外文翻譯--基于神經(jīng)網(wǎng)絡(luò)和遺傳算法的模糊系統(tǒng)的自動(dòng)設(shè)計(jì)（英文）

1、Neural Networks and Genetic Algorithm Approaches to Auto-Design of Fuzzy Systems ~ Hideyuki TAKAGI 1 and Michael LEE Computer Science Division, University of California, Berkeley, CA 94720 takagi~cs.berkeley.edu, lee~

2、cnmat.cnmat.berkeley.edu, FAX (510)642-5775 Abstract. This paper presents Neural Network and Genetic Algorithm approaches to fuzzy system design, which aims to shorten development time and increase system performance.

3、An approach that uses neural net- work to represent multi-dimensional nonlinear membership functions and an approach to tune membership function parameters are given. A genetic algorithm approach that integrates and a

4、utomates three fuzzy system de- sign stages is also proposed. 1 Introduction Fuzzy systems are frequently designed by hand. This poses two problems: (a) because hand design is time consuming, development costs can be

5、very high; (b) there is no guarantee of obtaining an optimal solution. To shorten the develop- ment time and increase performance of fuzzy systems, there are two separate approaches: develop support tools and automati

6、c design methods. The former includes developing environments to assist in fuzzy system design. Many environ- ments are already commercially available. The latter approach involves introduc- ing techniques to automate

7、 the design process. Though automatic design does not guarantee delivery of optimal solutions, they are preferable to manual techniques, because design is guided towards and an optimal solution by certain criteria. Th

8、ere are three major design decisions to make when designing fuzzy systems: (1) deciding the number of fuzzy rules, (2) deciding the shape of the membership functions, (3) deciding the consequent parameters. Furthermo

9、re, two other decisions must be made: (4) deciding the number of input variables, (5) deciding the reasoning method. (1) and (2) correspond to deciding how to cover the input space. They are highly dependent on each

10、other. (3) corresponds to determining the coefficients of the linear equation in the case of the TSK (Takagi-Sugeno-Kang) model [1], 0 This research is supported in part by NASA Grant NCC-2-275, MICRO State Program Awa

11、rd No.90-191, and EPRI Agreement RP8010-34. We would like to thank Prof. David Wessel and the Center for New Music and Audio Technologies at UC Berkeley for use of computing resources. 1 The author is a Visiting Indus

12、trial Fellow at UC Berkeley and a Senior Researcher of Central Research Laboratories, Matsushita Electric Industrial Co., Ltd. 70 a problem when the input variables are dependent. For example, consider an air condition

13、er controlled by a fuzzy system that uses temperature and humid- ity as inputs. In conventional design methods of fuzzy systems, the membership functions of temperature and humidity are designed independently. The resu

14、lt- ing fuzzy partitioning of the input space resembles Figure l(a). However, when the input variables are dependent, such as temperature and humidity, fuzzy par- titioning such as Figure l(b) is more appropriate. It

15、is very hard to construct such a nonlinear partitioning from one dimensional membership functions. Since NN-driven Fuzzy Reasoning constructs nonlinear multi-dimensional membership functions directly, it is possible t

16、o make the partitionings of Figure l(b). The design steps of NN-driven Fuzzy Reasoning had three steps: clustering the given training data, fuzzy partitioning the input space by neural networks, and designing the conseq

17、uent part of each partitioned space. The first step is to cluster the training data and decide the number of rules. Prior to this step, irrelevant input variables have already been eliminated using the backward eliminat

18、ion or information criteria methods. The backward elimination method arbitrarily eliminates one of the n input variables and trains the neural networks with n - 1 input variables. The performance of neural networks wit

19、h n and n - 1 is then compared. If the performance of the n - 1 input networks is similar or better than the n input networks, then the eliminated input variable is considered irrelevant. Next the training data is clu

20、stered and the distribution the data is obtained. The number of clusters is the number of rules. The second step is to decide the cluster boundaries from the cluster informa- tion obtained in step 1; the input space is

21、partitioned and the multi-dimensional input membership functions are decided. Supervised data is provided by the mem- bership grade of input data to the cluster that is obtained in step 1. First a neural network with

22、n inputs and c outputs, where n is the number of relevant input vari- ables and c is the number of clusters determined in step 1, is prepared. Training data for this network, NNme,n in Figure 2, is generated by from th

23、e clustering information given by step 1. Generally, each input vector is assigned to one of the clusters. The cluster assignment is combined with the input vector to form a training pattern. For example, in the case o

24、f four clusters and an input vector which belongs to cluster 2, the supervised portion of the training pattern will be (0,1,0,0). In some cases, the user may intervene and manually construct the super- vised portion i

25、f s/he believes an input data point shoutd be classified differently than given by the clustering. For example, if the user believes that a data point belongs equally to class one and two, an appropriate supervised out

26、put pattern might be (0.5,0.5,0,0). After training this neural network on this training data, the neural network computes the degrees to which a given input vector belongs to each cluster. Therefore, we assume that th

27、is neural network acquires the charac- teristics of the membership functions for all rules by learning and can generate the membership value that corresponds to any arbitrary input vector. The fuzzy sys- tems, which u

28、ses a neural network as the membership generator is the NN-driven Fuzzy Reasoning. The third step is the design of the consequent parts. Since we know which cluster to assign an input data to, we can train the consequen