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Differences between t‐norms in fuzzy control
Author(s) -
MesiarováZemánková Andrea,
Ahmad Khurshid
Publication year - 2012
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21541
Subject(s) - nilpotent , mathematics , fuzzy control system , fuzzy logic , norm (philosophy) , noncommutative geometry , t norm , sinc function , pure mathematics , mathematical optimization , discrete mathematics , computer science , fuzzy set operations , artificial intelligence , mathematical analysis , political science , law
Abstract The application of conjunctive aggregation functions in fuzzy control systems with n inputs is discussed, and the effect of the choice of a continuous t‐norm in the inference phase for Takagi–Sugeno–Kang (TSK) systems is computed. A continuous t‐norm modeling AND connective in antecedent part of fuzzy rules can be reduced just to strict or nilpotent t‐norm. The isomorphism of strict (nilpotent) t‐norms enables simpler fitting of TSK fuzzy system parameters and reduces the computational complexity. Similar principle can also be used in the case of some noncommutative conjunctive aggregation functions modeling AND connective. The effect of the choice of a continuous t‐norm is then evaluated on well‐known case studies in fuzzy control, the Sinc function, and the urban traffic noise control system.