Some Chaotic and Mixing Properties of Zadeh's Extension
نویسنده
چکیده
Let X be a compact metric space, let φ be a continuous self-map on X , and let F(X) denote the space of fuzzy sets on X equipped with the levelwise topology. In this paper we study relations between various dynamical properties of a given (crisp) dynamical system (X,φ) and its Zadeh’s extension Φ on F(X). Among other things we study various (weak, strong, mild etc.) mixing properties and also several kinds of chaotic behaviors (Li-Yorke chaos, ω-chaos, distributional chaos, topological chaos etc.). Keywords— Zadeh’s extension, fuzzification, chaos, mixing, transitivity, topological entropy.
منابع مشابه
THE CHAIN PROPERTIES AND LI-YORKE SENSITIVITY OF ZADEH'S EXTENSION ON THE SPACE OF UPPER SEMI-CONTINUOUS FUZZY SETS
Some characterizations on the chain recurrence, chain transitivity, chain mixing property,shadowing and $h$-shadowing for Zadeh's extension are obtained. Besides, it is provedthat a dynamical system is spatiotemporally chaotic provided that the Zadeh's extensionis Li-Yorke sensitive.
متن کاملA note on Zadeh's extension principle
For a mapping, fuzzy sets obtained by Zadeh's extension principle are images of other fuzzy sets on the domain of the mapping under the mapping. Some relationships between images of level sets of one or two fuzzy sets under a mapping and another fuzzy set obtained from the one or two fuzzy sets by Zadeh's extension principle are known. In the present paper, the known results are extended to mor...
متن کاملLaminar mixing of high-viscous fluids by a cylindrical chaotic mixer
Laminar mixing of glycerin in a chaotic mixer is carried by means of the blob deformation method. The mixer was a cylindrical vessel with two rotational blades which move along two different circular paths with a stepwise motion protocol. The flow visualization was performed by marking of the free surface of the flow with a tracer. The effects of controlling parameters such as rotational speed ...
متن کاملUsing finite difference method for solving linear two-point fuzzy boundary value problems based on extension principle
In this paper an efficient Algorithm based on Zadeh's extension principle has been investigated to approximate fuzzy solution of two-point fuzzy boundary value problems, with fuzzy boundary values. We use finite difference method in term of the upper bound and lower bound of $r$- level of fuzzy boundary values. The proposed approach gives a linear system with crisp tridiagonal coefficients matr...
متن کاملOn the structural properties for the cross product of fuzzy numbers with applications
In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...
متن کامل