Summary, Conclusion and Future Perspectives
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1 Chapter 6 Summary, Conclusion and Future Perspectives 6.1 Summary and Conclusions The work presented in this thesis belongs to the framework of Fuzzy Logic Control Technique versus Classical mathematical EEG Signal model. Here we have studied EEG Signal modeling and it s Classification Techniques (Fuzzy Logic Control), in order to design Fuzzy Logic Controlled EEG signal model. We used the FLC technique in virtual reality applications with three main objectives: 1) Increasing the information transfer rate of EEG signals model, 2) Designing interpretable EEG signal model and 3) Developing fuzzy logic controlled EEG signal modeling. In order to reach these objectives, we have proposed Hodgkin - Huxley Nobel Prize winning EEG signal model, and as the classification technique of EEG signal model, we have chosen a familiar Fuzzy Logic Control technique. Further it is shown how these two technologies are intimately 126
2 6.1 Summary and Conclusions 127 interwoven together and improve the whole performance of Classical EEG signal model. Concluding Remak In order to apply FLC technique on EEG signal model, this thesis presents the main three types of frequently used fuzzy inference rule based models: the Mamdani; Sugeno and Tsukamoto fuzzy rule based models. We discuss their strength and weakness and other related issues, such as I/P space partitioning and fuzzy modeling. Classical EEG Signal Model is designed using imprecise or vague input linguistic variables. It runs by executing large number of equations serially hence this model is relatively complex. Mechanism of this model is very time consuming and difficult to make it feasible. Designing of Fuzzy logic Controlled Mamdani model is convenient under such situations. This model runs by executing some of the few fuzzy if -then rules simultaneously instead of large number of equations serially. It gives target output result within convenient time period. Hence utility of this model is indispensable. The inference scheme of Tsukamoto is similar to that of TSK model (both use an inference, always equivalent to the weighted sum to the
3 6.2 Future Perspectives 128 conclusion of multiple rules into a final conclusion). These both models are designed using monotonic membership function in the consequent part of fuzzy if - then rules, so that the out put achieved by these technique are crisp in nature, hence these methods avoid defuzzification step in Mamdani s method. These methods provide target output result in a short time period as compare to that of classical EEG signal model. Concerning the Mamdani fuzzy inference system over EEG signal model Chapter 2 is devoted. The chapter 4 is designed using TSK fuzzy rule based model, whereas chapter 5 is concerning with the Tsukamoto fuzzy rule based model. 6.2 Future Perspectives In the present thesis many more concepts could not be discussed either because of space limitations or because they could not be considered ready for this thesis. To indicate the scope of future applications of utilization of Fuzzy Logic Controllers on EEG Signal models, we shall point out some of the most relevant subject areas: Support vector machine (SVM), Neural Networks, Stability analysis of fuzzy logic controlled rule based models (Mamdani, TSK and Tsukamoto).
4 6.2 Future Perspectives 129 FLC technique can be considered as a modeling language for vague and complex formal and factual structures. So far mainly the min - max version of FLC rule based model has been used and applied in our thesis, even though many other connectives, concepts and operations have been suggested in the literature such as Zadeh s connectives, Lukasiewicz connectives etc. [78]. There is much scope to extend our research work in this direction. Neuro - fuzzy controller will be of growing importance in the future and have ample space for future development. The research work in fuzzy model identification is the increasing visibility of neural network research in the late Because of the certain similarities between neural network and fuzzy logic control research began to investigate ways to combine the two technologies. The most important outcomes of this trend is the development of various techniques for identifying the parameters in a fuzzy system using neural network learning techniques. A system built in this way is called a neuro - fuzzy system. Bart - Kosko has been known for his contribution to neuro - fuzzy system.
5 6.3 The Comparison of Fuzzy Inference Systems and Neural Network The Comparison of Fuzzy Inference Systems and Neural Network Introduction The usage of artificial intelligence has been applied widely in most of the fields of computation studies. Main feature of this concept is the ability of self-learning and self-predicting some desired outputs. The learning may be done with a supervised or an unsupervised way. Neural Network study and Fuzzy Logic are the basic areas of artificial intelligence concept. Adaptive Neuro - Fuzzy study combines these two methods and uses the advantages of both methods. In order to see the capabilities of these three methods, we utilize Neuro - Fuzzy technique on the EEG signal model, that is we use I/P data of EEG Signal model to develop Neuro - Fuzzy controlled EEG signal model so as to provide required O/P result Fuzzy Logic Control (FLC) Fuzzy Logic concept is close to human thinking style because it uses linguistic terms. It allows membership degrees to the variables. Different cases of each input s fuzzy sets are evaluated according to if-then rules of the fuzzy system. As a result of this operation, the optimum outputs are obtained much close to the target outputs. The building of the optimum results for the system depends on the experience of the expert [23, 74].
6 6.3 The Comparison of Fuzzy Inference Systems and Neural Network Neural Network Neural networks are adaptive networks which are composed of simple elements operating in parallel. These elements are inspired by biological nervous systems. As in nature, the network function is determined largely by the connections between elements. Commonly, neural networks are adjusted or trained so that a particular input leads to specific target output. Neural networks have been trained to perform complex functions in various fields of applications including identification, classification, and control systems. When the inputs of the network and target outputs are given, back-propagation gradient descent method is used. Because there is no initial knowledge about connection weights and biases, these parameters should be determined by minimization of error method to feed forward networks. After their determination, errors are distributed between layers towards backward direction [4] Adaptive Neuro - Fuzzy Inference Systems (ANFIS) In this section, we describe a class of adaptive networks that are functionally equivalent to fuzzy inference systems (Kosko, 1992). The architecture is referred to as ANFIS, which stands for adaptive network-based fuzzy inference system. We describe how to decompose the parameter set to facilitate the hybrid learning rule for ANFIS architectures representing both
7 6.3 The Comparison of Fuzzy Inference Systems and Neural Network 132 the Sugeno and Tsukamoto fuzzy models. ANFIS architecture ANFIS is an adaptive network which permits the usage of neural network topology together with fuzzy logic. It not only includes the characteristics of both methods, but also eliminates some disadvantages of their lonely-used case. Operation of ANFIS looks like feed-forward back propagation network. Consequent parameters are calculated forward while premise parameters are calculated backward. There are two learning methods in neural section of the system: Hybrid learning method and backpropagation learning method. In fuzzy section, only zero or first order Sugeno inference system or Tsukamoto inference system can be used [3,7]. Output variables are obtained by applying fuzzy rules to fuzzy sets of input variables. For example, Rule 1: If x is A 1 and y is B 1 then f 1 = p 1 x+q 1 y +r 1 Rule 2: If x is A 2 and y is B 2 then f 2 = p 2 x+q 2 y +r 2 Figure1(a) shows graphically the first order Sugeno fuzzy inference system and Figure 1(b) shows its equivalent ANFIS architecture.
8 6.3 The Comparison of Fuzzy Inference Systems and Neural Network 133 Figure 1: (a)first order Sugeno FIS; (b) Corresponding ANFIS architecture. The extension from Sugeno ANFIS to Tsukamoto ANFIS is straightforward, as shown in Figure 2, where the output of each rule ( f i,i = 1,2) is induced jointly by a consequent membership function and a firing strength.
9 6.3 The Comparison of Fuzzy Inference Systems and Neural Network 134 Figure 2: (a) A two - input Tsukamoto fuzzy model with two rules; (b) Equivalent ANFIS architecture Since ANFIS combines both neural network and fuzzy logic, it is capable of handling complex and nonlinear problems. Even if the targets are not given, ANFIS may reach the optimum result rapidly. The architecture of ANFIS consists of five layers and the number of neurons in each layer equals to the number of rules. In addition, there is no vagueness in ANFIS as opposed to neural networks [66]. Naturally, a lot of work needs to be done in order to achieve the applications mentioned above. As FLC modeling is still a young research field, there is no doubt that the next years will witness tremendous advances
10 6.3 The Comparison of Fuzzy Inference Systems and Neural Network 135 in the field and, at the same time, will open the way to new and exciting research challenges To sum up, the fuzzy logic controlled approach to the designing of classical EEG signal model is the transformed designing process from jejune quantitative to genuine qualitative.
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