Mathematical Principles of Fuzzy Logic
Springer Science & Business Media, Aug 31, 1999 - Mathematics - 320 pages
Mathematical Principles of Fuzzy Logic provides a systematic study of the formal theory of fuzzy logic. The book is based on logical formalism demonstrating that fuzzy logic is a well-developed logical theory. It includes the theory of functional systems in fuzzy logic, providing an explanation of what can be represented, and how, by formulas of fuzzy logic calculi. It also presents a more general interpretation of fuzzy logic within the environment of other proper categories of fuzzy sets stemming either from the topos theory, or even generalizing the latter.
This book presents fuzzy logic as the mathematical theory of vagueness as well as the theory of commonsense human reasoning, based on the use of natural language, the distinguishing feature of which is the vagueness of its semantics.
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Analogously approximation assigned BL-algebra Boolean algebra characteristic morphism characterize classical logic completeness theorem concept conjunctive normal form connectives consistent construct contradictory corresponding defined definition defuzzification denote disjunction element equivalent evaluated formulas evaluating predications evaluating syntagms example exists extension fi-fuzzy set fi-set fi-subset filter finite Fj(T FL-functions FL-relation following lemma following theorem formal logical systems Furthermore fuzzy logic fuzzy predicate fuzzy set theory fuzzy theory given Hence Henkin Heyting algebra holds implication induction inference rules intension interpretation introduced isomorphic linguistic description logical axioms logical constants Lukasiewicz algebra membership function model theory modus ponens morphism multiformula MV-algebra n-ary natural language negation object obtain piecewise linear function predicate logic predicate symbol proof properties propositional fuzzy logic provability prove pullback represented residuated lattice respect semantics set of formulas special axioms structure subobject classifier subsection syntactic t-norm tautology topos truth values vagueness variable
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