## Applications of fuzzy sets to systems analysis |

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assignment automaton behaviour Boolean algebra category Set(L characteristic function clustering commutative complete lattice completely distributive lattice composition law concept of fuzzy Definition denote derivation chains dynamics elements equivalence relation example finite flou set FM(n functor fuzzy automata fuzzy decision fuzzy events fuzzy formula fuzzy function fuzzy goal fuzzy grammar fuzzy language fuzzy logic fuzzy matrices fuzzy morphisms fuzzy sets theory fuzzy subset fuzzy systems fuzzy theory fuzzy topological spaces fuzzy valid homomorphism if(U initial isomorphism L-sets Lemma Let us consider mathematical membership degree membership function minimal realization monoid Morgan algebra objects observe obtain operations optimal output map pair prime implicant problem Proof properties Proposition quotient set reachable response function satisfies semiring sequence structure sup Xd(x suppose theorem theory of fuzzy topological spaces transition tranzitive truth value Zadeh