Theory And Approaches Of T-S Fuzzy Inference Systems Identification With Structure Sparse Coding

Fuzzy inference system is an effective tool for approximation of complex nonlinearsystems with uncertainty by its linguistic and representable fuzzy rules. However, be-cause of the problem of “rule explosion” caused by the curse of dimensionality, it is quitetechnical to extract effective fuzzy rules from large complex input/output data set. Asa result, the problem of how to establish a compact fuzzy inference system with bettergeneralization has become a key problem as well as a significant challenge. In this paper,against to the key issues of how to effectively exploit structure information of fuzzy infer-ence system and how to determine the optimal fuzzy rules, a sparse coding based methodare developed for identification of fuzzy inference system. In summary, the major novelcontributions are as follows:1. A sparse coding approach is exploited for identification of singleton fuzzy infer-ence system (zero-order T-S fuzzy inference systems) with multiple-input-single-output(MISO). This method explicitly takes into account the structure information of fuzzysystems and cast the problems of singleton fuzzy inference systems identification and re-duction of fuzzy rules into an optimization problem by sparse coding for the parametersof fuzzy rules consequence. In such a way, the fuzzy rules are reduced by selecting themain important fuzzy rules and eliminating the redundant ones.2. Thanks to the property that the consequents of singleton fuzzy rule with respect todifferent output variable share a common antecedent part, a joint sparse coding methodis proposed for identification of singleton fuzzy inference system with multiple-input-multiple-output (MIMO). It is different from the traditional separation approaches to i-dentification of MIMO fuzzy inference systems, this method guarantees a common sparsepattern of the fuzzy rules’ consequent parameters across multiple output variables by us-ing joint sparse coding, and therefore can reduce the number of fuzzy rules by selectingthe main important fuzzy rules and eliminating the redundant ones with consideration ofdifferent output variables simultaneously.3. Taking into account the block structure information of1-order T-S fuzzy inferencesystem, a hierarchical structured sparse coding method is exploited for identification ofMISO1-order T-S fuzzy inference system. This method includes two levels: in the first level, block structure sparse coding of fuzzy rules’ consequents parameters is developedfor the reduction of fuzzy rules by selecting the important fuzzy rules and eliminatingthe redundant ones; In the second level, sparse coding for consequent parameters of theselected fuzzy rules is executed to guarantee more zero parameters in fuzzy rules andmake the fuzzy rules be more simpler.4. Thanks to the block structured information of MIMO1-order T-S fuzzy inferencesystem and the property that the affine functions of consequents with respect to differentoutput variable share a common antecedent part, a joint block structured sparse codingmethod is exploited for identification of MIMO1-order T-S fuzzy inference system. Thismethod guarantees a common block sparse pattern of the fuzzy rules’ consequent pa-rameters across multiple output variables by using joint block structure sparse coding,and therefore can reduce the number of MIMO fuzzy rules by consideration of differentoutput variables simultaneously.