Title :
Lipschitz Continuity of Approximate Reasoning
Author :
Mitsuishi, Takashi ; Terashima, Takanori ; Homma, Toshimichi ; Shidama, Yasunari
Author_Institution :
Univ. of Marketing & Distrib. Sci., Kobe
Abstract :
Lipschitz continuity of some approximate reasoning methods on the premise variables are described to guarantee the existence of the unique solution of the state equation of a fuzzy control. To obtain this result, some conditions must be given to the set of membership functions. Then we introduce some sets of membership functions used in Mamdani method, product-sum-gravity method and Larsen method and proved Lipschitz continuity of them.
Keywords :
fuzzy control; fuzzy set theory; inference mechanisms; Larsen method; Lipschitz continuity; Mamdani method; approximate reasoning; fuzzy control; membership function; product-sum-gravity method; state equation; Artificial intelligence; Bismuth; Control systems; Distributed computing; Equations; Fuzzy control; Fuzzy set theory; Production; Software engineering; Steam engines; Lipschitz continuity; approximate reasoning; fuzzy cpntrol;
Conference_Titel :
Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing, 2008. SNPD '08. Ninth ACIS International Conference on
Conference_Location :
Phuket
Print_ISBN :
978-0-7695-3263-9
DOI :
10.1109/SNPD.2008.115
