Aralık değerli tip-2 bulanık sistemler için bir Matlab/Simulink araç kutusu

The fuzzy logic has obtained attention of the researchers for last couple of decades. It has opened new scopes in both the academia and the industry site. Fuzzy logic was first introduced in 1965 by Prof. Lotfi A. Zadeh. Fuzzy logic is flexible application of classical logic rules and fuzzy sets are the extension of the classical logic set notation. Fuzzy logic defines the interval between the crisp values while classical logic is working with crisp values such as true or false. In addition, it is possible to define linguistic variables such as short, very short, tall, or very tall with fuzzy logic. Fuzzy logic sets proposed by Prof. Lotfi A. Zadeh in 1965 are knows as type-1 (ordinary) fuzzy sets. The systems that include at least one type-1 fuzzy set are called as type-1 fuzzy logic systems. These type of systems are used in many areas like robotics, modeling and control of nonlinear systems or image processing. Lately, it has been demonstrated that type-1 fuzzy sets might be inadequate to cover uncertainties and nonlinearities due to defining their members as a crisp number in an interval [0,1]. Type-2 fuzzy logic sets are also introduced by Prof. Lotfi A. Zadeh in 1975. The type-2 fuzzy sets are extension of the type-1 fuzzy sets. The systems that include at least one type-2 fuzzy sets are called as type-2 fuzzy logic systems. The studies have shown that, type-2 fuzzy logic systems are more successful than type-1 fuzzy logic systems to describe uncertainties and nonlinear behaviors. However, working with type-2 fuzzy logic systems are much more complicated than working with type-1 fuzzy logic systems. There are many additional computational costs while working with type-2 fuzzy logic systems. Therefore, interval type-2 fuzzy sets are proposed. Interval type-2 fuzzy sets are the special case of the type-2 fuzzy sets. In literature, there are many successful studies in interval type-2 fuzzy logic sets and systems. Interval type-2 fuzzy systems consists of five components: fuzzifier, inference, rules, type reducer and defuzzifier. The only different component between type-1 fuzzy logic systems and type-2 fuzzy logic systems is the type reducer. Interval type-2 fuzzy logic systems need to the type reducer block to convert type-2 fuzzy sets to type-1 fuzzy sets before defuzzifier. However, type reducer component brings some computation costs to the type-2 fuzzy logic systems. There are many type reduction method proposed in literature. The most widely used common type reduction method is the iterative Karnik and Mendel algorithm. The Karnik-Mendel algorithm aims to reduce the type-2 sets to type-1 sets by finding the optimal switching points iteratively. In literature, there are some studies that aim to enhance the Karnik Mendel Algorithm to improve the performance such as enhanced Karnik-Mendel algorithm. In addition, there some closed form type-reduction methods that find the solution without needing any iterative. In this thesis, firstly, type-1 fuzzy sets and systems are explained. Then, type-2 fuzzy sets and systems are introduced and interval type-2 fuzzy sets and systems are explained more in detail. In addition, differences between type-1 fuzzy sets and systems and interval type-2 fuzzy sets and systems are explained. The components of an interval type-2 fuzzy logic system are mentioned and the most known type reduction methods are explained. Interval type-2 fuzzy logic systems are quite complicated systems and it needs many steps to implement them from the first phase to implementation phase. Therefore, in this thesis, a Matlab/Simulink toolbox is developed and proposed to cover all phases of an interval type-2 fuzzy logic system design from the first description phase to the final implementation phase through type reduction. The proposed interval type-2 fuzzy logic toolbox allows users to design an interval type-2 fuzzy logic system by using the user interfaces. It makes the design of the interval type-2 fuzzy logic system so easy and understandable. The design of the interval type-2 fuzzy logic system toolbox starts by creating a structure in the Matlab workspace to save the information of the interval type-2 fuzzy logic system. Type reduction method, input and output variable types, the membership function parameters, the rules and the other information are saved to this structure. The interval type-2 fuzzy logic systems toolbox consists of four main pages: main editor, membership functions editor, rule editor and surface viewer. The input and output variables number of the interval type-2 fuzzy logic design is determined in main editor page. In addition, it is possible to choose the desired type reduction method from the main editor. The all type reduction methods that are explained in this thesis are implemented as a Matlab function and embedded to the toolbox via a pop-up menu in main editor. The user can select his desired type reduction method by using this menu easily. The membership function editor page allows to define the upper and lower membership functions of the each input and output variables. To provide this, the all membership functions of the Matlab fuzzy logic toolbox have been reused by adding an additional parameter into the end. The last parameter provides the opportunity to define the height of the lower membership functions. In addition, it is possible to define the membership functions of the output variables in either crisp or interval. Defining rules for the interval type-2 fuzzy logic system design is possible in the rule editor page. In addition, it is possible to view the surface of the current design from the surface viewer page. The interval type-2 fuzzy logic systems toolbox is designed to be working with Matlab/Simulink. To provide this feature, firstly a new Simulink library has been created for the interval type-2 fuzzy logic toolbox. The created Simulink library has two blocks. The first one in used to simulate the designed interval type-2 fuzzy logic controller, and the second one gives the user an opportunity to choose desired type reduction method. Also, it is possible to export the interval type-2 fuzzy logic system design from the toolbox to Simulink automatically by clicking a button. Then, it creates a Simulink model with current design and the user can start the simulations easily. In the last section of this thesis, an interval type-2 fuzzy logic system is created by using the proposed toolbox and some performance analysis are done. Firstly, an interval type-2 fuzzy logic controller is designed by using the toolbox. Then, the control surfaces of the different type reduction methods are given. The interval type-2 fuzzy logic controller exported to the Simulink and closed loop control system is created with a first order plus dead time system. Then, the performances of the same interval type-2 fuzzy logic controller with different type reduction methods are compared for the nominal system parameters. After that, the system parameters are perturbed several times and the simulations are repeated to compare the performances of the different type reduction methods In addition, the computational time of the each type reduction methods are measured and compared. In summary, a Matlab/Simulink toolbox for interval type-2 fuzzy logic systems is designed and proposed in this thesis. The proposed interval type-2 fuzzy logic toolbox covers the all phases of an interval type-2 fuzzy logic system design from the initial description phase to the final implementation phase including type reduction component. Then, an interval type-2 fuzzy logic controller is designed by using the toolbox and the simulations are done to compare the control performance of the different type reduction methods for the same system. In addition, the computational times of the each type reduction methods are measured and compared.