Fuzzy systems design: direct and indirect approaches
 Plamen Angelov,
 Costas Xydeas
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A systematic classification of the datadriven approaches for design of fuzzy systems is given in the paper. The possible ways to solve this modelling and identification problem are classified on the basis of the optimisation techniques used for this purpose. One algorithm for each of the two basic categories of design methods is presented and its advantages and disadvantages are discussed. Both types of algorithms are selflearning and do not require interaction during the process of fuzzy model design. They perform adaptation of both the fuzzy model structure (rulebase) and the parameters. The indirect approach exploits the dual nature of TakagiSugeno (TS) models and is based on recently introduced recursive clustering combined with Kalman filteringbased procedure for recursive estimation of the parameter of the local submodels. Both algorithms result in finding compact and transparent fuzzy models. The direct approach solves the optimisation problem directly, while the indirect one decomposes the original problem into online clustering and recursive estimation problems and finds a suboptimal solution in realtime. The later one is computationally very efficient and has a range of potential applications in realtime process control, moving images recognition, autonomous systems design etc. It is extended in this paper for the case of multiinput–multioutput (MIMO systems). Both approaches have been tested with real data from an engineering process.
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 Title
 Fuzzy systems design: direct and indirect approaches
 Journal

Soft Computing
Volume 10, Issue 9 , pp 836849
 Cover Date
 20060701
 DOI
 10.1007/s005000050006x
 Print ISSN
 14327643
 Online ISSN
 14337479
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Fuzzy models design
 TakagiSugeno and Mamdani fuzzy models
 Online clustering
 Recursive least squares estimation
 Genetic algorithms
 Industry Sectors
 Authors

 Plamen Angelov ^{(1)}
 Costas Xydeas ^{(1)}
 Author Affiliations

 1. Department of Communication Systems, Lancaster University Bialrigg, Lancaster, LA1 4WA, UK