Analysis and design of a fuzzy system based on fuzzy entropy of fuzzy partitions

In this paper, a new method of analysis and design of a fuzzy system is presented based on the concept of fuzzy entropy of fuzzy partitions of the system´s input space. Two cases, namely, linear partitions and nonlinear partitions of the system´s input space, are considered. Firstly, we establish the system´s fuzzy model. The linearly-divided system is expressed with Mamdani type rules, whose rules are gained through fuzzification of input-output data. The nonlinearly-divided system is represented with the relational partitioning of fuzzy rules due to Yager and Filev (1996), whose rules are abstracted through both samples clustering and neural network techniques. Then, we define fuzzy entropy functions of the two cases and propose their respective optimization algorithms, which permit us to add several rules or merge related rules if necessary. Finally, an example is given to illustrate the effectiveness and high efficiency of the proposed method, which shows that this method is robust with the initial knowledge of the system