Validation and Application of an Adaptive Transparent Defuzzification Strategy for Fuzzy Control zyx Saman K. Halgamuge, Tilman Wagner, Manfred Glesner Abstmx+--An extended parametrizable de- fuzzification method is implemented as a spe- cial transparent neural network, which can be considered as a global defuzzification approx- imater. The customization of the method to different applications and the analysing capa- bility of the trained solution are the key fea- tures here. The network is validated by show- ing its convergence to various existing defuzzi- fication methods. The results of an applica- tion example and a number of less known de- fuzzication methods are also discussed. I. INTRODUCTION The Center of Gravity (COG) and the Mean of Max- ima (MOM) are well known defuzzification meth- ods described in literature [DHR93]. There are also methods such zyxwvutsr as Midpoint of Area (MOA) that can be implemented in software and hardware effi- ciently. Let us denote U as the finite set of possi- ble normalized output values of a controller: zyxwvutsr U zyxwvuts = {Ul, U2 ..... U,,}, where zyxwvutsrq Vi, 0 < zyxwvu Ui < 1. The output of the rule block is a fuzzy output that must be de- fuzzified to get the crisp control output U,,t<U. The method MOA can be defined as: lUEpA pi . di = zyxwvu pi . di L:p. A new method described here is Center of Maxima (COM): where zyxwvutsrq pya= is the maximumof pi Vi and n denotes the zyxwvutsrqpo netwidth. The method MOM can be considered as a special case of COG, where as COM is a special case of MOA. Mailing Address: Darmstadt University of Technology, Institute of Microelectronic Systems, Karlstr. 15,D-64283 Darmstadt, Ger- many, Tel.: ++49 6151 16-4337, fix.: ++49 6151 16-4936 Email: samanBmicroe1ectronic.e-technik.th-darmstadt.de Many research has been reported on learning fuzzy systems, i.e., learning rules and fine tuning of mem- bership functions. Few papers could be found in describing the extraction of complete fuzzy systems from sample data. And serious efforts in adapting de- fuzzification to the specific nature of an application as reported in [YF93] is not very common. The appli- cation of different defuzzification methods may lead to completely different crisp outputs depending on the shape of the fuzzy outputs. Therefore, tuning to an application or customization of the defuzzication strategy is an interesting alternative to the conven- tional trial and error methods used. In a previous publication ([HG93]), the concept of Customizable BAsic Defuzzification Distributions was presented. The CBADD is an extension of well known BADD method proposed by Yager et a1 [FY91]. This paper describes the CBADD network in sec- tion 2 presenting simulation results in section 3 and showing the applicability in a real world problem in section 4. 11. CBADD TRANSPARENT NEURAL NETWORK CBADD uses a special transparent neural network with netwidth (n) number of inputs, each of them feeding a pi, the ith discrete value of the fuzzy out- put, where 0 < i < n to approximate the crisp output for Uout. It consists of several consecutive layers of // Figure 1: CBADD Transparent Neural Network 0-7803-1896-X/94 $4.00 01994 IEEE 1642