Group testing is a method of pooling a number of units together and performing a single test on the resulting group. It is an appealing option when few individual units are thought to be infected leading to reduced co...Group testing is a method of pooling a number of units together and performing a single test on the resulting group. It is an appealing option when few individual units are thought to be infected leading to reduced costs of testing as compared to individually testing the units. Group testing aims to identify the positive groups in all the groups tested or to estimate the proportion of positives (p) in a population. Interval estimation methods of the proportions in group testing for unequal group sizes adjusted for overdispersion have been examined. Lately improvement in statistical methods allows the construction of highly accurate confidence intervals (CIs). The aim here is to apply group testing for estimation and generate highly accurate Bootstrap confidence intervals (CIs) for the proportion of defective or positive units in particular. This study provided a comparison of several proven methods of constructing CIs for a binomial proportion after adjusting for overdispersion in group testing with groups of unequal sizes. Bootstrap resampling was applied on data simulated from binomial distribution, and confidence intervals with high coverage probabilities were produced. This data was assumed to be overdispersed and independent between groups but correlated within these groups. Interval estimation methods based on the Wald, the Logit and Complementary log-log (CLL) functions were considered. The criterion used in the comparisons is mainly the coverage probabilities attained by nominal 95% CIs, though interval width is also regarded. Bootstrapping produced CIs with high coverage probabilities for each of the three interval methods.展开更多
Let a（n） denote the number of non-isomorphic Abelian groups of order n. For afixed integer k≥1, letA<sub>k</sub>（x, h）:=sum from n=x【n≤x+h,a（n）=k to （1）If h≥x<sup>581/1744</sup>logx...Let a（n） denote the number of non-isomorphic Abelian groups of order n. For afixed integer k≥1, letA<sub>k</sub>（x, h）:=sum from n=x【n≤x+h,a（n）=k to （1）If h≥x<sup>581/1744</sup>logx=x<sup>0.33314…</sup>logx as x→∞,it was proved by A,Ivic thatA<sub>k</sub>（x, h）=（d<sub>k</sub>+o（1））h, （1）whered<sub>k</sub>=sum from n=1 to ∞ (1/2πn integral from n=-π to π(e<sup>ikt g<sub>t</sub>（n）dt≥0</sup>)),g<sub>t</sub>（n）=sum from n=d/n to (μ（n/d）e<sup>ita</sup>（d）).In Ref. [2], A. Ivic and P. Shiu improved the result. They showed that if h≥x<sup>877/2653</sup>（logx）<sup>c</sup>=x<sup>0.3305…</sup>（logx）<sup>c</sup>,then Eq.（1）is true, where C is a computable constant. Based on the estimate for △（1, 2, 2;x） in Ref.[2] and elementary discussion, thisnote proves the following theorem, which gives an improvement to the problem.展开更多
We propose a new consensus model for group decision making(GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized b...We propose a new consensus model for group decision making(GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized by interval type-2 fuzzy sets(IT2 FSs), because these can provide decision makers with greater freedom to express the vagueness in real-life situations. Consensus and proximity measures based on the arithmetic operations of IT2 FSs are used simultaneously to guide the decision-making process. The majority of previous studies have taken into account only the importance of the experts in the aggregation process, which may give unreasonable results. Thus, we propose a new feedback mechanism that generates different advice strategies for experts according to their levels of importance. In general, experts with a lower level of importance require a larger number of suggestions to change their initial preferences. Finally, we investigate a numerical example and execute comparable models and ours, to demonstrate the performance of our proposed model. The results indicate that the proposed model provides greater insight into the GDM process.展开更多
文摘Group testing is a method of pooling a number of units together and performing a single test on the resulting group. It is an appealing option when few individual units are thought to be infected leading to reduced costs of testing as compared to individually testing the units. Group testing aims to identify the positive groups in all the groups tested or to estimate the proportion of positives (p) in a population. Interval estimation methods of the proportions in group testing for unequal group sizes adjusted for overdispersion have been examined. Lately improvement in statistical methods allows the construction of highly accurate confidence intervals (CIs). The aim here is to apply group testing for estimation and generate highly accurate Bootstrap confidence intervals (CIs) for the proportion of defective or positive units in particular. This study provided a comparison of several proven methods of constructing CIs for a binomial proportion after adjusting for overdispersion in group testing with groups of unequal sizes. Bootstrap resampling was applied on data simulated from binomial distribution, and confidence intervals with high coverage probabilities were produced. This data was assumed to be overdispersed and independent between groups but correlated within these groups. Interval estimation methods based on the Wald, the Logit and Complementary log-log (CLL) functions were considered. The criterion used in the comparisons is mainly the coverage probabilities attained by nominal 95% CIs, though interval width is also regarded. Bootstrapping produced CIs with high coverage probabilities for each of the three interval methods.
文摘Let a（n） denote the number of non-isomorphic Abelian groups of order n. For afixed integer k≥1, letA<sub>k</sub>（x, h）:=sum from n=x【n≤x+h,a（n）=k to （1）If h≥x<sup>581/1744</sup>logx=x<sup>0.33314…</sup>logx as x→∞,it was proved by A,Ivic thatA<sub>k</sub>（x, h）=（d<sub>k</sub>+o（1））h, （1）whered<sub>k</sub>=sum from n=1 to ∞ (1/2πn integral from n=-π to π(e<sup>ikt g<sub>t</sub>（n）dt≥0</sup>)),g<sub>t</sub>（n）=sum from n=d/n to (μ（n/d）e<sup>ita</sup>（d）).In Ref. [2], A. Ivic and P. Shiu improved the result. They showed that if h≥x<sup>877/2653</sup>（logx）<sup>c</sup>=x<sup>0.3305…</sup>（logx）<sup>c</sup>,then Eq.（1）is true, where C is a computable constant. Based on the estimate for △（1, 2, 2;x） in Ref.[2] and elementary discussion, thisnote proves the following theorem, which gives an improvement to the problem.
基金Project supported by the National Natural Science Foundation of China(Nos.71501182 and 71571185)
文摘We propose a new consensus model for group decision making(GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized by interval type-2 fuzzy sets(IT2 FSs), because these can provide decision makers with greater freedom to express the vagueness in real-life situations. Consensus and proximity measures based on the arithmetic operations of IT2 FSs are used simultaneously to guide the decision-making process. The majority of previous studies have taken into account only the importance of the experts in the aggregation process, which may give unreasonable results. Thus, we propose a new feedback mechanism that generates different advice strategies for experts according to their levels of importance. In general, experts with a lower level of importance require a larger number of suggestions to change their initial preferences. Finally, we investigate a numerical example and execute comparable models and ours, to demonstrate the performance of our proposed model. The results indicate that the proposed model provides greater insight into the GDM process.
