— The paper uses the LU-parametric representation of fuzzy numbers and fuzzy-valued functions, to obtain valid approximations of fuzzy generalized derivative and to solve fuzzy differential equations. The main result is that a fuzzy differential initial-value problem can be translated into a system of in nitely many ordinary differential equations and, by the LU-parametric representation, the i...

A novel fractional order (FO) fuzzy Proportional-Integral-Derivative (PID) controller has been proposed in this paper which works on the closed loop error and its fractional derivative as the input and has a fractional integrator in its output. The fractional order differ-integrations in the proposed fuzzy logic controller (FLC) are kept as design variables along with the input-output scaling f...

In this work we solve numerically a boundary value problem for second order fuzzy differential equations under generalized differentiability in the form y′′(t) = p(t)y′(t) + q(t)y(t) + F(t) y(0) = γ, y(`) = λ where t ∈ T = [0, `], p(t) ≥ 0, q(t) ≥ 0 are continuous functions on [0, `] and [γ]α = [γα ,γα ], [λ ] α = [λ α ,λ α ] are fuzzy numbers. There are four different solutions of the problem ...

In this paper, we study the classical Sumudu transform in fuzzy environment, referred to as the fuzzy Sumudu transform (FST). We also propose some results on the properties of the FST, such as linearity, preserving, fuzzy derivative, shifting and convolution theorem. In order to show the capability of the FST, we provide a detailed procedure to solve fuzzy differential equations (FDEs). A numer...

In this paper, new observer design approaches are presented for TakagiSugeno (T-S) fuzzy models with measurement output noises. In order to decouple the measurement noise, an augmented fuzzy descriptor model is first constructed. Then a fuzzy descriptor proportional and derivative (PD) observer is developed. When the fuzzy subsystems have the same output matrices, another fuzzy descriptor obser...

Fuzzy Tracking Control of Linear Dynamical Systems for a fixed reference input under granular derivative

Using the concept of Hukuhara difference, in this paper we introduce a class of new derivatives called Hukuhara delta derivative and a class of new integrals called Hukuhara delta integral for fuzzy setvalued functions on time scales. Moreover, some corresponding properties of Hukuhara delta derivative and Hukuhara delta integral are discussed. Furthermore, sufficient conditions are established...

We aim at clarifying the relationship between laws of large numbers for fuzzy sets or possibility distributions and laws of large numbers for fuzzy or possi-bilistic variables. We contend that these two frameworks are different and present the relationships between them that explain why this fact was unrecognized so far. A classical result in Probability Theory is the law of large numbers. If ξ...

In this paper, we define the fuzzy Henstock-Δ-integral and Δ-derivative on time scales(or briefly FH-Δ-integral, Δ-derivative). Then, give some convergence theorems for kind of nonabsolute convergent integrals. Finally, obtain an existence theorem global solutions generalized differential systems.

In this paper, we investigate the existence and calculation of the expression of periodic solutions for fuzzy differential equations with three types of forcing terms, by using Hukuhara derivative. In particular, Theorems 3.2, 4.2 and 5.2 are the results of existences of periodic solutions for fuzzy differential equations ™,a andb, respectively. These results will help us to study phenomena wit...