A similarity measure is a measure that indicates the degree of similarity between two objects. The purpose of this work is to investigate the monotonicity properties and applications of similarity measures on interval-valued fuzzy sets. Through analyzing the intuitions of similarities, three kinds of monotonic similarity measures are defined. Furthermore, their properties and relationships with entropy and inclusion measure are investigated and discussed. Finally, some applications of the proposed monotonic similarity measures, such as pattern recognition, medical recognition, and medical diagnosis are presented.
In allusion to a difference equation of single-species models with harvesting coefficient, the presence of chaotic phenomenon is validated by computing Lyapunov exponent and giving its change with the parameter. Tiny control based on the basic ideas in the classical OGY method and tracking control based on the exact feedback linearization are used to control chaos in the model respectively, we obtain the following results: 1)the sufficient conditions of the species that stabilizes in the fixed points and the trajectory of period-2 are obtained and chaotic phenomenon is eliminated; 2)any orbits can be reached by using tracking control method. Contrast on two kinds of control method, we draw the conclusion that tracking control method is more flexible than the OGY method. The effectiveness of the conclusions are validated by simulation.
In allusion to a discrete coupled Logistic model with symbiotic interaction, the presence of chaos was validated by computing Lyapunov exponent measure. More complex phenomena were found by analyzing bifurcation diagrams of system with varieties of parameter elaborately. By applying tracking control of chaos to stabilize the species to the unstable fixed points, chaotic trajectories in the system were controlled in the anticipant trajectory and chaotic phenomena were eliminated. The correctness of the conclusion was validated by simulation.
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