This paper presents a general framework for the study of rough fuzzy sets in which fuzzy sets are approximated in a crisp approximation space. By the constructive approach, a pair of lower and upper generalized rough fuzzy approximation operators is first defined. The rough fuzzy approximation operators are represented by a class of generalized crisp approximation operators. Properties of rough...

Value function is usually used to deal with the reinforcement learning problems. In large or even continuous states, function approximation must be used to represent value function. Much of the current work carried out, however, has to design the structure of function approximation in advanced which cannot be adjusted during learning. In this paper, we propose a novel function approximation cal...

In Gerla [2000] a fuzzy logic in narrow sense is proposed as a theoretical framework for triangular norm based fuzzy control. In this note we show that the resulting theory is also able to express the implicationbased fuzzy control. Introduction The aim of control theory is to define a function f : X → Y whose intended meaning is that f(x) is the correct answer given the input x. Fuzzy approach...

In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equations of the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and convert a two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equations of the second kind in crisp case. We can use Adomian decomposition method for n...

A novel function-link fuzzy cerebelarmodel-articulation-controller (CMAC) is developed in this study. It is a generalization of a fuzzy neural network and of a conventional CMAC. Then, a control system comprising a function-link fuzzy CMAC and a fuzzy compensator is proposed for multi-input multi-output (MIMO) nonlinear chaotic systems. The function-link fuzzy CAMC is used to mimic an ideal con...

In this paper, we propose a constructive method to develop a fuzzy system having a monotonic input–output relationship and prove that the developed fuzzy system can approximate any continuously differentiable monotonic function with any desired degree of accuracy. The fuzzy system is constructed with complete and consistent input membership functions and imposes special parametric constraints o...

This paper presents a general framework for the study of rough set approximation operators in fuzzy environment in which both constructive and axiomatic approaches are used. In constructive approach, a pair of lower and upper generalized fuzzy rough (and rough fuzzy, respectively) approximation operators is first defined. The representations of both fuzzy rough approximation operators and rough...

In this paper, we present two results concerning the fuzzy modeling and control of nonlinear systems. The first result is on the approximation of smooth nonlinear dynamical systems using linear Takagi-Sugeno fuzzy models. The second result is on the approximation of smooth nonlinear state-feedback controllers using the the so-called parallel distributed compensation (PDC) controller. Both resul...