Defuzzification functionals are homogeneous, restrictive additive and normalized functions

Authors:
Witold Kosiński;Agnieszka Rosa;Dorota Cendrowska;Katarzyna Węgrzyn-Wolska
Affiliations:
Polish-Japanese Institute of Information Technology, Warsaw, Poland;Kazimierz-Wielki University, Bydgoszcz, Poland;Polish-Japanese Institute of Information Technology, Warsaw, Poland;École Supérieure d'Ingénieurs en Informatique et Génie de, Télécommunication (ESIGETEL), France
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

Defuzzification operators, that play the main role when dealing with fuzzy controllers and fuzzy inference systems, are discussed for convex as well for ordered fuzzy numbers. Three characteristic conditions are formulated for them. It is shown that most of known defuzzification functionals meet these requirements. Some approximation methods for determining of the functionals are given and then applied.