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A probabilistic and statistical view of fuzzy methods. (With discussion). (English) Zbl 0837.62081

Summary: 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.

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62P99 Applications of statistics
62N99 Survival analysis and censored data
62A01 Foundations and philosophical topics in statistics
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