A NEW TECHNIQUE FOR COMPAIRING FUZZY NUMBERS USING AN INDEX OF OPTIMISM

Fuzzy numbers are convenient for representing imprecise numerical quantities in a vague environment, and their comparison or ranking is very important for application purposes. Despite many methods suggested in the literature, there is no single measure that is universally applicable to a wide variety of situations. This paper suggested a new method for comparing fuzzy numbers based on the combination of maximizing possibility and minimizing possibility using an index of optimism in [0,1] reflecting the decision makers’ risk taking attitude. The method is simple, but has many comparative advantages.

Influential Observations in Stochastic Model of Divisia Index Numbers with AR(1) Errors

We use the general form of hat matrix and DFBETA measures to detect the influential observations in order to estimate the Divisia price index number when the error structure is first order serial correlation. An example is presented with reference to price data of Pakistan. Hat values show the noteworthy findings that the corresponding weights of consumer items have large influence on the parameter estimates and are not affected by the parameter of autoregressive process AR(1). Whereas DFBETAs for Divisia index numbers depend on both the weights and autoregressive parameter.

Extracting the Influential Commodities in Stochastic Model of Simple Laspeyre Price Index Numbers with AR(2) Errors

This paper, on the first hand, deals with the problem of estimation of Laspeyre price index number when the errors are assumed to be generated from AR(2) process. The general expression of hat matrix and DFBETA measure to find the influential consumer commodities in stochastic Laspeyre price model with AR(2) errors are developed on the other. The hat values show the noteworthy findings that the corresponding weights of consumer items have large influence on the parameter estimates for simple Laspeyre price index number and are not affected by the parameter of autoregressive process of order two. While, DFBETA measures are the functions of both weights and autocorrelation parameters. Lastly, an example is presented with reference to price data of Pakistan, and shows its practical importance in financial time series.

An Adaptive Parameter-Free Optimal Number of Market Segments Estimation Algorithm Based on a New Internal Validity Index

An appropriate optimal number of market segments(ONS)estimation is essential for an enterprise to achieve successful market segmentation,but at present,there is a serious lack of attention to this issue in market segmentation.In our study,an independent adaptive ONS estimation method BWCON-NSDK-means++is proposed by integrating a newinternal validity index(IVI)Between-Within-Connectivity(BWCON)and a newstable clustering algorithmNatural-SDK-means++(NSDK-means++)in a novel way.First,to complete the evaluation dimensions of the existing IVIs,we designed a connectivity formula based on the neighbor relationship and proposed the BWCON by integrating the connectivity with other two commonly considered measures of compactness and separation.Then,considering the stability,number of parameters and clustering performance,we proposed the NSDK-means++to participate in the integrationwhere the natural neighbor was used to optimize the initial cluster centers(ICCs)determination strategy in the SDK-means++.At last,to ensure the objectivity of the estimatedONS,we designed a BWCON-based ONS estimation framework that does not require the user to set any parameters in advance and integrated the NSDK-means++into this framework forming a practical ONS estimation tool BWCON-NSDK-means++.The final experimental results showthat the proposed BWCONand NSDK-means++are significantlymore suitable than their respective existing models to participate in the integration for determining theONS,and the proposed BWCON-NSDK-means++is demonstrably superior to the BWCON-KMA,BWCONMBK,BWCON-KM++,BWCON-RKM++,BWCON-SDKM++,BWCON-Single linkage,BWCON-Complete linkage,BWCON-Average linkage and BWCON-Ward linkage in terms of the ONS estimation.Moreover,as an independentmarket segmentation tool,the BWCON-NSDK-means++also outperforms the existing models with respect to the inter-market differentiation and sub-market size.

THE ASYMPTOTIC SOLUTION OF THE UNSTEADY PLANAR PARALLEL GAS FLOW FOR THE CASE TEAT THE ADIABATIC INDEX NUMBER γ IS BIG

In ref I,under the condition that the components of velocity are only the functions of time and polar angleθ,Drornikov solved eqss.(1.1)(1.3)of the ideal gas unsteady planar parallel potential flow.It was pointed out in ref.[1]that in general cases,the evident solutions could not he obtained.Only for two especial cases,the evident solutions were obtained.In this paper,the author studies the same prohlein as that in ref.[1].In the first section we obtain the evident solution of equations(1.1)-(1.3)under the condition that the sonic velocity is restricted by some complemental conditions.In the second section,we obtain the first-order approximate solutions of the fundamental equation for the case thatγ>>1.

Relationship between Regional Rainstorm Index and Flood Disaster Ratio of Crop

According to the daily precipitation data in Beijing area from 1985 to 2008,rainstorm weather index （10.4-38.8 mm） and climate index （daily precipitation ≥27.5 mm） in Beijing area were obtained by using the determination method of extreme climate event index recommended by IPCC. Based on rainstorm weather index,rainstorm climate index and national rainstorm standard,the number of rainstorm days and rainfall amount in past years were calculated,and the correlation of annual number of rainy days,rainstorm days,precipitation and rainstorm amount with the flood disaster ratio of crop was analyzed,and the results showed that annual number of rainy days and rainstorm days couldn＇t reflect flood disaster ratio of crop truly,while annual precipitation and rainstorm amount had obvious linear positive correlation with the flood disaster ratio of crop. In addition,the correlation degree between rainstorm amount calculated by regional climate index and flood disaster ratio of crop was the highest,so it was suggested that rainstorm amount calculated by regional rainstorm climate index could be used to predict and evaluate flood disaster.

K-th Number Query问题的改进算法研究

K-th number query是计算机算法中的一个基础问题,被广泛作为很多算法实现的重要步骤。对该问题进行了深入研究,并找到了单询问渐近时间复杂度最优的算法。目前一般对于多询问的K-th number query问题使用平衡二叉树解决,询问的时间复杂度为O(lbn)。但该算法实现比较复杂,并且常系数较大,提出了基于Bit Indexed Tree数据结构的算法解决,在同等时间复杂度的前提下,实现简单,隐含的常系数很小。最后进行了实验测试,分析显示该新算法不论在时间上还是空间上都优于现有的算法。

The effects of temperature and acid number of crude oil on the wettability of acid volcanic reservoir rock from the Hailar Oilfi eld

Wettability of acid volcanic reservoir rock from the Hailar Oilfield, China, was studied with crude oils of different acid numbers generated from an original crude oil with an acid number of 3.05 mg KOH/g. The modifed oils and their resultant acid numbers were： A （2.09 mg KOH/g）, B （0.75 mg KOH/g）, C （0.47 mg KOH/g）, D （0.30 mg KOH/g）, and E （0.18 mg KOH/g）. Contact angles and improved Amott water indexes were measured to study the effects of temperature and acid number on the wettability of the acid volcanic reservoir rock. Experimental results indicated that the wettability was not sensitive to variation in temperature when using the same oil, but the acid number of the crude oil was a key factor in changing the wettability of the rock. The Amott water index, Iw was an exponential function of the acid number, and the Amott water index increased as the acid number decreased （i.e. Amott water index exponentially decreased with the acid number increase）. The Iw value of the core saturated with oil A, with an acid number of 2.09 mg KOH/g, ranged from 0.06 to 0.11, which indicated low water wetness. If the acid number of the oil decreased to 0.18 mg KOH/g, the Iw value increased to 0.95, which indicated strong water wetness. The contact angle decreased from 80~ to 35~ when the aid number decreased from 0.75 to 0.18 mg KOH/g, indicating a change towards more water wet conditions. The oil recovery by spontaneous imbibition of water also increased as the acid number of the oil decreased. As an example, at 80 ~C, the recovery of Oil A with an acid number of 2.09 mg KOH/g was only 7.6%, while Oil E with an acid number of 0.18 mg KOH/g produced 56.4%, i.e. an increase of 48.8%.

On relationship between curve numbers and phi indices

The curve number and phi(4)-index models each provide a simple one-parameter relationship between storm-event rainfall and runoff. It is shown that the curve number and 4-index models can both be used to segregate the rainfall hyetograph into initial abstraction, retention, and runoff amounts. However, the principal advantages of the 4-index model are that both rainfall distribution and duration can be explicitly taken into account in calculating runoff, and the 4 index is more physically based than the curve number. The quantitative relationship between the curve number and the 4 index is presented and validated with field measurements. Knowing the relationship between the curve number and the 4 index is useful in that it facilitates using the extensive database of curve numbers in the more realistic 4-index model in calculating a runoff hydrograph from a given rainfall hyetograph. It is demonstrated that conventional adjustments to curve numbers can be largely explained by variations in storm duration, which suggests that variable rainfall duration can possibly be an essential factor in accounting for deviations from the median curve number of a catchment.

PRECISE ASYMPTOTICS IN SELF-NORMALIZED SUMS OF ITERATED LOGARITHM FOR MULTIDIMENSIONALLY INDEXED RANDOM VARIABLES

In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑n1/｜n｜（log｜n｜dP（｜Sn/Vn｜≥ε√log log｜n｜） and ∑n（logn｜）b/｜n｜（log｜n｜）^d-1P（｜Sn/Vn｜≥ε√log n）,as ε↓0,is established.