facet of uncertainty that is disregarded in Professor Lindley's comment is that, in many real-world settings, uncertainty is not probabilistic. For example, interval analysis deals with uncertainty, but no probabilities are involved.In recent years, a variety of theories of uncertainty have been advanced, some of which are mentioned in Professor Lindley's statement. In the main, such theories are generalizations of standard probability theory rather than alternative approaches to uncertainty.Fundamentally, uncertainty is an attribute of information. In general, information may be represented as a collection of so called generalized constraintsconstraints which include probabilistic constraints as a special case. The concept of a generalized constraint is the centerpiece of a theory ofResearch supported in part by ONR NOOO14-02-1-0294, ONR NOOO14-00-1-062land the BISC Program of UC Berkeley