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.

The tuning of a fuzzy model is discussed in the context of choices made between different t-norms. The effects of the choice is illustrated by looking at two fuzzy models initially generated, respectively, by grid partition and a novel variant of subtractive clustering. The new variant of subtractive clustering introduced in the paper is based on the standard method of subtractive clustering, where in this new method, the measure of similarity and thus also cluster shapes depend on a choice of t-norm T. © 2010 Wiley Periodicals, Inc.

We bring an overview of fuzzy integrals, including historical remarks. These integrals can be viewed as an average membership value of fuzzy sets, and they are related to fuzzy measures. The Choquet integral can be traced back to 1925. The Sugeno integral has a predecessor in the Shilkret integral from 1971. Some other fuzzy integrals and the corresponding discrete integrals are introduced too. A closer look to the geometric interpretation of fuzzy integrals is also given, resulting among others the weakest and the strongest regular fuzzy integral. An application of the Choquet integral to additive impreciseness measuring of fuzzy quantities with interesting consequences for fuzzy measures is presented. Finally, recent development and streaming of the fuzzy integral theory is discussed. © 2008 Wiley Periodicals, Inc.