Transformation between type-2 TSK fuzzy systems and an uncertain Gaussian mixture model

Qinli Zhang, Fu Lai Korris Chung, Shitong Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


In this paper, an interval extension of the Gaussian mixture model called uncertain Gaussian mixture model (UGMM) is proposed and its transformation into the additive type-2 TSK fuzzy systems is presented. The conditions under which a UGMM becomes a corresponding type-2 TSK fuzzy system are derived theoretically. Furthermore, the mathematical equivalence between the conditional mean of a UGMM and the defuzzified output of a type-2 TSK fuzzy system is proved. Our results provide a new perspective for type-2 TSK fuzzy systems, i. e., interpreting them from a probabilistic viewpoint. Thus, instead of directly estimating the parameters of the fuzzy rules in a type-2 TSK fuzzy system, we can first estimate the parameters of the corresponding UGMM using any popular density estimation algorithm like the expectation maximization (EM) algorithm. Our experimental results clearly indicate that a type-2 fuzzy system trained in such a new way has higher approximation accuracy and stronger robustness than current type-2 fuzzy systems.
Original languageEnglish
Pages (from-to)701-711
Number of pages11
JournalSoft Computing
Issue number7
Publication statusPublished - 1 May 2010


  • Additive fuzzy models
  • Gaussian mixture models
  • TSK models
  • Type-2 fuzzy systems

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Geometry and Topology


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