## Fuzzy Set Theory: Foundations and Applications |

## Fuzzy Set Theory: Foundations and Applications |

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applications of fuzzy assigned binary fuzzy relation binary relations called Cartesian product characteristic functions characterized classical logic classical set theory closed intervals compatibility relation complement complex propositions concept conclusion conjunction connection consider convex crisp sets cutworthy cylindric extensions definitions degree of truth denned denoted describe determine diagram disjunction elements equivalence relation Euclidean space example expressed false Figure formula fuzzy controllers fuzzy logic fuzzy numbers fuzzy propositions fuzzy set theory given fuzzy graph Hence illustrated implication individual inference rules intersection introduced in Sec linguistic terms meaning membership degree membership function membership grades method n-dimensional natural language negation obtain ordered pairs partial ordering partition premises projections propositional form real numbers reflexive rela represented sentence shown in Fig standard fuzzy subset symbol symmetric tall tautology textbook three-valued logic tion transitive true truth qualifier truth table truth values uncertainty union universal set variable