基于区间值模糊集的聚类分析

对于区间数 ,提出了反映决策者心态的心态指标的概念 ,在此基础上 ,给出了基于区间值模糊集之聚类分析的两种方法 :心态分类法、数 -区间分类法 ,对后一种分类法 ,引入了一种指标 。

Application of uncertain type of AHP to condition assessment of cable-stayed bridges

In order to guarantee the safety service and life-span of long-span cable-stayed bridges, the uncertain type of analytic hierarchy process （AHP） method is adopted to access the bridge condition. The correlative theory and applied objects of uncertain type of AHP are introduced, and then the optimal transitive matrix method is chosen to calculate the interval number judgment matrix, which makes the weights of indices more reliable and accurate. Finally, with Harbin Songhua River Cable-Stayed Bridge as an example, an index system and an assessment model are proposed for the condition assessment of this bridge, and by using uncertain type of AHP, the weights of assessment indices are fixed and the final assessment results of the bridge are calculated, which proves the feasibility and practicability of this method. The application of this assessment method can provide the scientific basis for maintenance and management of long-span cable-stayed bridges.

A New Method of Ranking Fuzzy Number Based on α-Cut

This paper presents a new method of comparing or ranking of interval and fuzzy numbers. Based on another way of understanding fuzzy concept, the paper proposes the concept of number meaning of interval and the comparison method of interval. The paper defines the new ranking method by the α cut intervals of fuzzy number, and proves that the new inequality relation of fuzzy numbers is transitive. Our approach is a simple way of considering all the existence levels and can be calculated at different exact level according to different applications.

Statistical Analysis for the Birnbaum-Saunders Fatigue Life Distribution under Type-Ⅱ Bilateral Censoring and Multiply Type-II Censoring

In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this paper, we also get the interval estimations of the scale parameters.

Multi-attributed decision making for mining methods based on grey system and interval numbers

In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.

Mapping of quantitative trait loci using the skew-normal distribution

In standard interval mapping (IM) of quantitative trait loci (QTL), the QTL effect is described by a normal mixture model. When this assumption of normality is violated, the most commonly adopted strategy is to use the previous model after data transformation. However, an appropriate transformation may not exist or may be difficult to find. Also this approach can raise interpretation issues. An interesting alternative is to consider a skew-normal mixture model in standard IM, and the resulting method is here denoted as skew-normal IM. This flexible model that includes the usual symmetric normal distribution as a special case is important, allowing continuous variation from normality to non-normality. In this paper we briefly introduce the main peculiarities of the skew-normal distribution. The maximum likelihood estimates of parameters of the skew-normal distribution are obtained by the expectation-maximization (EM) algorithm. The proposed model is illustrated with real data from an intercross experiment that shows a significant departure from the normality assumption. The performance of the skew-normal IM is assessed via stochastic simulation. The results indicate that the skew-normal IM has higher power for QTL detection and better precision of QTL location as compared to standard IM and nonparametric IM.

CYP1A1 Ile462Val polymorphism contributes to colorectal cancer risk:A meta-analysis

AIM:To study the relation between CYP1A1 Ile462Val polymorphism and colorectal cancer risk by meta-analysis. METHODS:A meta-analysis was performed to investigate the relation between CYP1A1 Ile462Val polymorphism and colorectal cancer risk by reviewing the related studies until September 2010.Data were extracted and analyzed.Crude odds ratio(OR) with 95% confidence interval(CI) was used to assess the strength of relation between CYP1A1 Ile462Val polymorphism and colorectal cancer risk. RESULTS:Thirteen published case-control studies including 5336 cases and 6226 controls were acquired. The pooled OR with 95%CI indicated that CYP1A1 Ile462Val polymorphism was significantly related with colorectal cancer risk(Val/Val vs Ile/Ile:OR=1.47,95%CI:1.16-1.86,P=0.002;dominant model:OR= 1.33,95%CI:1.01-1.75,P=0.04;recessive model:OR=1.49,95%CI:1.18-1.88,P=0.0009) .Subgroup ethnicity analysis showed that CYP1A1 Ile462Val polymorphism was also significantly related with colorectal cancer risk in Europeans(Ile/Val vs Ile/Ile:OR=1.22,95%CI:1.05-1.42,P=0.008;dominant model:OR= 1.24,95%CI:1.07-1.43,P=0.004) and Asians(Val/ Val vs Ile/Ile:OR=1.40,95%CI:1.07-1.82,P=0.01;recessive model:OR=1.46,95%CI:1.12-1.89,P= 0.005) . CONCLUSION:CYP1A1 Ile462Val may be an increased risk factor for colorectal cancer.

Rules for confidence intervals of permeability coefficients for water flow in over-broken rock mass

Based on the steady-state seepage method, we used the Mechanical Testing and Simulation 815.02 System and a self-designed seepage instrument for over-broken stone to measure seepage properties of water flows in three types of crushed rock samples. Three methods of confidence interval in describing permeability coefficients are presented: the secure interval, the calculated interval and the systemic interval. The lower bound of the secure interval can be applied to water-inrush and the upper bound can solve the problem of connectivity. For the calculated interval, as the axial pressure increases, the length of confidence interval is shortened and the upper and lower bounds are reduced. For the systemic interval, the length of its confidence interval, as well as the upper and lower bounds, clearly vary under low axial pressure but are fairly similar under high axial pressure. These three methods provide useful information and references for analyzing the permeability coefficient of over-broken rock.

Study on productivity of horizontal wells with segmental perforation based on pseudo steady-state flow

Segmental perforation is widely used for horizontal wells. However,the flow of fluid in porous media is a complex problem. Using the Fourier transform,principle of potential superposition,trigonometric function transform,asymptotic analyses,a pressure solution of a pseudo steady-state flow model in 3D circular-boxed media has been established. Comparing with the productivity of vertical wells,an equivalence radius model can be obtained. Based on the model,a method of evaluating the productivity of segmental perforation horizontal well is presented by means of principle of superposition. It shows that the equivalence radius is different for various positions of horizontal wells; the output of both ends of horizontal wells is greater than the others under the same length of perforation interval; it is more important to obtain high productivity by increasing the length of perforation interval than enlarging the spacing between perforation intervals. The result of this research can be used to ascertain the yield of each perforated interval.

Application of Two-Order Difference to Gap Statistic

Gap statistic is a well-known index of clustering validity, but its realization is difficult to be comprehended and accurately determined. A direct method is presented to improve the performance of the Gap statistic, which applies the two-order difference of within-cluster dispersion to replace the constructed null reference distribution in the Gap statistic. Hence, the realization of the Gap statistic becomes easy and is reformulated, and its uncertainty in applications is reduced. Also, the limitation of the Gap statistic is analyzed by two typical examples, that is, the Gap statistic is difficult to be applied to the dataset that contains strong-overlap or uneven-density clusters. Experiments verify the usefulness of the proposed method.

Changes to the Natural Regional Boundaries in China During 1961-2007

Daily temperature data from 599 stations across China for the years 1961 to 2007 were used to analyze the changes in the natural regional boundaries. The results show that the accumulated temperature ≥10℃ and its duration changed dramatically from the end of 1990s to the early 21 st century. The amplitude of natural regional boundaries was greater in the 21st century than it was in the 20th century. In the eastern region of China, the climatic zones were migrating generally northward, with the northern edge of the subtropical zone and the eastern section of the warm temperate zone showing an obvious northward shift of up to 1-3° of latitude. The climatic zones moved south in the Qinghal-Tibet Plateau, western Inner Mongolia, and some areas of western Xinjiang, and slightly to the north in other parts of the western region.

Shear-wave Splitting in the Crust beneath Shandong and Its Adjacent Area

Based on the seismic data of near-field source from the Shandong Digital Seismic Network,this study obtained the shear-wave splitting parameters from multiple stations. The results show that dominant directions of polarizations of fast shear-waves reflect the spatial distribution characteristics of tectonic stress in this area,CHD and LIS stations show 2 dominant directions,and reveals that the crustal seismic anisotropy in the Shandong area is constrained by the regional stress background,local failure and structure.

Tidal Response Characteristics of the Well Water Level in the Sichuan-Yunnan Region

In this paper,the long time series data of the well water-level data of 12 wells in the Sichuan and Yunnan area is analyzed by the Baytap-G tidal analysis software,and well water level tidal response characteristic parameters( amplitude ratio and phase change)are extracted. We analyzed the features of the shape and stage change,and characteristic parameters of the tidal response of well water level before and after the earthquakes,which can provide a new method and approach to analyzing the response relationships between well water level and earth tide and barometric pressure. The results show that Luguhu Well and 9 other wells are affected by earth tides,and their well water level amplitude ratios and phases are relatively stable; the Nanxi Well and Dayao Well water level changes are affected by the barometric pressure combined with tide force,and their well water level amplitude ratios and phases are more discrete. The water level amplitude ratios and phases of Jiangyou Well,Luguhu Well and Dongchuan Well are significant to large earthquakes,and the relationship between seismic energy density and water level amplitude ratios and phases of M_2 wave of the three wells are presented.

NOVEL GREY DECISION MAKING MODEL AND ITS NUMERICAL SIMULATION

A grey multi-stage decision making method is proposed for a type of grey multi-index decision problems with weighted values completely unknown and attributes as interval grey numbers. Firstly, a method for compar- ing two grey numbers based on probability is developed to calculate weighted values of the attributes. Secondly, the experts＇ evaluation scores for attribute values are presented in terms of internal grey numbers. Finally, a weight solving method for multiple-stages evaluation is proposed. An example analysis verifies the availability of the proposed method. The method provides a new way of thinking for solving grey decision problem.

NOVEL GENERALIZED GREY INCIDENCE MODEL BASED ON INTERVAL GREY NUMBERS

To extend the traditional generalized grey incidence model, a novel grey incidence model based on inter- val grey numbers is constructed. Considering the numerical information of indexes cannot be accurately obtained and can be defined as interval grey numbers, the interval grey numbers are defined as standard interval grey num- bers which are split in white part and grey part. The absolute degree of incidence and relative degree of incidence based on the interval grey numbers are constructed and their arithmetic are given. Finally, an example about commercial aircraft index selection illuminates the effectiveness of the model. The results show that the model can sort indexes better and can extend the grey incidence models significantly.

Approach to obtaining weights of uncertain ordered weighted geometric averaging operator

The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the comparison between interval numbers is introduced. It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented. Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known. A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.

ENTROPY MEASUREMENT OF INTERVAL GREY SEQUENCE AND ITS APPLICATION

The uncertainty measurement method for grey information theory and the metric formula are established, and its application in decision-making is researched. The entropy measurement of grey sequence based on the limited interval grey number sequence is different from the Shannon probability entropy. The measurement formula of grey number and its properties are studied, such as the invariance, the applicable conditions, and the grey entropy of union and intersection of two grey numbers, and so on. Finally, the algorithm for interval grey sequence and an example are given to show the effectiveness of the method.

Prevalence of and risk factors for postprandial hypotension in older Chinese men

Objective To assess the prevalence of and risk factors for postprandial hypotension （PPH） among old and very old Chinese men. Methods The study included 349 Chinese men aged 65 and older, grouped into two age categories： group 1 （old） included 163 men aged 65 to 80 years; group 2 （very old） included 186 men aged over 80 years. Blood pressure changes after meals were assessed every 15 min by ambulatory blood pressure monitoring. Symptoms after meal ingestion and after standing up and changes in the baseline condition relative to blood pressure changes were observed continuously. Additional baseline data included body mass index, medical history, and medication use Results The prevalence of PPH was 59.3% overall and was significantly higher in group 2 than group 1 （63.4% vs. 54.6%, P 〈 0.05）. In group 2, the prevalence of PPH after breakfast （33.8%） and lunch （32.1%） were higher than that after supper （20.9%）, P 〈 0.05. Hypertension and age were significant risk factors for PPH （OR = 2.188, 95% CI： 1.134-4.223, P = 0.02; OR = 1.86, 95% CI： 1.112-3.11, P = 0.018, respectively）. In contrast, acarbose use was protective against PPH （OR = 0.4, 95% CI： 0.189-0.847, P = 0.017）. The decrease in blood pres- sure during PPH was 20-40 mmHg and the maximum was 90 mmHg. PPH usually occurred at 30-60 min after a meal and lasted 30-120 rnin. Conclusions These findings demonstrate that the prevalence of PPH in men aged over 80 years is significantly higher than those in men aged 65 to 80 years, and the blood pressure decline is also higher for men aged over 80 years. In addition, hypertension and age were main risk factors for PPH in the older men, which suggest that preventing and treating PPH is worthwhile.

Study on the Grey Polynomial Geometric Programming

In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory, and using some analysis strategies, a model of grey polynomial geometric programming, a model of θ positioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem. This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.

Combining TOPSIS and GRA for supplier selection problem with interval numbers

Supplier selection can be regarded as a typical multiple attribute decision-making problem. In real-world situation, the values of the alternative attributes and their weights are always being nondeterministic, and as a result of this, the values are considered interval numbers. In addition, the common approach to measure the similarity between alternatives through their distance suffers from some minor shortcomings. To address these problems, this study develops a novel hybrid decision-making method by combining the technique for order preference by similarity to an ideal solution （TOPSIS） with grey relational analysis （GRA） for supplier selection with interval numbers. By introducing the intervals theory, the extensions of Euclidean distance and grey relational grade are defined. And then a new comprehensive closeness coefficient is constituted for supplier alternatives evaluation based on the interval Euclidean distance and the interval grey relational grade, which could indicate the distance-based similarity and the shape-based similarity simultaneously. A mtmerical example is taken to validate the flexibility of the proposed method, and result shows that this method can tackle the uncertainty in real-world supplier selection and also help decision makers to effectively select optimal suppliers.