Supervised Learning of Fuzzy Logic Systems

2011 ◽  
pp. 1510-1517 ◽  
Author(s):  
M. Mohammadian
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Fuzzy Logic ◽  
Complex Systems ◽  
Supervised Learning ◽  
Fuzzy Logic System ◽  
Fuzzy Rules ◽  
Fuzzy Logic Systems ◽  
Complex Nonlinear Systems ◽  
Logic System

Conventionally modelling and simulation of complex nonlinear systems has been to construct a mathematical model and examine the system’s evolution or its control. This kind of approach can fail for many of the very large non-linear and complex systems being currently studied. With the invention of new advanced high-speed computers and the application of artificial intelligence paradigms new techniques have become available. Particularly neural networks and fuzzy logic for nonlinear modelling and genetic algorithms [Goldberg, D. (1989)] and evolutionary algorithms for optimisation methods have created new opportunities to solve complex systems [Bai, Y., Zhuang H. and Wang, D. (2006)]. This paper considers issues in design of multi-layer and hierarchical fuzzy logic systems. It proposes a decomposition technique for complex systems into hierarchical and multi-layered fuzzy logic sub-systems. The learning of fuzzy rules and internal parameters in a supervised manner is performed using genetic algorithms. The decomposition of complex nonlinear systems into hierarchical and multi-layered fuzzy logic sub-systems reduces greatly the number of fuzzy rules to be defined and improves the learning speed for such systems. In this paper a method for combining subsystems to create a hierarchical and multilayer fuzzy logic system is also described. Application areas considered are - the prediction of interest rate, unemployment rate predication and electricity usage prediction. Genetic Algorithms can be used as a tool for design and generation of fuzzy rules for a fuzzy logic system. This automatic design and generation of fuzzy rules, via genetic algorithms, can be categorised into two learning techniques namely, supervised and unsupervised. In supervised learning there are two distinct phases to the operation. In the first phase each individual is assessed based on the input signal that is propagated through the system producing output respond. The actual respond produced is then compared with a desired response, generating error signals that are then used as the fitness for the individual in the population of genetic algorithms. Supervised learning has successfully applied to solve some difficult problems. In this paper design and development of a genetic algorithm based supervised learning for fuzzy models with application to several problems is considered. A hybrid integrated architecture incorporating fuzzy logic and genetic algorithm can generate fuzzy rules that can be used in a fuzzy logic system for modelling, control and prediction

Designing Unsupervised Hierarchical Fuzzy Logic Systems

2011 ◽  
pp. 456-463
Author(s):  
M. Mohammadian
Keyword(s):  
Genetic Algorithms ◽  
Fuzzy Logic ◽  
Unsupervised Learning ◽  
Input Data ◽  
Fuzzy Logic System ◽  
Fuzzy Rules ◽  
Fuzzy Logic Systems ◽  
Logic Systems ◽  
The Individual ◽  
Logic System

Systems such as robotic systems and systems with large input-output data tend to be difficult to model using mathematical techniques. These systems have typically high dimensionality and have degrees of uncertainty in many parameters. Artificial intelligence techniques such as neural networks, fuzzy logic, genetic algorithms and evolutionary algorithms have created new opportunities to solve complex systems. Application of fuzzy logic [Bai, Y., Zhuang H. and Wang, D. (2006)] in particular, to model and solve industrial problems is now wide spread and has universal acceptance. Fuzzy modelling or fuzzy identification has numerous practical applications in control, prediction and inference. It has been found useful when the system is either difficult to predict and or difficult to model by conventional methods. Fuzzy set theory provides a means for representing uncertainties. The underlying power of fuzzy logic is its ability to represent imprecise values in an understandable form. The majority of fuzzy logic systems to date have been static and based upon knowledge derived from imprecise heuristic knowledge of experienced operators, and where applicable also upon physical laws that governs the dynamics of the process. Although its application to industrial problems has often produced results superior to classical control, the design procedures are limited by the heuristic rules of the system. It is simply assumed that the rules for the system are readily available or can be obtained. This implicit assumption limits the application of fuzzy logic to the cases of the system with a few parameters. The number of parameters of a system could be large. The number of fuzzy rules of a system is directly dependent on these parameters. As the number of parameters increase, the number of fuzzy rules of the system grows exponentially. Genetic Algorithms can be used as a tool for the generation of fuzzy rules for a fuzzy logic system. This automatic generation of fuzzy rules, via genetic algorithms, can be categorised into two learning techniques, supervised and unsupervised. In this paper unsupervised learning of fuzzy rules of hierarchical and multi-layer fuzzy logic control systems are considered. In unsupervised learning there is no external teacher or critic to oversee the learning process. In other words, there are no specific examples of the function to be learned by the system. Rather, provision is made for a task-independent measure of the quality or representation that the system is required to learn. That is the system learns statistical regularities of the input data and it develops the ability to learn the feature of the input data and thereby create new classes automatically [Mohammadian, M., Nainar, I. and Kingham, M. (1997)]. To perform unsupervised learning, a competitive learning strategy may be used. The individual strings of genetic algorithms compete with each other for the “opportunity” to respond to features contained in the input data. In its simplest form, the system operates in accordance with the strategy that ‘the fittest wins and survives’. That is the individual chromosome in a population with greatest fitness ‘wins’ the competition and gets selected for the genetic algorithms operations (cross-over and mutation). The other individuals in the population then have to compete with fit individual to survive. The diversity of the learning tasks shown in this paper indicates genetic algorithm’s universality for concept learning in unsupervised manner. A hybrid integrated architecture incorporating fuzzy logic and genetic algorithm can generate fuzzy rules for problems requiring supervised or unsupervised learning. In this paper only unsupervised learning of fuzzy logic systems is considered. The learning of fuzzy rules and internal parameters in an unsupervised manner is performed using genetic algorithms. Simulations results have shown that the proposed system is capable of learning the control rules for hierarchical and multi-layer fuzzy logic systems. Application areas considered are, hierarchical control of a network of traffic light control and robotic systems. A first step in the construction of a fuzzy logic system is to determine which variables are fundamentally important. Any number of these decision variables may appear, but the more that are used, the larger the rule set that must be found. It is known [Raju, S., Zhou J. and Kisner, R. A. (1990), Raju G. V. S. and Zhou, J. (1993), Kingham, M., Mohammadian, M, and Stonier, R. J. (1998)], that the total number of rules in a system is an exponential function of the number of system variables. In order to design a fuzzy system with the required accuracy, the number of rules increases exponentially with the number of input variables and its associated fuzzy sets for the fuzzy logic system. A way to avoid the explosion of fuzzy rule bases in fuzzy logic systems is to consider Hierarchical Fuzzy Logic Control (HFLC) [Raju G. V. S. and Zhou, J. (1993)]. A learning approach based on genetic algorithms [Goldberg, D. (1989)] is discussed in this paper for the determination of the rule bases of hierarchical fuzzy logic systems.

Designing Unsupervised Hierarchical Fuzzy Logic Systems

2012 ◽  
pp. 253-261
Author(s):  
M. Mohammadian
Keyword(s):  
Genetic Algorithms ◽  
Fuzzy Logic ◽  
Unsupervised Learning ◽  
Input Data ◽  
Fuzzy Logic System ◽  
Fuzzy Rules ◽  
Fuzzy Logic Systems ◽  
Logic Systems ◽  
The Individual ◽  
Logic System

Systems such as robotic systems and systems with large input-output data tend to be difficult to model using mathematical techniques. These systems have typically high dimensionality and have degrees of uncertainty in many parameters. Artificial intelligence techniques such as neural networks, fuzzy logic, genetic algorithms and evolutionary algorithms have created new opportunities to solve complex systems. Application of fuzzy logic [Bai, Y., Zhuang H. and Wang, D. (2006)] in particular, to model and solve industrial problems is now wide spread and has universal acceptance. Fuzzy modelling or fuzzy identification has numerous practical applications in control, prediction and inference. It has been found useful when the system is either difficult to predict and or difficult to model by conventional methods. Fuzzy set theory provides a means for representing uncertainties. The underlying power of fuzzy logic is its ability to represent imprecise values in an understandable form. The majority of fuzzy logic systems to date have been static and based upon knowledge derived from imprecise heuristic knowledge of experienced operators, and where applicable also upon physical laws that governs the dynamics of the process. Although its application to industrial problems has often produced results superior to classical control, the design procedures are limited by the heuristic rules of the system. It is simply assumed that the rules for the system are readily available or can be obtained. This implicit assumption limits the application of fuzzy logic to the cases of the system with a few parameters. The number of parameters of a system could be large. The number of fuzzy rules of a system is directly dependent on these parameters. As the number of parameters increase, the number of fuzzy rules of the system grows exponentially. Genetic Algorithms can be used as a tool for the generation of fuzzy rules for a fuzzy logic system. This automatic generation of fuzzy rules, via genetic algorithms, can be categorised into two learning techniques, supervised and unsupervised. In this paper unsupervised learning of fuzzy rules of hierarchical and multi-layer fuzzy logic control systems are considered. In unsupervised learning there is no external teacher or critic to oversee the learning process. In other words, there are no specific examples of the function to be learned by the system. Rather, provision is made for a task-independent measure of the quality or representation that the system is required to learn. That is the system learns statistical regularities of the input data and it develops the ability to learn the feature of the input data and thereby create new classes automatically [Mohammadian, M., Nainar, I. and Kingham, M. (1997)]. To perform unsupervised learning, a competitive learning strategy may be used. The individual strings of genetic algorithms compete with each other for the “opportunity” to respond to features contained in the input data. In its simplest form, the system operates in accordance with the strategy that ‘the fittest wins and survives’. That is the individual chromosome in a population with greatest fitness ‘wins’ the competition and gets selected for the genetic algorithms operations (cross-over and mutation). The other individuals in the population then have to compete with fit individual to survive. The diversity of the learning tasks shown in this paper indicates genetic algorithm’s universality for concept learning in unsupervised manner. A hybrid integrated architecture incorporating fuzzy logic and genetic algorithm can generate fuzzy rules for problems requiring supervised or unsupervised learning. In this paper only unsupervised learning of fuzzy logic systems is considered. The learning of fuzzy rules and internal parameters in an unsupervised manner is performed using genetic algorithms. Simulations results have shown that the proposed system is capable of learning the control rules for hierarchical and multi-layer fuzzy logic systems. Application areas considered are, hierarchical control of a network of traffic light control and robotic systems. A first step in the construction of a fuzzy logic system is to determine which variables are fundamentally important. Any number of these decision variables may appear, but the more that are used, the larger the rule set that must be found. It is known [Raju, S., Zhou J. and Kisner, R. A. (1990), Raju G. V. S. and Zhou, J. (1993), Kingham, M., Mohammadian, M, and Stonier, R. J. (1998)], that the total number of rules in a system is an exponential function of the number of system variables. In order to design a fuzzy system with the required accuracy, the number of rules increases exponentially with the number of input variables and its associated fuzzy sets for the fuzzy logic system. A way to avoid the explosion of fuzzy rule bases in fuzzy logic systems is to consider Hierarchical Fuzzy Logic Control (HFLC) [Raju G. V. S. and Zhou, J. (1993)]. A learning approach based on genetic algorithms [Goldberg, D. (1989)] is discussed in this paper for the determination of the rule bases of hierarchical fuzzy logic systems.

Designing Layers in Hierarchical Fuzzy Logic Systems Using Genetic Algorithms

2011 ◽  
pp. 76-87
Author(s):  
Masoud Mohammadian ◽  
Russel Stonier
Keyword(s):  
Genetic Algorithms ◽  
Fuzzy Logic ◽  
Interest Rate ◽  
Fuzzy Logic System ◽  
Good Prediction ◽  
Design And Development ◽  
Fuzzy Logic Systems ◽  
Financial Modelling ◽  
Logic Systems ◽  
Logic System

In this paper the design and development of hierarchical fuzzy logic systems is investigated using genetic algorithms. This research study is unique in the way the proposed method is applied to the design and development of hierarchical fuzzy logic systems. The new method proposed determines the number of layers in the hierarchical fuzzy logic system. The proposed method is then applied to financial modelling and prediction. A hierarchical fuzzy logic system is developed to predict quarterly interest rates in Australia. The advantages and disadvantages of using hierarchical fuzzy logic systems for financial modelling is also considered. Good prediction of quarterly interest rate in Australia is obtained using the above method. The number of fuzzy rules used is reduced dramatically and prediction of interest rate is improved.

scholarly journals Fuzzy Adaptation Algorithms’ Control for Robot Manipulators with Uncertainty Modelling Errors

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Yongqing Fan ◽  
Keyi Xing ◽  
Xiangkui Jiang
Keyword(s):  
Fuzzy Logic ◽  
Online Learning ◽  
Reference Model ◽  
Robot Manipulators ◽  
Fuzzy Logic System ◽  
Fuzzy Rules ◽  
Fuzzy Logic Systems ◽  
Control Scheme ◽  
Logic Systems ◽  
Logic System

A novel fuzzy control scheme with adaptation algorithms is developed for robot manipulators’ system. At the beginning, one adjustable parameter is introduced in the fuzzy logic system, the robot manipulators system with uncertain nonlinear terms as the master device and a reference model dynamic system as the slave robot system. To overcome the limitations such as online learning computation burden and logic structure in conventional fuzzy logic systems, a parameter should be used in fuzzy logic system, which composes fuzzy logic system with updated parameter laws, and can be formed for a new fashioned adaptation algorithms controller. The error closed-loop dynamical system can be stabilized based on Lyapunov analysis, the number of online learning computation burdens can be reduced greatly, and the different kinds of fuzzy logic systems with fuzzy rules or without any fuzzy rules are also suited. Finally, effectiveness of the proposed approach has been shown in simulation example.

COMPARISON OF DEDUCTION THEOREMS IN DIVERSE LOGIC SYSTEMS

2005 ◽  
Vol 01 (01) ◽  
pp. 65-77 ◽  
Author(s):  
GUO-JUN WANG
Keyword(s):  
Mathematical Logic ◽  
Fuzzy Logic ◽  
Weak Form ◽  
Fuzzy Logic System ◽  
Deduction Theorem ◽  
Fuzzy Logic Systems ◽  
Product Logic ◽  
System Product ◽  
Logic Systems ◽  
Logic System

Deduction theorem and its weak forms in classical mathematical logic system, Łukasiewicz logic system, Gödel logic system, product logic system, and the fuzzy logic system ℒ* are discussed and compared. It is pointed out that the weak form of deduction theorem in ℒ* has a clear structure and can be employed to define the concept of consistency degrees of finite theories. Moreover, it is clarified that the negation operator of Gödel type is too strong and is therefore unsuitable for establishing fuzzy logic systems.

Innovative Hierarchical Fuzzy Logic for Modelling Using Evolutionary Algorithms

2016 ◽  
pp. 770-796
Author(s):  
M. Mohammadian ◽  
R. J. Stonier
Keyword(s):  
Fuzzy Logic ◽  
Hierarchical Control ◽  
Fuzzy Logic System ◽  
Fuzzy Rules ◽  
Complete Class ◽  
Learning Speed ◽  
Internal Parameters ◽  
Model Complex ◽  
Complex Nonlinear Systems ◽  
Control Feedback

This paper considers issues in the design and construction of a fuzzy logic system to model complex (nonlinear) systems. Several important applications are considered and methods for the decomposition of complex systems into hierarchical and multi-layered fuzzy logic sub-systems are proposed. The learning of fuzzy rules and internal parameters is performed using evolutionary computing. The proposed method using decomposition and conversion of systems into hierarchical and multi-layered fuzzy logic sub-systems reduces greatly the number of fuzzy rules to be defined and improves the learning speed for such systems. However such decomposition is not unique and may give rise to variables with no physical significance. This can raise then major difficulties in obtaining a complete class of rules from experts even when the number of variables is small. Application areas considered are: the prediction of interest rate, hierarchical control of the inverted pendulum, robot control, feedback boundary control for a distributed optimal control system and image processing.

scholarly journals Wall-Following Behavior for a Disinfection Robot Using Type 1 and Type 2 Fuzzy Logic Systems

Sensors ◽  
2020 ◽  
Vol 20 (16) ◽  
pp. 4445
Author(s):  
M. A. Viraj J. Muthugala ◽  
S. M. Bhagya P. Samarakoon ◽  
Madan Mohan Rayguru ◽  
Balakrishnan Ramalingam ◽  
Mohan Rajesh Elara
Keyword(s):  
Fuzzy Logic ◽  
Infectious Diseases ◽  
Fuzzy Logic System ◽  
Superior Performance ◽  
Fuzzy Logic Systems ◽  
Interval Type ◽  
Wall Following ◽  
Logic System

Infectious diseases are caused by pathogenic microorganisms, whose transmission can lead to global pandemics like COVID-19. Contact with contaminated surfaces or objects is one of the major channels of spreading infectious diseases among the community. Therefore, the typical contaminable surfaces, such as walls and handrails, should often be cleaned using disinfectants. Nevertheless, safety and efficiency are the major concerns of the utilization of human labor in this process. Thereby, attention has drifted toward developing robotic solutions for the disinfection of contaminable surfaces. A robot intended for disinfecting walls should be capable of following the wall concerned, while maintaining a given distance, to be effective. The ability to operate in an unknown environment while coping with uncertainties is crucial for a wall disinfection robot intended for deployment in public spaces. Therefore, this paper contributes to the state-of-the-art by proposing a novel method of establishing the wall-following behavior for a wall disinfection robot using fuzzy logic. A non-singleton Type 1 Fuzzy Logic System (T1-FLS) and a non-singleton Interval Type 2 Fuzzy Logic System (IT2-FLS) are developed in this regard. The wall-following behavior of the two fuzzy systems was evaluated through simulations by considering heterogeneous wall arrangements. The simulation results validate the real-world applicability of the proposed FLSs for establishing the wall-following behavior for a wall disinfection robot. Furthermore, the statistical outcomes show that the IT2-FLS has significantly superior performance than the T1-FLS in this application.

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