Approximation of fuzzy numbers by convolution method

In this paper we consider how to use the convolution method to construct approximations, which consist of fuzzy numbers sequences with good properties, for a general fuzzy number. It shows that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers which have finite non-differentiable points. In the previous work, this convolution method only can be used to construct differentiable approximations for continuous fuzzy numbers whose possible non-differentiable points are the two endpoints of 1-cut. The constructing of smoothers is a key step in the construction process of approximations. It further points out that, if appropriately choose the smoothers, then one can use the convolution method to provide approximations which are differentiable, Lipschitz and preserve the core at the same time.Comment: Submitted to Fuzzy Sets and System at Sep 18 201

Fuzzy measures and discreteness

AbstractThe main result is to show that the space of nonmonotonic fuzzy measures on a measurable space (X,X) with total variation norm is separable if and only if the σ-algebra X is a finite set. Our result is related to fuzzy analysis, functional spaces and discrete mathematics

A New Characterization of Compact Sets in Fuzzy Number Spaces

We give a new characterization of compact subsets of the fuzzy number space equipped with the level convergence topology. Based on this, it is shown that compactness is equivalent to sequential compactness on the fuzzy number space endowed with the level convergence topology. Our results imply that some previous compactness criteria are wrong. A counterexample also is given to validate this judgment

A Characterization for Compact Sets in the Space of Fuzzy Star-Shaped Numbers with L

By means of some auxiliary lemmas, we obtain a characterization of compact subsets in the space of all fuzzy star-shaped numbers with Lp metric for 1≤p<∞. The result further completes and develops the previous characterization of compact subsets given by Wu and Zhao in 2008

Effects of Stepwise Denervation of the Stellate Ganglion: Novel Insights from an Acute Canine Study

Background The stellate ganglion (SG) is important for cardiac autonomic control. SG modification is an option for treating refractory ventricular tachyarrhythmias. The optimal extent of left- and right-sided SG denervation necessary for antiarrhythmic effect, however, remains to be learned. Objective The purpose of this study was to evaluate the effects of stepwise SG denervation on hemodynamic and electrophysiological parameters in dogs. Methods After sequential left and right thoracotomy in 8 healthy dogs, the SG was exposed by dissection. Two pacing wires were placed in the upper SG to deliver high-frequency stimulation. The lower SG, ansae subclaviae, and upper SG were removed in a stepwise manner. The same protocol was performed on the right side. Blood pressure (BP), heart rate, and electrophysiological parameters were recorded at baseline and after 5 minutes of stimulation. Results Systolic and diastolic BP significantly increased during stimulation of the upper left SG. The mean increase in systolic BP from baseline was 49.4 ± 26.6 mm Hg (P = .007), 25.5 ± 14.1 mm Hg after the lower SG was removed (P = .02), and 8.6 ± 3.4 mm Hg after resection of the ipsilateral ansae subclaviae (P = .048). Heart rate and other electrophysiological parameters did not change significantly. After the complete removal of the left SG, systolic BP increased by 34.0 ± 17.6 mm Hg (P = .005) after stimulation of the right SG. Conclusion Sympathetic output remains after the lower SG is removed, and sympathetic output from the right SG remains after the complete resection of the left SG and ansae subclaviae. Thus, some patients who undergo left SG denervation can still have significant sympathetic response via right SG regulation

The serum matrix metalloproteinase-9 level is an independent predictor of recurrence after ablation of persistent atrial fibrillation

OBJECTIVES: This study investigated whether the serum matrix metalloproteinase-9 level is an independent predictor of recurrence after catheter ablation for persistent atrial fibrillation. METHODS: Fifty-eight consecutive patients with persistent atrial fibrillation were enrolled and underwent catheter ablation. The serum matrix metalloproteinase-9 level was detected before ablation and its relationship with recurrent arrhythmia was analyzed at the end of the follow-up. RESULTS: After a mean follow-up of 12.1±7.2 months, 21 (36.2%) patients had a recurrence of their arrhythmia after catheter ablation. At baseline, the matrix metalloproteinase-9 level was higher in the patients with recurrence than in the non-recurrent group (305.77±88.90 vs 234.41±93.36 ng/ml, respectively, p=0.006). A multivariate analysis showed that the matrix metalloproteinase-9 level was an independent predictor of arrhythmia recurrence, as was a history of atrial fibrillation and the diameter of the left atrium. CONCLUSION: The serum matrix metalloproteinase-9 level is an independent predictor of recurrent arrhythmia after catheter ablation in patients with persistent atrial fibrillation

On the space of (s)-integrable functions for a monotonic measure

In this paper we introduce and study the space of real-valued (s)-integrable functions for a monotonic measure, and consider some relations between this space and the space of real-valued measurable functions