Improved Wang-Mendel Method Based On SOM And Cooperation Among Input Variables

Many industrial productions are nonlinear, uncertain and high-dimension. So theeffective mode is hard to be determined with classical mathematic in this kind ofindustrial production. The fuzzy system theory can simulate the methods by whichpeople deal with complex and uncertain problems in reality. The theory makes theknowledge interpreted by natural language into mathematical form, so that theknowledge can reasonably be applied to industrial control. The core of the fuzzysystem is the rule base. A fuzzy system based on a benign fuzzy rule base can becreated with higher approximation properties compared the original model. So theresearch on generating a correct and complete fuzzy rule base quickly is of significantacademic and practical values to the modern industrial control systems.Wang-Mendel algorithm (termed as WM algorithm) is a relatively classical methodin fuzzy rule extraction. It can extract fuzzy rules effectively from numerical data. Itssimplicity and practicality make it widely used. However, WM algorithm is severelyconstrained by the sample. If there are some problems in the sample, the fuzzy rulebase extracted by WM algorithm may go wrong. Classic WM algorithm lacks ofcompleteness and robustness. When extracting fuzzy rules from large-scale sample,efficiency of the algorithm is low.If the sample set is complete and of small scale without bad data, the classical WMalgorithm can quickly get a fuzzy rule base with completeness and goodapproximation performance. If problems arise from the sample set, problems of thefuzzy rule base which is generated by WM will come out correspondingly.Since the source of the problem is the sample set, these problems can be solvedthrough it. Analyzing the sample set, we know that there are definite relations amongthe input variables. We can predict the absence rule in the sample and reduce theinterference of the bad data with these relations. This paper proposes an improvedWM algorithm to generate fuzzy rule based on cooperation among input variables. The research, which thoroughly analyses the distribution of the sample, revealscertain regularity of the sample. With this distribution regularity, we can adjust the data which deviates from the regularity. At the same time, we can downsize the scaleof the sample on the premise of maintaining the original distribution regularity so asto improve the extraction efficiency of the WM algorithm. Accordingly, anassumption of improving WM algorithm based on SOM is put forward. In response tothe advantage and disadvantage of these two improvements, this paper put forwardimproved WM algorithm which combines SOM algorithm and the coordinationrelationship between input variables.