Implications on Ordered Fuzzy Numbers and Fuzzy Sets of Type Two

Ordered fuzzy numbers (OFN) as generalization of convex fuzzy numbers represented in parametric form and invented by the second and the third authors and their coworker in 2002, make possible to utilize the fuzzy arithmetic and to construct the lattice structure on them. Fuzzy inference mechanism and implications are proposed together with step fuzzy numbers that may be used for approximations as well as for constructing new fuzzy sets of type two.

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