Mathematical Principles of Fuzzy LogicMathematical 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. |
Contents
WHAT WHY FOR WHICH? | 1 |
ALGEBRAIC STRUCTURES FOR LOGICAL CALCULI | 15 |
LOGICAL CALCULI AND MODEL THEORY | 61 |
FUZZY LOGIC IN NARROW SENSE 95 | 94 |
FUNCTIONAL SYSTEMS IN FUZZY LOGIC THEORIES | 179 |
FUZZY LOGIC IN BROADER SENSE | 223 |
TOPOI AND CATEGORIES OF FUZZY SETS | 259 |
FEW HISTORICAL AND CONCLUDING REMARKS 299 | 298 |
Index 315 | 314 |
Other editions - View all
Mathematical Principles of Fuzzy Logic Vilém Novák,Irina Perfilieva,J. Mockor No preview available - 2012 |
Common terms and phrases
A₁ Analogously approximation assigned b₁ BL-algebra Boolean algebra calculus characterize classical logic completeness theorem concept conjunction conjunctive normal form connectives consistent construct corresponding d₁ defined DEFINITION defuzzification denote disjunction element equivalent evaluated formulas evaluating predications evaluating syntagms example exists extension filter finite FJ(T FL-functions FL-relation following lemma 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 M₁₂ membership function model theory modus ponens morphism multiformula MV-algebra n-ary N-fuzzy set N-set N-subset natural language negation normal forms object obtain piecewise linear function predicate logic predicate symbol proof properties provability prove represented residuated lattice semantics set of formulas special axioms structure subobject classifier subset syntactic t-norm t₁ tautology truth values vagueness variable Vx)B