NDLI: Stochastic and fuzzy logics (1975)

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Stochastic and fuzzy logics (1975)

Content Provider	CiteSeerX
Author	Gaines, Brian R.
Abstract	It is shown that it is possible to regard stochastic and fuzzy logics as being derived from two different constraints on a probability logic: statistical independence (stochastic) and logical implication (fuzzy). To contrast the merits of the two logics, some published data on a fuzzylogic controller is reanalysed using stochastic logic and it is shown that no significant difference results in the control policy. Fuzzy logic as probability logic The literature on fuzzy logic (Lee, 1972; Zadeh 1973) treats it very much as a new concept, distinct from that of probability logic (Rescher, 1969), even though both ascribe to events numbers in the interval [0, 1]. This suggests that a new theoretical framework is required in which to analyse the results of practical applications of fuzzy logic. This letter is to demonstrate that fuzzy logic may be treated in terms of probability theory. This is possible because probability logic is itself not truth functional (Rescher, 1969)—the truth value of a logical expression is not uniquely determined by those of its components, and additional assumptions are necessary to determine it. It will be shown that, if a relationship of logical implication is assumed between variables, the rules of fuzzy logic apply. Conversely, if these rules do apply,
File Format	PDF
Journal	Electronics Letters
Language	English
Publisher Date	1975-01-01
Access Restriction	Open
Subject Keyword	Fuzzy Logic Probability Logic Logical Implication Logical Expression Statistical Independence Stochastic Logic Different Constraint New Concept Practical Application Fuzzylogic Controller Additional Assumption Event Number Truth Value New Theoretical Framework Significant Difference Result Probability Theory Fuzzy Logic Apply Control Policy
Content Type	Text
Resource Type	Article

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