Pub Date : 2018-10-03DOI: 10.1201/9781315219264-11
Hongxing Li, C. Chen, Han-Pang Huang
In this chapter, we introduce variable universes-based adaptive fuzzy controllers. The concept comes from interpolation forms of fuzzy control introduced in Chapter 8. First, we define monotonicity of control rules, and we prove that the monotonicity of interpolation functions of fuzzy control is equivalent to the monotonicity of control rules. This means that there is no contradiction among the control rules under the condition for the control rules being monotonic. Then the structure of the contraction-expansion factor is discussed. At last, based on variable universes, we present three models of adaptive fuzzy control, namely, an adaptive fuzzy control model with potential heredity, adaptive fuzzy control model with obvious heredity and adaptive fuzzy control model with successively obvious heredity.
{"title":"Adaptive Fuzzy Controllers Based on Variable Universes","authors":"Hongxing Li, C. Chen, Han-Pang Huang","doi":"10.1201/9781315219264-11","DOIUrl":"https://doi.org/10.1201/9781315219264-11","url":null,"abstract":"In this chapter, we introduce variable universes-based adaptive fuzzy controllers. The concept comes from interpolation forms of fuzzy control introduced in Chapter 8. First, we define monotonicity of control rules, and we prove that the monotonicity of interpolation functions of fuzzy control is equivalent to the monotonicity of control rules. This means that there is no contradiction among the control rules under the condition for the control rules being monotonic. Then the structure of the contraction-expansion factor is discussed. At last, based on variable universes, we present three models of adaptive fuzzy control, namely, an adaptive fuzzy control model with potential heredity, adaptive fuzzy control model with obvious heredity and adaptive fuzzy control model with successively obvious heredity.","PeriodicalId":239984,"journal":{"name":"Fuzzy Neural Intelligent Systems","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116814066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2000-09-21DOI: 10.1201/9781420057997.CH4
Hongxing Li, C. L. P. Chen, Han-Pang Huang
This chapter focuses on functional-link neural networks. Beginning with the XOR problem, we discuss the mathematical essence and the structures of functional-link neural networks. Extending this idea, we give the visualization means of mathematical methods. We also give neural network representations of linear programming and fuzzy linear programming. A single-layer neural network, first studied by Minsky and Papert, was named perceptron in 1969 [l]. It is well known that a single-layer perceptron network cannot solve a nonlinear problem. A typical problem is the Exclusive-OR (XOR) problem. Generally, there are two approaches to solve this nonlinear problem by modifying the architecture of this single-layer perceptron. The first one is to increase number of the hidden layers, and the second one is to add higher order input terms. There are numerous applications using either of these approaches [2-41. Here we will illustrate that these two approaches, in fact, are essentially mathematical equivalence. is the same neuron with a higher order term, 2 1 .x2 shows a simple neuron with two inputs.
{"title":"Functional-link Neural Networks and Visualization Means of Some Mathematical Methods","authors":"Hongxing Li, C. L. P. Chen, Han-Pang Huang","doi":"10.1201/9781420057997.CH4","DOIUrl":"https://doi.org/10.1201/9781420057997.CH4","url":null,"abstract":"This chapter focuses on functional-link neural networks. Beginning with the XOR problem, we discuss the mathematical essence and the structures of functional-link neural networks. Extending this idea, we give the visualization means of mathematical methods. We also give neural network representations of linear programming and fuzzy linear programming. A single-layer neural network, first studied by Minsky and Papert, was named perceptron in 1969 [l]. It is well known that a single-layer perceptron network cannot solve a nonlinear problem. A typical problem is the Exclusive-OR (XOR) problem. Generally, there are two approaches to solve this nonlinear problem by modifying the architecture of this single-layer perceptron. The first one is to increase number of the hidden layers, and the second one is to add higher order input terms. There are numerous applications using either of these approaches [2-41. Here we will illustrate that these two approaches, in fact, are essentially mathematical equivalence. is the same neuron with a higher order term, 2 1 .x2 shows a simple neuron with two inputs.","PeriodicalId":239984,"journal":{"name":"Fuzzy Neural Intelligent Systems","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124729285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2000-09-21DOI: 10.1201/9781420057997.CH13
Hongxing Li, C. L. P. Chen, Han-Pang Huang
{"title":"Neuron Models Based on Factor Spaces Theory and Factor Space Canes","authors":"Hongxing Li, C. L. P. Chen, Han-Pang Huang","doi":"10.1201/9781420057997.CH13","DOIUrl":"https://doi.org/10.1201/9781420057997.CH13","url":null,"abstract":"","PeriodicalId":239984,"journal":{"name":"Fuzzy Neural Intelligent Systems","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131954996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2000-09-21DOI: 10.1201/9781420057997.CH1
Hongxing Li, C. L. P. Chen, Han-Pang Huang
{"title":"Foundation of Fuzzy Systems","authors":"Hongxing Li, C. L. P. Chen, Han-Pang Huang","doi":"10.1201/9781420057997.CH1","DOIUrl":"https://doi.org/10.1201/9781420057997.CH1","url":null,"abstract":"","PeriodicalId":239984,"journal":{"name":"Fuzzy Neural Intelligent Systems","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121131486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2000-09-21DOI: 10.1201/9781420057997.CH8
Hongxing Li, C. L. P. Chen, Han-Pang Huang
In this chapter, a new family of multifactorial function, called generalized additive weighted multifactorial function, is proposed and discussed in detail. First, its properties in n-dimensional space are discussed and then our results are extended to the infinite dimensional space. Second, the implication of its constant coefficients is explained by fuzzy integral. Finally, its application in fuzzy inference is discussed and we show that it is a usual kind of composition operator in fuzzy neural networks.
{"title":"Generalized Additive Weighted Multifactorial Function and its Applications to Fuzzy Inference and Neural Networks","authors":"Hongxing Li, C. L. P. Chen, Han-Pang Huang","doi":"10.1201/9781420057997.CH8","DOIUrl":"https://doi.org/10.1201/9781420057997.CH8","url":null,"abstract":"In this chapter, a new family of multifactorial function, called generalized additive weighted multifactorial function, is proposed and discussed in detail. First, its properties in n-dimensional space are discussed and then our results are extended to the infinite dimensional space. Second, the implication of its constant coefficients is explained by fuzzy integral. Finally, its application in fuzzy inference is discussed and we show that it is a usual kind of composition operator in fuzzy neural networks.","PeriodicalId":239984,"journal":{"name":"Fuzzy Neural Intelligent Systems","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132996404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2000-09-21DOI: 10.1201/9781420057997.CH2
Hongxing Li, C. L. P. Chen, Han-Pang Huang
In our natural world and daily lives, we experience all kinds of phenomena; broadly speaking, we can divide them into two types: phenomena of certainty and phenomena of uncertainty. The class of uncertain phenomena can further be subdivided into random (stochastic) phenomena and fuzzy phenomena. Therefore, we have three categories of phenomena and their associated mathematical models: 1. Deterministic mathematical models-This is a class of models where the relationships between objects are fixed or known with certainty. 2. Random (stochastic) mathematical models-This is a class of models where the relationships between objects are uncertain or random in nature. 3. Fuzzy mathematical models-This is a class of models where objects and relationships between objects are fuzzy. The main distinction between random phenomena and fuzzy phenomena is that random events themselves have clear and well-defined meaning, whereas a fuzzy concept does not have a precise extension because it is hard to judge if an object belongs to the concept. We may say that randomness is a deficiency of the law of causality and that fuzziness is a deficiency of the law of the excluded middlc. Probability theory applies the random concept to generalized laws of causality-laws of probability. Fuzzy set theory applies the fuzzy property to the generalized law of the excluded middle-the law of membership from fuzziness. Probability reflects the internal relations and interactions of events under certain conditions. It could be very objective if a stable frequency is available from re-
{"title":"Determination of Membership Functions","authors":"Hongxing Li, C. L. P. Chen, Han-Pang Huang","doi":"10.1201/9781420057997.CH2","DOIUrl":"https://doi.org/10.1201/9781420057997.CH2","url":null,"abstract":"In our natural world and daily lives, we experience all kinds of phenomena; broadly speaking, we can divide them into two types: phenomena of certainty and phenomena of uncertainty. The class of uncertain phenomena can further be subdivided into random (stochastic) phenomena and fuzzy phenomena. Therefore, we have three categories of phenomena and their associated mathematical models: 1. Deterministic mathematical models-This is a class of models where the relationships between objects are fixed or known with certainty. 2. Random (stochastic) mathematical models-This is a class of models where the relationships between objects are uncertain or random in nature. 3. Fuzzy mathematical models-This is a class of models where objects and relationships between objects are fuzzy. The main distinction between random phenomena and fuzzy phenomena is that random events themselves have clear and well-defined meaning, whereas a fuzzy concept does not have a precise extension because it is hard to judge if an object belongs to the concept. We may say that randomness is a deficiency of the law of causality and that fuzziness is a deficiency of the law of the excluded middlc. Probability theory applies the random concept to generalized laws of causality-laws of probability. Fuzzy set theory applies the fuzzy property to the generalized law of the excluded middle-the law of membership from fuzziness. Probability reflects the internal relations and interactions of events under certain conditions. It could be very objective if a stable frequency is available from re-","PeriodicalId":239984,"journal":{"name":"Fuzzy Neural Intelligent Systems","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127980699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2000-09-21DOI: 10.1201/9781420057997.CH12
Hongxing Li, C. L. P. Chen, Han-Pang Huang
The original definition of “factor spaces” was proposed by Peizhuang Wang [l]. He used factor spaces to explain the source of randomness and the essence of probability laws. In 1982, he gave an axiomatic definition of factor spaces [2]. Since then he has applied factor spaces to the study of artificial intelligence [3-51. Several applications in the area of fuzzy information processing have been discussed [6]. This chapter provides an introduction to the basic concepts and methods of applications of factor spaces.
{"title":"The Basics of Factor Spaces","authors":"Hongxing Li, C. L. P. Chen, Han-Pang Huang","doi":"10.1201/9781420057997.CH12","DOIUrl":"https://doi.org/10.1201/9781420057997.CH12","url":null,"abstract":"The original definition of “factor spaces” was proposed by Peizhuang Wang [l]. He used factor spaces to explain the source of randomness and the essence of probability laws. In 1982, he gave an axiomatic definition of factor spaces [2]. Since then he has applied factor spaces to the study of artificial intelligence [3-51. Several applications in the area of fuzzy information processing have been discussed [6]. This chapter provides an introduction to the basic concepts and methods of applications of factor spaces.","PeriodicalId":239984,"journal":{"name":"Fuzzy Neural Intelligent Systems","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129037410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2000-09-21DOI: 10.1201/9781420057997.CH16
Hongxing Li, C. L. P. Chen, Han-Pang Huang
A flexible robot arm is a distributed system per se. Its dynamics are very complicated and coupled with the non-minimum phase nature due to the non-collocated construction of the sensor and actuator. This gives rise to difficulty in the control of a flexible arm. In particular, the control of a flexible arm usually suffers from control spillover and observation spillover due to the use of a linear and approximate model. The robustness and reliability of the fuzzy control have been demonstrated in many applications, particularly, it is perfect for a nonlinear system without knowing the exact system model. However, a fuzzy control usually needs a lot of computation time. In order to alleviate this restraint, a simplified fuzzy controller is developed for real-time control of a flexible robot arm. Furthermore, the self-organizing control based on the simplified fuzzy controller is also developed. The simulation results show that the simplified fuzzy control can achieve the desired performance and the computation time is less than 10 m s so that the real-time control is possible.
灵活的机械臂本身就是一个分布式系统。由于传感器和作动器的非配置结构，其动力学非常复杂，且具有非最小相位特性。这就给灵活的手臂的控制带来了困难。特别是，由于使用线性和近似模型，柔性臂的控制通常会受到控制溢出和观察溢出的影响。模糊控制的鲁棒性和可靠性已在许多应用中得到证明，特别是对于不知道确切系统模型的非线性系统，它是完美的。然而，模糊控制通常需要大量的计算时间。为了减轻这种约束，开发了一种简化的模糊控制器，用于柔性机械臂的实时控制。在此基础上，提出了基于简化模糊控制器的自组织控制方法。仿真结果表明，简化后的模糊控制可以达到预期的性能，计算时间小于10 m s，可以实现实时控制。
{"title":"Control of a Flexible Robot Arm using a Simplified Fuzzy Controller","authors":"Hongxing Li, C. L. P. Chen, Han-Pang Huang","doi":"10.1201/9781420057997.CH16","DOIUrl":"https://doi.org/10.1201/9781420057997.CH16","url":null,"abstract":"A flexible robot arm is a distributed system per se. Its dynamics are very complicated and coupled with the non-minimum phase nature due to the non-collocated construction of the sensor and actuator. This gives rise to difficulty in the control of a flexible arm. In particular, the control of a flexible arm usually suffers from control spillover and observation spillover due to the use of a linear and approximate model. The robustness and reliability of the fuzzy control have been demonstrated in many applications, particularly, it is perfect for a nonlinear system without knowing the exact system model. However, a fuzzy control usually needs a lot of computation time. In order to alleviate this restraint, a simplified fuzzy controller is developed for real-time control of a flexible robot arm. Furthermore, the self-organizing control based on the simplified fuzzy controller is also developed. The simulation results show that the simplified fuzzy control can achieve the desired performance and the computation time is less than 10 m s so that the real-time control is possible.","PeriodicalId":239984,"journal":{"name":"Fuzzy Neural Intelligent Systems","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121865714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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