Precise Past - Fuzzy Future

This paper examines the motivation and foundations of fuzzy sets theory, now some 20 years old, particularly possible misconceptions about possible operators and relations to probability theory. It presents a standard uncertainty logic (SUI.) that subsumes standard propositional, fuzzy and probability logics, and shows how many key results may be derived within SUL without further constraints. These include resolutions of standard paradoxes such as those of the bald man and of the barber, decision rules used in pattern recognition and control, the derivation of numeric truth values from the axiomatic form of the SUL, and the derivation of operators such as the arithmetic mean. The addition of the constraint of truth-functionality to a SUL is shown to give fuzzy, or Lukasiewicz infinitely-valued, logic. The addition of the constraint of the law of the excluded middle to a SUL is shown to give probability, or modal $5, logic. An example is given of the use of the two logics in combination to give a possibility vector when modelling sequential behaviour with uncertain observations. This paper is based on the banquet address with the same title given at NAFIP-1, the First North American Fuzzy Information Processing Group Workshop, held at Utah State University, May 1982.