Optimal control is a very important field of study not only in theory but in applications, and stochastic optimal control is also a significant branch of research in theory and applications. Based on the concept of fuzzy process introduced by Liu, we present a fuzzy optimal control problem. Applying Bellman’s optimal principle, we obtain the principle of optimality for fuzzy optimal control, an...

Abstract: A new adaptive fuzzy fault-tolerant control scheme for complex non-linear systems is proposed in this paper. The approach presented here combines fuzzy T-S dynamic model with Riccati equation. In each local linear model of the fuzzy dynamic model, Riccati equation is used in the design of fault-tolerant control. These local models are linked together by fuzzy membership functions to f...

Optimal control is a very important field of study not only in theory but in applications, and stochastic optimal control is also a significant branch of research in theory and applications. Based on the concept of fuzzy process, a fuzzy optimal control problem presented. Applying Bellman’s Principle of Optimality, the principle of optimality for fuzzy optimal control is derived, and then a fun...

In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{Ax_n+x_{n-1}}{B+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $A, B$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.

Throughout the paper it is shown that the classical definition of a fuzzy subset carries additional structures. The concept of a fuzzy subset is regarded from an alternative point of view: namely, the characteristic function of a fuzzy subset may be reinterpreted in terms of a Sincov’s functional equation in two variables. Since the solutions of a Sincov’s functional equation are also closely r...

in this paper, a fuzzy hunter-saxton equation is solved by using the adomian'sdecomposition method (adm) and homotopy analysis method (ham). theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a recursive relation. the existenceand uniqueness of the solution and the convergence of the proposed methodsare proved. a nume...

In this paper, fuzzy dynamical system is introduced via fuzzy differential equation. Some examples are illustrated the existence of such system. Some concepts about stability are introduced to evaluate a fuzzy dynamical system.

Besides of these there are many equation based effort estimation techniques like Halstead Model, Bailey-Basil Model, and Walston-Felix Model. Cost and effort estimation are the major concern of any software industry. They are identified with the help of Kilo Line Code (KLOC) which denotes number of, line of code in software. For example if a software contain 2000 lines then it has 2 kilo line o...

The π-derivative for fuzzy function is considered. Consequently, using this π-derivative we study fuzzy differentuial equations. In particular, we build a solution for a fuzzy differential equation with the help of a system of ordinary differential equations which is generates of the π-derivative. Keywords— π-derivative for set valued functions, derivative for fuzzy functions, fuzzy differentia...

This paper first reviews different types of uncertainty. In order to construct fuzzy counterparts of Brownian motion and stochastic calculus, this paper proposes some basic concepts of fuzzy process, including fuzzy calculus and fuzzy differential equation. Those new concepts are also extended to hybrid process and uncertain process. A basic stock model is presented, thus opening up a way to fu...