Exact inversion of decomposable interval type-2 fuzzy logic systems

Kumbasar T. , EKSIN İ. , Güzelkaya M. , YESIL E.

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, vol.54, no.2, pp.253-272, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 2
  • Publication Date: 2013
  • Doi Number: 10.1016/j.ijar.2012.11.005
  • Page Numbers: pp.253-272


It has been demonstrated that type-2 fuzzy logic systems are much more powerful tools than ordinary (type-1) fuzzy logic systems to represent highly nonlinear and/or uncertain systems. As a consequence, type-2 fuzzy logic systems have been applied in various areas especially in control system design and modelling. In this study, an exact inversion methodology is developed for decomposable interval type-2 fuzzy logic system. In this context, the decomposition property is extended and generalized to interval type-2 fuzzy logic sets. Based on this property, the interval type-2 fuzzy logic system is decomposed into several interval type-2 fuzzy logic subsystems under a certain condition on the input space of the fuzzy logic system. Then, the analytical formulation of the inverse interval type-2 fuzzy logic subsystem output is explicitly driven for certain switching points of the Karnik-Mendel type reduction method. The proposed exact inversion methodology driven for the interval type-2 fuzzy logic subsystem is generalized to the overall interval type-2 fuzzy logic system via the decomposition property. In order to demonstrate the feasibility of the proposed methodology, a simulation study is given where the beneficial sides of the proposed exact inversion methodology are shown clearly. (c) 2012 Elsevier Inc. All rights reserved.