In this paper, we investigate hybrid adaptive synchronization issue for a class of perturbed fractional-order chaotic systems with nondeterministic nonlinear terms. On the basis of fractional-order extended version of Lyapunov stability criterion, a novel fuzzy adaptive synchronization control protocol coupled with backstepping-based method is constructed, ensuring that the synchronization errors converge to a sufficiently small region of the origin. In order to avert the occurrence of “explosion of complexity”, we take advantage of a fuzzy logic system to estimate the unknown systematic term approximately in every backstepping step. Finally, some numerical simulations are given to exemplify the effectiveness of the proposed approach.

We consider a type of fuzzy viscoelastic integro‐differential model in this paper. With the aid of some appropriate hypotheses, a unified method and the multiplier technique are implemented to get priori estimates precisely without constructing any auxiliary function. By establishing the estimation of energy function, we derive the stability result of the global solution, and we calculate the estimations of energy attenuation in exponential and polynomial forms, respectively.

Crisp antimatroid is a combinatorial abstraction of convexity. It also can be incorporated into the greedy algorithm in order to seek the optimal solutions. Nevertheless, this kind of significant classical structure has inherent limitations in addressing fuzzy optimization problems and abstracting fuzzy convexities. This paper introduces the concept of L -fuzzifying antimatroid associated with an L -fuzzifying family of feasible sets. Several relevant fundamental properties are obtained. We also propose the concept of L -fuzzifying rank functions for L -fuzzifying antimatroids, and then investigate their axiomatic characterizations. Finally, we shed light upon the bijective correspondence between an L -fuzzifying antimatroid and its L -fuzzifying rank function.