In this paper, the probability significance of fuzzy systems is revealed. It is pointed out that COG method, a defuzzification technique used commonly in fuzzy systems, is reasonable and is the optimal method in the s...In this paper, the probability significance of fuzzy systems is revealed. It is pointed out that COG method, a defuzzification technique used commonly in fuzzy systems, is reasonable and is the optimal method in the sense of mean square. Based on different fuzzy implication operators, several typical probability distributions such as Zadeh distribution, Mamdani distribution, Lukasiewicz distribution, etc, are given. Those distributions act as ＂inner kernels＂ of fuzzy systems. Furthermore, by some properties of probability distributions of fuzzy systems, it is also demonstrated that CRI method, proposed by Zadeh, for constructing fuzzy systems is basically reasonable and effective. Besides, the special action of uniform probability distributions in fuzzy systems is characterized. Finally, the relationship between CRI method and triple I method is discussed. In the sense of construction of fuzzy systems, when restricting three fuzzy implication operators in triple I method to the same operator, CRI method and triple I method may be related in the following three basic ways： 1） Two methods are equivalent; 2） the latter is a degeneration of the former; 3） the latter is trivial whereas the former is not. When three fuzzy implication operators in triple I method are not restricted to the same operator, CRI method is a special case of triple I method; that is, triple I method is a more comprehensive algorithm. Since triple I method has a good logical foundation and comprises an idea of optimization of reasoning, triple I method will possess a beautiful vista of application.展开更多
The Cr-Mo-N films were deposited on high speed steel（HSS） substrates by a DC reactive magnetron sputtering equipment coupled with two horizontal magnetron sources.The effects of substrate negative bias voltage（Vb）...The Cr-Mo-N films were deposited on high speed steel（HSS） substrates by a DC reactive magnetron sputtering equipment coupled with two horizontal magnetron sources.The effects of substrate negative bias voltage（Vb）,substrate temperature（Ts） and gas flow ratio（R= N2/（N2+ Ar）） on the microstructure,morphology,as well as the mechanical and tribological properties of the Cr-Mo-N films were investigated by virtue of X-ray diffraction（XRD） analysis,X-ray photoelectron spectroscopy（XPS）,field emission scanning electron microscopy（FESEM）,atomic force microscopy（AFM）,nano-indentation test,ball-on-disk tribometer,and Rockwell indenter et al.With increasing Vbto-100 V,the preferred orientation of the films changed from（111） to（200） and their mechanical and tribological properties were improved gradually,too.It was also found that Tsgave a significant effect on mechanical property enhancement.When the Tsreached 300 ℃,the film obtained the highest hardness and effective elastic modulus of approximately 30.1 and 420.5 GPa,respectively and its critical load increased to about 54 N.With increasing R,the phase transformation from body-centered-cubic（bcc） Cr and hexagonal CrMoNxmultiphase to single face-centered-cubic（fcc） solid solution phase was observed.The correlations between values of hardness（H）,effective elastic modulus（E*）,HIE*,H3/E*2,elastic recovery（1/14） and tribological properties of the films were also investigated.The results showed that the elastic recovery played an important role in the tribological behavior.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.60474023).
文摘In this paper, the probability significance of fuzzy systems is revealed. It is pointed out that COG method, a defuzzification technique used commonly in fuzzy systems, is reasonable and is the optimal method in the sense of mean square. Based on different fuzzy implication operators, several typical probability distributions such as Zadeh distribution, Mamdani distribution, Lukasiewicz distribution, etc, are given. Those distributions act as ＂inner kernels＂ of fuzzy systems. Furthermore, by some properties of probability distributions of fuzzy systems, it is also demonstrated that CRI method, proposed by Zadeh, for constructing fuzzy systems is basically reasonable and effective. Besides, the special action of uniform probability distributions in fuzzy systems is characterized. Finally, the relationship between CRI method and triple I method is discussed. In the sense of construction of fuzzy systems, when restricting three fuzzy implication operators in triple I method to the same operator, CRI method and triple I method may be related in the following three basic ways： 1） Two methods are equivalent; 2） the latter is a degeneration of the former; 3） the latter is trivial whereas the former is not. When three fuzzy implication operators in triple I method are not restricted to the same operator, CRI method is a special case of triple I method; that is, triple I method is a more comprehensive algorithm. Since triple I method has a good logical foundation and comprises an idea of optimization of reasoning, triple I method will possess a beautiful vista of application.
基金supported by the National Key Basic Research Program of China (973 Program, No. 2012CB625100)the National Natural Science Foundation of China (NSFC, No. 51171197)the Natural Science Foundation of Liaoning Province of China (No. 2013020093)
文摘The Cr-Mo-N films were deposited on high speed steel（HSS） substrates by a DC reactive magnetron sputtering equipment coupled with two horizontal magnetron sources.The effects of substrate negative bias voltage（Vb）,substrate temperature（Ts） and gas flow ratio（R= N2/（N2+ Ar）） on the microstructure,morphology,as well as the mechanical and tribological properties of the Cr-Mo-N films were investigated by virtue of X-ray diffraction（XRD） analysis,X-ray photoelectron spectroscopy（XPS）,field emission scanning electron microscopy（FESEM）,atomic force microscopy（AFM）,nano-indentation test,ball-on-disk tribometer,and Rockwell indenter et al.With increasing Vbto-100 V,the preferred orientation of the films changed from（111） to（200） and their mechanical and tribological properties were improved gradually,too.It was also found that Tsgave a significant effect on mechanical property enhancement.When the Tsreached 300 ℃,the film obtained the highest hardness and effective elastic modulus of approximately 30.1 and 420.5 GPa,respectively and its critical load increased to about 54 N.With increasing R,the phase transformation from body-centered-cubic（bcc） Cr and hexagonal CrMoNxmultiphase to single face-centered-cubic（fcc） solid solution phase was observed.The correlations between values of hardness（H）,effective elastic modulus（E*）,HIE*,H3/E*2,elastic recovery（1/14） and tribological properties of the films were also investigated.The results showed that the elastic recovery played an important role in the tribological behavior.
