A Probabilistic and Statistical View of Fuzzy Methods

Michael LAVIOLEUE

Department of Mathematics and Statistics

University of Missouri-Rolla MO 65401-0249

John W. SEAMAN, Jr.

Department of Information Systems Statistics and Institute of Graduate Baylor

University Rolla, Waco, TX 76798-8005

J. Douglas BARRETT and William H. WOODALL

Department of Management Science and Statistics University of Alabama Tuscaloosa, AL 35487-0226

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Fuzzy set theory has primarily been associated with control theory and with the representation of un- certainty 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 forecast- ing, 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.

KEY WORDS:

Applied probability; Control theory; Fuzzy set theory; Statistical quality control