...Infinite FRE to a complete browerian lattices 162 1.28 Semantics of implication operators and fuzzy relational products 164 Chapter Two SO... ...orithm to problems in chemical industries 199 2.11 Semantics of implication operators and fuzzy relational products applied to HIV/AIDS pat... ...ransitivity. When a relation R is not i-transitive, we define its i-transitive closure as a relation R τ (i) that is the smallest i-transitive rela... ... i-transitive relation, containing R. To investigate properties of i-transitive closure let R (n) = R o i R (n – 1) n = 2, 3,… where R is a fu... ... R on X 2 , the fuzzy relation R τ (i) = U ∞ =1 ) ( n n R is the i-transitive closure of R. Prove if R be a reflexive fuzzy relation on X 2 , wh... ... , , , , 0 b a b a b a t Max-SO and min-SO are extensions of the α and the σ operators defined by Sanchez [84] for the min t-norm. The max-SO ex... ...andomly generated population and progress to improve solutions by using genetic operators such as crossover and mutation operators. In each interact... ...for y x q y cl D D x for D x some for y x q y X X (2) where cl denotes the closure of a set. Especially, we put α q ~ (x) : = α q ~ ({x}) for ... ... relation is called anti-transitive Given a relation R N (X, X) its transitive closure R NT (x, X) can be analyzed in the following way. The tran...