Framework for Optimization of Intuitionistic and Type-2 Fuzzy Systems in Control Applications

Abstract

In this paper a framework for finding the optimal design of intuitionistic fuzzy systems in control applications is presented. Traditional models deal with type-0 values, which mean using precise numbers in the models, but since the seminal work of Prof. Zadeh in 1965, type-1 fuzzy models emerged as a powerful way to represent human knowledge and natural phenomena. Later type-2 fuzzy models were also proposed by Prof. Zadeh in 1975 and more recently have been studied and applied in real world problems by many researchers. In addition, as another extension of type-1 fuzzy logic, Prof. Atanassov proposed Intuitionistic Fuzzy Logic, which is a very powerful theory in its own right. Previous works of the author and other researchers have shown that certain problems can be appropriately solved by using type-1, and others by interval type-2, while others by using intuitionistic fuzzy logic. Bio-inspired and meta-heuristic optimization algorithms have been commonly used to find optimal designs of type-1, type-2 or intuitionistic fuzzy models for applications in control, robotics, pattern recognition, time series prediction, just to mention a few. However, the question still remains about if even more complex problems (meaning non-linearity, noisy, dynamic environments, etc.) may require even higher types, orders or extensions of type-1 fuzzy models to obtain better solutions to real world problems. In this paper a framework for solving this problem of finding the optimal fuzzy model for a particular problem is presented. To the knowledge of the author, this is the first work to propose a systematic approach to solve this problem, and we envision that in the future this approach will serve as a basis for developing more efficient algorithms for the same task of finding the optimal fuzzy system.