Implications on ordered fuzzy numbers and fuzzy sets of type two

Authors:
Magdalena Kacprzak;Witold Kosiński;Piotr Prokopowicz
Affiliations:
Polish-Japanese Institute of Information Technology, Warsaw, Poland;Polish-Japanese Institute of Information Technology, Warsaw, Poland,Kazimierz-Wielki University, Bydgoszcz, Poland;Kazimierz-Wielki University, Bydgoszcz, Poland
Venue:
ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part I
Year:
2012

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Abstract

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.