Abstract

It is often the case in reasoning problems that propositions are neither entirely true nor entirely false. In fuzzy logic,¹,² the truth values of propositions are not restricted to true or false, but rather may range between zero (absolutely false) and one (absolutely true), allowing a quantitative representation and evaluation of vague propositions. For example, the proposition, "Marsden is a boring speaker" is neither totally true nor totally false, but might have a value 0.30.³ Many existing Boolean reasoning methods can be extended to include fuzzy truth values. However, since Boolean operators such as AND and OR are undefined on non-Boolean data, analogous fuzzy operators must be defined for these algorithms to be useful. It has been shown that MIN and MAX have desirable properties when used as extensions of AND and OR, respectively.¹

© 1991 Optical Society of America