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Paper   IPM / Cognitive / 13832
School of Cognitive Sciences
  Title:   Generating flexible convex hyper-polygon validity regions viasigmoid-based membership functions in TS modeling
1.  A. Kalhor
2.  B. Araabi
3.  C. Lucas
  Status:   Published
  Journal: Applied Soft Computing
  Vol.:  28
  Year:  2015
  Pages:   589-598
  Supported by:  IPM
Using suitable Membership Functions (MFs) has a substantial impact on increasing of the accuracy andreduction of redundancy in a neuro-fuzzy modeling approach. In this paper, we suggest sigmoid-basedMFs which can generate flexible convex hyper-polygon validity regions in Takagi–Sugeno (TS) fuzzymodels. To this end, the sigmoid-based function is equal to the product of some sigmoid functions whosearguments are hyperplane equations. It is discussed that such function can represent a soft, convex, flatregion with arbitrary number of hyperplane borders (edges). Afterwards, we introduce first-order andhigh-order TS fuzzy models, where, the suggested sigmoid-based functions are utilized in the premiseparts of the fuzzy rules and linear models or quadratic functions are used as submodels in consequenceparts. It is shown that utilized submodels can be optimized locally and globally. An incremental learningalgorithm is then suggested to identify both first-order and high-order TS fuzzy models. The performanceof introduced TS fuzzy models are examined and compared with existing models in prediction of achaotic time series as well as in function approximation of a sun sensor. Obtained results demonstratehigh accuracy and low redundancy of the suggested high-order TS fuzzy model. Finally, the learningperformance of two introduced first-order and high-order TS fuzzy models are compared with eachother in identification of a steam generator model.

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