Abstract
This work presents the use of local fuzzy prototypes as a new idea to obtain accurate local semantics-based Takagi–Sugeno–Kang (TSK) rules. This allow us to start from prototypes considering the interaction between input and output variables and taking into account the fuzzy nature of the TSK rules. To do so, a two-stage evolutionary algorithm based on MOGUL (a methodology to obtain Genetic Fuzzy Rule-Based Systems under the Iterative Rule Learning approach) has been developed to consider the interaction between input and output variables. The first stage performs a local identification of prototypes to obtain a set of initial local semantics-based TSK rules, following the Iterative Rule Learning approach and based on an evolutionary generation process within MOGUL (taking as a base some initial linguistic fuzzy partitions). Because this generation method induces competition among the fuzzy rules, a postprocessing stage to improve the global system performance is needed. Two different processes are considered at this stage, a genetic niching-based selection process to remove redundant rules and a genetic tuning process to refine the fuzzy model parameters. The proposal has been tested with two real-world problems, achieving good results. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 909–941, 2007.
Highlights
One of the most important areas for the application of Fuzzy Set Theory is Fuzzy Rule-Based Systems ~FRBSs!
We propose the use of local semantics-based Mamdani fuzzy rules as local fuzzy prototypes from which to obtain accurate local semanticsbased TSK rules
Once the values of e, v, and k ~defined in the previous subsection! are given by the GFRBS designer, the method for identification of local semantics-based TSK FRBSs may be summarized in the following algorithm: Initializations: ~a! Initialize the set of examples Ep to EN . ~b! Set the example covering degree CV @l # R 0, l ϭ 1, . . . , N. ~c! Initialize the final set of prototypes Bi to empty
Summary
One of the most important areas for the application of Fuzzy Set Theory is Fuzzy Rule-Based Systems ~FRBSs!. The cluster centers or estimates for the parameters are poor.[13] This behavior is far from the TSK fuzzy nature These kinds of learning techniques have been taken into account as prototype-identification algorithms, summarizing a data set by a number of representative prototypes ~objects lying in the same space as the sample points!. We propose the use of local semantics-based Mamdani fuzzy rules as local fuzzy prototypes from which to obtain accurate local semanticsbased TSK rules This new idea allows us to start from prototypes considering the interaction between input and output variables and taking into account the fuzzy.
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