General derivation and analysis for input-output relations in interval type-2 fuzzy logic systems

Aliasghary M., EKSIN İ., Güzelkaya M., KUMBASAR T.

SOFT COMPUTING, vol.19, no.5, pp.1283-1293, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 5
  • Publication Date: 2015
  • Doi Number: 10.1007/s00500-014-1340-7
  • Journal Name: SOFT COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1283-1293
  • Istanbul Technical University Affiliated: Yes


In this paper, analytical closed-form expressions are derived for the input-output relation related to an interval type-2 fuzzy logic system. It has been assumed that the related fuzzy system possesses diamond-shaped type-2 fuzzy sets for each input and singletons for output. Moreover, the Nie-Tan inference engine that provides a closed-form is preferred. The footprint of uncertainty in diamond-shaped type-2 membership functions generates four times as many regions in analytical closed-form expression as generated by standard triangular type-1 membership functions. The derived mathematical relationships provide a chance to examine the internal structure of an interval type-2 fuzzy system. These extra regions may enhance the performance of an interval type-2 fuzzy logic system over the type-1 counterpart. An important advantage of the proposed technique is that the analytical input-output relations are applicable for any number of input fuzzy sets. Analytical structures of two special cases of interval type-2 fuzzy logic systems which use different number of membership functions for each input are derived in detail.