In this study, a new fuzzy integral model with adaptation capability called as “Adaptive Fuzzy Integral” was proposed to use in particularly control systems instead of conventional fuzzy integral. Until now, in the fuzzy integral applications, the fuzzy density values of control criterias were defined fixed. But this structure is not suitable for dynamic characteristic of control systems. There...

We study conditions under which the solutions of a fuzzy integral equation are bounded. 1. Introduction. The concept of set-valued functions and their calculus [2] were found useful in some problems in economics [3], as well as in control theory [17]. Later on, the notion of H-differentiability was introduced by Puri and Ralesku in order to extend the differential of set-valued functions to tha...

In this paper, an uncertainty and disturbance estimator (UDE)-based control is employed to ensure the finite-time tracking rejection performance for a class of Takagi–Sugeno fuzzy switched systems including additive time-varying delays, unknown uncertainties disturbances. To be precise, robust achieved by estimating disturbances with aid low-pass filter means appropriate bandwidth choice desire...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of...

I n recent years, many numerical methods have been proposed for solving fuzzy linear integral equations. For example, in [10], the authors used the divided differences and finite differences methods for solving a parametric of the fuzzy Fredholm integral equations of the second kind. Also, in [9], a numerical method is proposed for the approximate solution of fuzzy linear Fredholm functional in...

An adaptive fuzzy integral sliding mode controller for mismatched time-varying linear systems is presented in this paper. The proposed fuzzy integral sliding mode controller is designed to have zero steady state system error under step inputs and alleviate the undesired chattering around the sliding surface. The parameters in the fuzzy mechanism are adapted on-line to improve the performance of...

In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...