[Reprinted] fuzzy system: Challenges and opportunities coexist-Insights from ten years of research Wang Lixin

[Reprinted]Fuzzy System: Challenges and opportunities coexist--Insights from ten years of research Wang Lixin

Http://www.ee.ust.hk/ece.php Http://www.ee.ust.hk /~ Eewang/ Fuzzy System: Challenges and opportunities coexist-Insights from ten years of research Wang Lixin Wang Lixin received his bachelor's degree and master's degree from Northwestern University of Technology in 1984 and 1987 respectively, and obtained his doctorate degree from the University of Southern California in 1992. He has taught at the Electrical and Electronic Engineering Department of Xianggang University of Science and Technology since 1993. The research results have been widely cited. He is now the deputy editor of automatic and IEEE transaction on fuzzy systems. Reviews papers on fuzzy control, fuzzy neural networks, and approximate performance of fuzzy systems. Fuzzy systems have always been a controversial field. I have been in this field for ten years since 1990. I have never left this field since I first graduated from the U. S. doctoral student, Professor Zadeh, the founder of fuzzy theory, and now the deputy editor of automation and IEEE transaction on fuzzy systems. It is hard to work in a controversial area. I have seen a lot of insights from the cold and hot areas from widespread suspicion to basic acceptance. This is an opportunity to share some of the points of sentiment with you. These ideas are personal and sensitive and controversial, so please take a look at them. We welcome your criticism and discussion. 1. Challenges As a researcher in the field of fuzzy systems, my biggest pain is that, in many cases, people have already been classified as Class-1 people without opening their mouths. These people do not have a strict scientific attitude and Positive enterprising spirit. If such people do not have strict theoretical results, they will be "Vague, these people do not have a solid foundation to solve the difficulties in the traditional field, so they come to the "fuzzy" field to seek gold and propose innovative ideas. Why are researchers in many traditional fields skeptical about fuzzy theory? I would like to have the following reasons: 1.1 Reasons for disputes caused by Fuzzy Theory Cause 1: Some starting points of fuzzy theory have problems. In the introduction of some fuzzy theory papers (including some classic papers), we often see such a discourse: the requirements of traditional theories are too detailed and it is increasingly difficult to solve increasingly complex practical problems, therefore, we need a "Vague" theory. In other words, strict proof, derivation and verification are not required here. Fuzzy: I am not sure how many fuzzy theory researchers hold this point of view, but there are certainly not a few such researchers. In addition, this idea is constantly spread on different occasions. The supporters of such ideas certainly have their own reasons. Due to limited space, we cannot discuss this advantage in depth here. All I can say is that I personally disagree with this idea very much. It is strictly the basic principle that must be adhered to under any circumstances and cannot be abandoned on the pretext of complicated problems. Cause 2: the fuzzy theory system is imperfect. From the perspective of engineering application, the fuzzy system theory before 1990s has two weaknesses. First, there is no systematic and effective way to obtain knowledge. Instead, you can only use an expert questionnaire, which is time-consuming and difficult to obtain satisfactory results; second, the lack of a complete theoretical system to ensure system stability, convergence, and other basic requirements. Since 1990s, the theory of fuzzy system has made breakthroughs in these two aspects. using various learning algorithms, we can now learn knowledge from data (so-called fuzzy neural networks ). The emergence of more and more fuzzy control papers with strict mathematical proofs (such as most of the papers in this journal) makes fuzzy control no longer a simple controller that can only be based on experience, it is a high-performance nonlinear controller with strict theoretical support. Therefore, in recent years, there have been fewer and fewer criticisms of Fuzzy Control Based on this reason. We are glad to see that the theoretical pillar of the fuzzy system has been basically established, and our task is to constantly improve it. Cause 3: the quality of the papers in the fuzzy field is uneven. One of the characteristics of fuzzy control is that it is easy to get started with: several rules, several simulations, and the results are good-A paper is a good method for emergency response (graduation, delivery, and job retention. Can emergency responders write their papers? Traditional domains (such as classic control theory) are different. They must undergo rigorous training and take many courses to get started. Therefore, it is difficult for traditional fields to respond to emergencies (compared with the fuzzy field). If there are more papers with poor quality in a field, people will naturally evaluate it less. However, after all, good papers will emerge. This field gradually matures when the accumulated papers become more advanced. It is a great pleasure to personally experience this mature process and grow together with the field. Welcome to join us. Cause 4: Fuzzy Theory Researchers criticize and reject traditional fields without analyzing them. This is directly related to the advantages in cause 1. These papers first negate the traditional theory, saying that the traditional theory cannot solve such a problem, so fuzzy theory is required. A large part of such criticism is not based on in-depth analysis of traditional theories. The consequence of such criticism is to contradict the fuzzy theory with the traditional theory and make the fuzzy theory the target of the public. In recent years, the "Soft Computing" proposed by Zadeh has attempted to integrate the theory of modemy with other traditional and emerging theories. "Strengthening cooperation to avoid confrontation" has achieved good results. The above are general reasons, and there are some technical reasons, that is, some specific questions frequently asked by fuzzy theory. Below are some typical FAQs. 1.2 Questions Frequently Asked About Fuzzy Theory Question 1: Can I give an example that can only be solved by fuzzy control, but cannot be solved by other methods? (This is a question that is frequently asked at major control meetings) Answer. There are two answers, one simple and one complex. The simple answer is that this question should not be asked. Because no theory is the only way to solve a problem (for most engineering theories ). What problems can be solved only by linear control theory, rather than other control schemes? The problem is that the method is good or bad, not the only one. Fuzzy control is one of the many control schemes. It is very likely to give control results better than other control schemes for some problems. These problems have the following characteristics: first, there is no available mathematical model, the controlled object is strongly nonlinear (so it is difficult to use modern control and PID control). Another characteristic is that it has good expert experience and can greatly improve the control performance. This leads to the second complex answer. This is an example. This example has only the above two features. Due to space limitations, the task of constructing a specific example is left to the reader. Question 2: we do not need fuzzy theory, because the problems that can be solved by fuzzy theory can also be solved by probability theory and will be better solved (this is the most prominent argument in fuzzy and random debates ). Answer. To answer this question, we must first understand the cause of this problem. one of the starting points of Zadeh's fuzzy theory is to describe uncertainty. There are various uncertainties, such as ambiguity and randomness. Randomness is described by the probability distribution function, while ambiguity is described by the membership function of the fuzzy set, which is one of the basic starting points for introducing the fuzzy set. The supporter of the concept is the basic starting point of suspicion. They believe that the so-called fuzzy uncertainty can also be described using probability distribution functions. They believe that the supporters of the fuzzy theory only mention the frequency interpretation of probability when evaluating probability theory, while ignoring the subjective interpretation of the concept, that is, subjective probability and Bayesian theory. Therefore, a special fuzzy theory is not needed to describe fuzzy uncertainty. It is enough to use probability theory. Based on the rich connotation of probability theory and the complete theoretical system, a better result can be obtained. This is a highly controversial topic. If I only want to describe uncertainty, I personally agree with the viewpoint supported by probability theory. The problem is to describe what to do later. I use a function to describe an uncertain phenomenon. For example, "very hot" is not important (fuzzy membership function or probability distribution function ). What is important is what to do next and how to deal with this letter. This is the branch of fuzzy theory and probability theory. The principle system of probability theory imposes strict limitations on operations, fuzzy theory is much more loose and flexible. It is precisely this loose and flexibility that makes fuzzy theory easy to describe the various complexities of human language communication and the phenomenon full of yundun. Therefore, fuzzy theory is more suitable for describing the knowledge expressed in human language and applying the knowledge to various specific problems. Probability theory is more suitable for describing the uncertainty of data, in addition, the core content represented by pivot data is removed from these uncertainties. Question 3 The method you are talking about is not vague. Why is it called the fuzzy system method? (This is a frequently asked question after I read a thesis ). Answer. People often misunderstand that the fuzzy system method is to blur the problem. In fact, the opposite is true. fuzzy phenomena are represented by definite mathematical functions. Thus, the fuzzy problem becomes clearer, that is, the fuzzy method is actually a fuzzy solution, rather than a model intensification. "Very Hot" is a fuzzy phenomenon. Once a membership function is used to describe "very hot", "very hot" will not be blurred, and "very hot" will wait for this membership function. How to determine this membership function is another problem, not related to fuzzy. For example, the membership function can be determined through data learning, and the expert questionnaire method can also be used. Question 4: What are the advantages of a fuzzy system compared with other non-linear modeling methods, such as neural networks, piecewise polynomials (spline), decision trees, and wavelet series? (This is my favorite question, because once the questioner accepts my answer, it is very likely that he or she will try to use the fuzzy system method in future research and application) Answer. Fuzzy Systems, neural networks, piecewise polynomials, decision trees, and wavelet series are all used to describe nonlinear relationships. There is no absolute Optimal Method in the world of nonlinear modeling. Because a non-linear relationship contains all possible relationships, we can always find a non-linear relationship suitable for a specific method, so that this method is optimal for this type of non-linear relationship. It is for this reason that many of the above nonlinear modeling methods have been developed. So how can we compare the quality of different methods? I think we can consider the following four aspects: 1) balance between precision and complexity of Approximation The above methods are all omnipotent Inspector, that is, the methods above can be used to approach any nonlinear function to any precision using enough items and parameters. The more items and parameters, the higher the complexity of the system, and the higher the approximation accuracy. The problem now is that for the close complexity, which method can express the non-linear relationship is more flexible and more general. In this regard, fuzzy systems, neural networks, piecewise polynomials, and decision trees are all very good. Specifically, you can select the function location, shape, and different combinations. Fuzzy Systems can flexibly describe various non-linear relationships. Neural Networks have projection-like characteristics, so they can automatically find non-linear orientations for effective expression. The piecewise polynomials and decision trees use the flexible division of regions to simplify and make use of traditional methods with high efficiency. The wavelet series is almost the same. Because the original starting point of wavelet series is the decomposition of one-dimensional signals, the efficiency becomes lower after being directly promoted to high dimensions. 2) convergence speed of Learning Algorithms Generally, it is considered that the speed of Multi-number or convergence of neural networks and segments is slow. However, this is not the case, and neural networks and piecewise polynomials are constantly improving. A fast algorithm is introduced, and the convergence speed is not bad. There are also many clever algorithms for wavelet series. If it can be effectively promoted to high-dimensional situations. Is a recommended method. The decision tree is based on the clever algorithm. Since data only needs to be processed once without loops, the convergence speed is fast. Fuzzy systems have multiple learning algorithms, one Processing Method for Data similar to decision trees, and BP algorithms similar to neural networks. The convergence speed is no less than that of other methods. In terms of the convergence speed of learning algorithms, decision trees and fuzzy systems are faster than neural networks and piecewise polynomials. Of course, this is definitely not a final conclusion, because new algorithms are constantly emerging, while old algorithms are constantly improving. 3) interpretability of results That is, whether the physical meaning of the structure and parameters can be given can be easily understood and accepted by ordinary people. In this respect, the fuzzy system has outstanding superiority. The fuzzy system is composed of if-then rules, so the structure and parameters of the system can be naturally explained by the IF-IHEN rules, which is very easy to understand. Neural Networks are poor in this regard, and the meaning of parameters is hard to be explained and understood by experts. The physical meaning of decision trees and piecewise polynomials is easy for professionals to understand, and it is hard for general people to say. Even for professionals, such explanations are complex and not as simple as if-then rules. 4) Make full use of various forms of information The purpose of nonlinear modeling is to establish the mathematical relationship between a level-1 variable and another level-1 variable. What do we rely on to establish this relationship? We can obtain various information about the relationship between the two variables. This information can be the sample data, that is, the value of another group of variables when a group of variables take a specific value. It can also be a general description. For example, if a variable is large, a variable is small; it can also be an approximate mathematical relationship. A good way should be to make full use of different forms of information as much as possible. In this respect, the fuzzy system has outstanding advantages. The fuzzy system can not only use the sampled data, but also include general descriptions in the system, data information and language information can be organically combined, while other Parties can only use data information. Based on the above four points, I have concluded that, in addition to its own unique advantages, fuzzy systems include strong interpretability and available language information. In other aspects, for example, the convergence speed of approximation accuracy and efficiency learning algorithms is no less than that of other methods. Based on this conclusion, despite the difficulties in the past few years, I have never left the field of fuzzy system research. Why should we give up such a good method? Question 5: Why is fuzzy theory easy to accept in the East? Is it related to the thinking philosophy of the East? (After answering some challenging and technical questions, I will answer this question as a very easy topic. Sorry ). Answer. What should I do? Maybe so. The orients like the circle, and they push the circle to the left or right. Is it fuzzy? You blur, I blur, everyone together, pour out experience, pour out the level, pour it on, don't bubble, don't sink in the middle, don't block, pour out a black and white integrated peace of life, an academic class in which scholars and scammers coexist. As an important part of Chinese culture, the doctrine of the mean of the middle and the rare confusion are passed on from generation to generation. It promotes social stability, enhances the cohesion of the nation, and creates a gentle character for the Chinese. Its biggest side effect is its serious corrosion of the most beautiful ingredients in human nature-sincerity! In many cases, what people next say is far different from what they really think. In the fog of the cloud, it's easy for you to understand. Maturity is defined as knowing but not knowing. Due to lack of sincerity, it is difficult to establish a role between people. It's just a blur when you have to interact. There are many similar examples. All this shows that the way of thinking left by our ancestors is indeed closely related to the word "fuzzy. It's no wonder that "Fuzzy Theory" was introduced in the west and we soon accepted it. I went to the United States only after I completed my master's degree in China. At that time, I was very familiar with some big and comprehensive ideas, such as the unification of the second theory (information theory and artificial intelligence theory). I also liked the large system theory and published a paper on the C3I system (C3I: command, Control, Communication and intelligence ). When I arrived in the United States, I found myself in another world. The details are the most important, and no details are the same as nothing. That is to say, if a theory only gives concepts without details, then this theory is nothing. In that case, we seldom discuss ideas, but are only busy solving specific problems. How can this motor be better controlled? Can the convergence condition of this algorithm be weakened. In our words, this is called "just pulling your car without looking up at the road", and in their words, it is "just do it ". I am deeply touched by the differences in education in the West. Therefore, if we say that the fuzzy theory is similar to that of the orients. At least for me, this is because of people's misunderstanding of fuzzy theory. As I have mentioned in the answer to question 3, fuzzy theory is not vague, but a precise theory is used to describe fuzzy phenomena. Some people may ask why fuzzy theory is also popular in Japan? I think the main reason is that Fu is transliteration in Japanese. Just like many foreign technical words, such as computer, are transliteration, they are just a symbol representing a new technology and are irrelevant to the meaning of fuzzy words. Chinese users like free translation. Misunderstanding of "seeing the world from the Chinese Perspective" is easy to happen. Maybe you want to know why Zadeh chose the word "Fu? I asked Zadeh this question at lunch. He replied that I couldn't come up with better words. I asked him again, but now it seems that the answer is correct and the answer is wrong. He replied that he was right in terms of field promotion. Now many people are discussing Fu and doing research in this area. If you choose other general words, such as continuous or smooth, it is likely to be a branch of another field, it is difficult to form an independent school as it is now. I don't know how to evaluate it. please think about it yourself. The blurred and beautiful veil is revealed in front of a black and white fuzzy system theory. Do people still like it? Especially our orients? 2. Opportunities If you are still satisfied with my answers to all kinds of questions in the last "challenge" and accept my points of view (of course, partially accepted), then the opportunity is coming. This is a young field with many issues to be resolved. As I have said before, growing together with the field is a very refreshing thing. The following research directions can provide you with new opportunities (and other directions of course). The order of these directions is from simplicity to difficulty. Direction 1 combines fuzzy control with non-fuzzy control. On the one hand, we use methods in traditional control theory to solve the problem of fuzzy control, and on the other hand, we use the concept of fuzzy control to provide new ideas for solving various control problems. One of the most popular practices is to apply the LMS and H infinity theories to the analysis and design of fuzzy controllers. It also uses the traditional optimal control theory to design the optimal fuzzy controller, and uses the sliding mode control method to analyze the performance of the fuzzy controller. It also draws on some concepts of adaptive control theory to design an adaptive fuzzy controller. These applications are directly integrated. More methods need to be improved and promoted to adapt to the problem of fuzzy control. At present, the shortcomings of such research are that the characteristics of fuzzy control are not clear enough. That is, there are few special results that apply only to fuzzy controllers. These results are often general. Fuzzy Controller is just a non-linear approximation. It is a meaningful research direction to consider the details of the structure of the fuzzy controller. Direction 2: in-depth analysis of the structure characteristics and Approximation Accuracy of the fuzzy system, and establishment of a complete theoretical system, so that people can be aware of the application of the fuzzy system. One of the advantages of classical nonlinear structures (such as piecewise polynomials) is that they have been studied for dozens or even hundreds of years and have accumulated a lot of theoretical results. In recent years, neural networks have also made great strides in this area. If we compare these non-linear structures to different animals, the more detailed the anatomy of these animals, the more thorough we understand them, the more you know What it applies to and what it does not apply. For a fuzzy system, the inner volume of this research includes how different structural parameters affect the approximation accuracy, and the rate at which the approximation error decreases as the number of parameters increases. Can the locality and global condition be balanced? What kind of non-linear structure is especially suitable for representation. In the past decade, some progress has been made in these areas. However, due to its late start, there is still a significant gap with piecewise polynomials, neural networks, and wavelet series. Direction 3 is applicable to the proposal of different learning algorithms for Fuzzy Systems, convergence analysis of algorithms, and Performance Analysis of Fuzzy Systems after learning. If we compare the study of direction 2 to the static anatomy of animals, it is to study the dynamic characteristics of Motion During running. Obviously, this direction is relatively difficult. The research in this direction can be further divided into two situations: one is that the data can be randomly sampled or the probability distribution of known data, and the number of data can be assumed to be infinite. In another case, only a limited number of data sampling points are provided, and the data distribution cannot be controlled manually. In the first case, it is easy to come up with more in-depth theoretical results. However, it is assumed that the conditions are too strong, which is inconsistent with most actual conditions. The second case is closer to the actual situation. However, theoretical analysis is much more difficult. Although both cases are necessary, the focus should be on the second case. At present, theoretical research in both directions is very lacking. People often only give the specific steps of the algorithm, and then perform a lot of simulation, rarely see strict theoretical analysis and proof. Neural Networks have little research achievements in this field, because neural network parameters are short of specific physical meanings. The analysis is more difficult than the fuzzy system. A research idea in this direction is to simplify the decomposition feature of the fuzzy system in a small part to obtain the convergence result. Direction 4: The fuzzy system method for high-dimensional situations (large number of input variables. Suppose our problem is to predict the value of a major variable. So we use this variable as the output of the fuzzy system, and the various factors that affect this variable as the input of the fuzzy system. In many cases, there are many factors that affect the main variable. The more factors, the more input variables, then, what is the better result of the prediction? Unfortunately, this is not the case. The higher the dimension, the lower the possibility of finding a real nonlinear relationship. This is mainly because the sampling data becomes increasingly sparse as the dimension increases. Considering that the one-dimensional interval [100] Has sampling points, the data is very confidential. Placing 100 pieces of data on a two-dimensional plane [] 2 is not so confidential. Consider the 100 data points in the third-dimensional Center [] 3, which can be said to be a rare Lala. So what will happen if we put 100 data points in four-dimensional, five-dimensional, and higher-dimensional spaces? Most of the areas in the middle do not have sampling points. If there is no sampling point in a region, how can I know the value of the output variable when the input variable falls into this region? This is the core difficulty of the high-dimensional problem. It is called the "evil dimension" by Bellman ). There are two ways to solve the high-dimensional problem: one is to reduce the number of input variables. That is, ignore secondary factors only when considering important factors. Second, find or effectively portray the interdependence between input variables, and introduce structures in the input center to limit the search range. The first approach is relatively simple, but it requires an effective method to sort the importance of variables. Finding such a method is a very useful research direction. The second approach is a very good research direction. Currently, there are not many research achievements in this direction. Multi-layer fuzzy systems are one of the methods. Using the concept of decision tree to divide the input space is also worth further research. After the new structure is proposed, static anatomy and dynamic analysis of the system will be performed as stated in directions 2 and 3. In the classic method, projection follow is a good method for high-dimensional problems. Because the structure of neural networks has the characteristics of projection follow, it is more general than projection follow, therefore, neural networks have been successfully applied to many practical problems (most practical problems are high-dimensional ). Standard fuzzy systems do not have the characteristics of adapting to high dimensions. Therefore, they must be reformed to propose a new structure and corresponding learning algorithms to adapt to high dimensions. Direction 5: a fuzzy system that can use other knowledge and information expressions. The existing fuzzy system can only use if-then rules. However, we humans express knowledge and information in a variety of ways. For example, "analogy" is a very important way for us humans to express and acquire knowledge. We say, "the truth for this person is like playing the piano", which is very important information. Based on this information, we can predict what kind of reaction we will receive if we preach to this person. The difficulty here is that "playing the piano" and "telling the truth to this person" happen in two irrelevant aspects. It is not easy to express them in the same mathematical space. It is not enough to give the idea only, and no details are equal to nothing. A fuzzy system that can use analogy information must be a specific mathematical expression and can be used for numerical calculation. At the same time, it must comply with common sense and be explanatory. This is a very challenging direction. Once a breakthrough is made in this direction, the foundation of the fuzzy system will be expanded in essence. In this way, our field is greatly expanded. These are the five most important research directions I think. Before finishing this visit, I would like to emphasize that the above research direction is only for the field of fuzzy systems (including fuzzy control. The fuzzy system is only a branch of the entire fuzzy theory. Other important branches of the fuzzy theory include fuzzy mathematics, fuzzy optimization, and fuzzy logic. These fields also have very important research directions. This article is not discussed. In addition, the above research parties belong to the scope of theoretical research. It is very important and interesting to skillfully use these methods to solve various practical problems. Only when these applications are successful can the theoretical methods be well established and widely welcomed. 3. Conclusion At the beginning of this article, I have repeatedly stressed that it is difficult to work in this controversial field. In fact, it is only one aspect of the problem. What I want to add is that I am very excited when I work in this controversial field. Through hard research, I use facts to answer extremely challenging and even provocative questions, it is a very happy thing. I hope more friends can learn this truth from my "sentiment" and join us to share this happiness with me! Thank you!