Shenggang Li

The synchronization of fractional-order chaotic systems is investigated using command-filtered adaptive fuzzy control with a disturbance observer, where an event-triggered mechanism and backstepping control technique are employed. In order to relieve the pressure of the continuous update of the controller and improve the resource utilization, an event-triggered control strategy is constructed to reduce the amount of communication for the actuator. Under the framework of adaptive fuzzy backstepping recursive design, fuzzy logical systems and disturbance observers are proposed to estimate the unknown parametric uncertainties and external disturbances, respectively. Moreover, a tracking differentiator is introduced to eliminate the drawback of the explosion of complexity in traditional backstepping. By applying the fractional-order stability theory, all closed-loop signals are bounded and chaos synchronization is achieved. Finally, a simulation example is provided to confirm the effectiveness of the designed method.

Polya’s plausible reasoning methods are crucial not only in discovery of mathematics results, modeling methods, and data processing methods but also in many practical problems’ solving. This paper exemplifies how to use Polya’s plausible reasoning methods to generalize the popularized notion of 2-connectedness of graphs to a more universal notion of the connected degree of fuzzifying matroids. We introduce the connectedness of fuzzifying matroids, which is generalized from 2-connectedness of graphs, connectedness of matroids, and 2-connectedness of fuzzy graphs. Moreover, the connected degree of fuzzifying matroids is presented by considering the fuzziness degree of connectedness. It is proved that a fuzzifying matroid is connected, which is equivalent to its connectedness degree is the biggest (i.e., ). This, together with other properties of the connected degree of fuzzifying matroids, demonstrates the rationality of the proposed notion. Finally, we describe the concepts of this paper through some examples.

An L , M -fuzzy topological convergence structure on a set X is a mapping which defines a degree in M for any L -filter (of crisp degree) on X to be convergent to a molecule in L X . By means of L , M -fuzzy topological neighborhood operators, we show that the category of L , M -fuzzy topological convergence spaces is isomorphic to the category of L , M -fuzzy topological spaces. Moreover, two characterizations of L -topological spaces are presented and the relationship with other convergence spaces is concretely constructed.

This paper shows an application of plausible reasoning methods (mainly, specialization and analogous) in mathematical modeling. Our attention is how a practitioner to determine analogously a more balanced scientific model to assist the desire during solving the entire problem. Taking interval samples modeling as a problem, we exemplify (with consideration paid to the motivation and course of discovering) how to discover, based on the classical corresponding methods, three linear regression models and two linear-like interpolation models relying on n-variable interval input-1-variable interval output samples. The rationality of these recommended models are proved, and applications of them are illuminated in detail by examples. Strategies to model further interval samples towards satisfactory are also exposed.