Defuzzification and implication within ordered fuzzy numbers

Ordered fuzzy numbers (OFN) invented by the first author and his two coworkers in 2002 make possible to utilize the fuzzy arithmetic and to construct the Abelian group of fuzzy numbers and then an ordered ring. This new model uses the extension of the parametric representation of convex fuzzy numbers and overcomes known drawbacks of the classical approach. Addition and multiplication by positive scalar are the same as in convex number case if numbers have the same orientation. However, subtraction, multiplication and division give quit different results. Several new defuzzification operations are introduced together with fuzzy implications which can play a new role in evolutionary fuzzy systems.