A Probabilistic and Statistical View of Fuzzy Methods

Abstract

Fuzzy set theory has primarily been associated with control theory and with the representation of uncertainty in applications in artificial intelligence. More recently, fuzzy methods have been proposed as alternatives to traditional statistical methods in statistical quality control, linear regression, and forecasting, among other areas. We review some basic concepts of fuzzy methods, point out some philosophical and practical problems, and offer simpler alternatives based on traditional probability and statistical theory. Applications in control theory and statistical quality control serve as our primary examples.