CN101567050A - Grey clustering analysis method - Google Patents

Abstract

The invention relates to a grey clustering analysis method, comprising the steps of: (1) providing a clustering albetion function: selecting n clustering objects to obtain m clustering indexes and construct an n*m table; (2) inputting the clustering albetion function into a computer and getting into the algorithm of grey clustering analysis and evaluation, comprising: performing equalization nondimensionalization treatment to the clustering albetion; determining the grey type of each clustering index value of each clustering object; calculating the albetion weight function value of each grey type by an estimation method or interpolation method; demarcating a clustering weight grey matrix; and constructing a clustering matrix; and (3) performing grey evaluation according to the result of step (2). The method overcomes the defect of great influence caused by individual factor in single factor evaluation, reflects the influence of the evaluation factors in an all-round way, and has objective evaluation result, convenient and rapid calculation, accurate result, wide applicability, precise evaluation and high sensitivity.

Description

A kind of grey clustering analysis method

Technical field

The invention belongs to the system science technical field, particularly relate to a kind of grey clustering analysis method.

Background technology

The grey clustering analysis theory is founded by the famous scholar Deng Julong of China professor one the independently new subject of system science.Its research object is " small sample ", " poor information " uncertain system of " partial information is known, partial information the unknown ".It is by going to grasp the total system ruuning situation and the evolution rule in future to the assurance of " part " Given information.Can on the basis of limited information amount, do accurately and objective appraisal because of it, therefore be applicable to multiple subject the combination property of system.But because calculated amount is big, relate to many complex mathematical problems, personnel are had very high mathematical knowledge requirement, therefore limited the application of grey clustering analysis theory in actual production greatly.

Summary of the invention

Technical matters to be solved by this invention provides a kind of algorithm based on grey clustering analysis, the computing machine that uses adopts MATLAB software programming universal program, in use only need the grey clustering analysis method of operation result just can directly be appearred in the data input.

The technical solution adopted for the present invention to solve the technical problems is: a kind of grey clustering analysis method is provided, it is characterized in that: comprise the following steps:

(1) provides cluster albefaction number: choose n cluster object, obtain m cluster index, construct a n * m table;

(2) with cluster albefaction number input computing machine, enter the algorithm that grey clustering analysis is estimated, comprise that cluster albefaction number is carried out the equalization nondimensionalization to be handled; Determine the grey class that each cluster desired value of each cluster object is affiliated; Adopt technique of estimation or method of interpolation to obtain the albefaction weight function value of each grey class; Demarcate cluster and weigh grey matrix number; Structure cluster matrix;

(3) result according to step (2) carries out grey evaluation.

Described cluster object is that bamboo fibre, cotton fiber, viscose rayon, terylene, Model, Tencel, male silk are as the cluster object; Described cluster index is that fracture strength and elastic recovery rate represent that the index of fibre machinery performance and regain and mass specific resistance represent that the index of fiber comfort property is as the cluster index.

Described cluster object is the Coolmax yarn for choosing warp thread, and weft yarn is that fabric, the warp thread of Coolmax yarn is the Coolmax yarn, weft yarn be bamboo former/fabric of cotton 55/45 yarn and the cotton textiles of same specification, pure bamboo is former and wash/bafta is the cluster object; Described cluster index is Air permenbility, vapor transfer rate, measure wicking height, leads wet overall target as the cluster index.

Described cluster object for choose length of bow Ling Kuang, Long Yankuang, Orebody in Jingtieshan ore deposit, Mei Shankuang, Cheng Chaokuang, Da Yekuang, Kingsoft Dian Kuang are the cluster object; Described cluster index is that functional department's management index, dust control by ventilation equipment control index, operating environment management index, worker health management index are the cluster index.

Principle of the present invention is:

(1) provides cluster albefaction number

The described cluster albefaction number that provides is for choosing several n cluster objects, a n of m cluster index structure * m table.

(2) write universal program according to the algorithm of grey clustering analysis evaluation

The algorithm of described grey clustering analysis evaluation is:

1. carry out the equalization nondimensionalization according to formula (1) and handle the cluster albefaction is several.

$X_{\mathrm{ij}}=\frac{d_{\mathrm{ij}}}{\frac{1}{n}\underset{1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}}---\left(1\right)$

2. ask albefaction weight function value matrix

Ask albefaction weight function value to be divided into for three steps:

I obtains the good k of each cluster index performance according to formula (2) ₁Ash class, middle k ₂Ash class, difference k ₃The interval of ash class; Definition j index is to k ash class (k=k ₁, k ₂, k ₃) interval method is as follows:

$Q_{{k1}_1}^j=[\stackrel{\‾}{X_{\mathrm{ij}}}+\frac{1}{6}{d}_j,\max \left(X_{\mathrm{ij}}\right)],Q_{K2}^j=[\stackrel{\‾}{X_{\mathrm{ij}}}-\frac{1}{6}{d}_j,\stackrel{\‾}{X_{\mathrm{ij}}}+\frac{1}{6}{d}_j],$

$Q_{K3}^j=[\min \left(X_{\mathrm{ij}}\right),\stackrel{\‾}{X_{\mathrm{ij}}}-\frac{1}{6}{d}_j]---\left(2\right)$

Wherein, produce 1,2 ..., m; d _jBe x _IjExtreme difference (i=1,2 ... n); Max (x _Ij) be x _IjMaximal value (i=1,2 ... .n); Min (X _Ij) be x _IjMinimum value (i=1,2 ... .n).

Ii determines the grey class under each cluster desired value of each cluster object

Iii adopts technique of estimation or method of interpolation to obtain the albefaction weight function value of each grey class

With albefaction weight function value f (x in the quantitative technique of estimation decision formula _Ij) x _Ij, promptly as cluster ash number k ₁, k ₂, k ₃F during with the measured value ad eundem ^*Get 1, k ₁And k ₃F when differing a grade with measured value ^*Get 0.5, k ₂F when differing a grade and during measured value with measured value ^*Get 0.25, k ₁And k ₃F when differing two grades and during measured value with measured value ^*Get 0.

Method of interpolation asks albefaction weight function value-based algorithm as follows:

X wherein _j, Y _j, Z _jBe respectively k ₁, k ₂, k ₃Interval mid point

3. ask the demarcation cluster to weigh grey matrix number

Ask the demarcation cluster to weigh grey matrix number and at first define λ _j ^kBe j index k subclass boundary value, calculate by formula (3):

${\mathrm{\η}}_j^k=\frac{{\mathrm{\λ}}_j^k}{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\λ}}_j^k}---\left(3\right)$

4. construct the cluster matrix

Calculate the grey cluster coefficient that the i object belongs to k ash class by formula (4):

${\mathrm{\σ}}_i^k=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{f}_{\mathrm{ij}}^k\left(x_{\mathrm{ij}}\right)*{\mathrm{\η}}_j^k---\left(4\right)$

According to the grey cluster factor sigma that calculates _i ^k, list cluster coefficients matrix (σ _i ^k) _m

(3) carry out grey evaluation according to the result

σ _i ^kWhat value was maximum is the affiliated grey class of evaluation object.

Beneficial effect

The present invention overcomes and is subjected to individual factor to influence big defective in the single factor evaluation, has reflected the influence of each factor of evaluation more all sidedly, and evaluation result is objective; Convenience of calculation is quick, and the result is accurate, and is widely applicable; Estimate accurately, the susceptibility height does not have special requirement to the experimenter.

Embodiment

Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiment only to be used to the present invention is described and be not used in and limit the scope of the invention.Should be understood that in addition those skilled in the art can make various changes or modifications the present invention after the content of having read the present invention's instruction, these equivalent form of values fall within the application's appended claims institute restricted portion equally.

Embodiment 1

The present invention is applicable to the material field, comes the performance of various materials is carried out comprehensive evaluation with the present invention.

(1) chooses bamboo fibre, cotton fiber, viscose rayon, terylene, Model, Tencel, male silk as the cluster object, choose index that fracture strength and elastic recovery rate represent that the index of fibre machinery performance and regain and mass specific resistance represent the fiber comfort property as the cluster index, cluster albefaction number sees Table 1.

The performance number of the various fibers of table 1

(2) bring cluster albefaction number into write universal program

(3) carry out grey evaluation according to the result

1. technique of estimation result

ans＝

0.5081 0.6250 0.5107

0.2550 0.6250 0.7566

0.6295 0.4375 0.3810

0.4900 0.2500 0.4869

0.6335 0.8125 0.3863

0.6394 0.4375 0.3940

0.5040 0.6250 0.5053

The sample that performance is good has: viscose rayon, polyster fibre, Tencel fiber

Sample in the performance has: bamboo fibre, Model fiber, male silk

The sample of poor performance has: cotton fiber

2. method of interpolation result

ans＝

0.3590 0.2834 0.3777

0.1029 0.3424 0.5599

0.5098 0.1337 0.3717

0.4902 0 0.4871

0.2240 0.6664 0.1279

0.5323 0.2515 0.2460

0.1394 0.5801 0.2908

The sample of good combination property has: viscose rayon, polyster fibre, Tencel fiber

Sample in the combination property has: Model fiber, male silk

The sample of combination property difference has: bamboo fibre, cotton fiber

Embodiment 2

The present invention is applicable to field of textiles, comes doing comprehensive evaluation by a kind of wet-guide quick-drying performance of new polyester yarn design textile with the present invention, and the wet-guide quick-drying performance comprises Air permenbility, vapor transfer rate, measure wicking height, leads wet overall target.

(1) choosing warp thread is the Coolmax yarn, and weft yarn is that fabric, the warp thread of Coolmax yarn is the Coolmax yarn, weft yarn be bamboo former/fabric of cotton 55/45 yarn and the cotton textiles of same specification, pure bamboo is former and wash/bafta is the cluster object; Choose Air permenbility, vapor transfer rate, measure wicking height, lead wet overall target as the cluster index.

With pure Coolmax fabric, Coolmax and the bamboo of being knitted former/it is 1, No. 2 that fabric that cotton interweaves is compiled respectively, three kinds are numbered 3,4,5 respectively in addition, cluster albefaction number sees Table 2.

Table 2 fabric performance test table

(2) bring cluster albefaction number into write universal program

(3) carry out grey evaluation according to the result

1. technique of estimation result

ans＝

0.6498 0.4375 0.4074

0.7657 0.6250 0.2706

0.4686 0.2500 0.4588

0.1160 0.4375 0.8631

0.4686 0.2500 0.4588

2. method of interpolation result

ans＝

0.5314 0.2260 0.2994

0.5263 0.3231 0.1975

0.3424 0.1358 0.4588

0 0.1953 0.7862

0.4686 0.0009 0.4580

Technique of estimation and method of interpolation result all illustrate fabric that pure Coolmax yarn is developed and Coolmax yarn and bamboo former/the wet comfort property of the fabric that cotton interweaves is best.

Embodiment 3

The present invention is applicable to management domain, comes comprehensive evaluation is done in the dust control by ventilation work of bargh with the present invention.

(1) choose length of bow Ling Kuang, Long Yankuang, Orebody in Jingtieshan ore deposit, Mei Shankuang, Cheng Chaokuang, Da Yekuang, Kingsoft Dian Kuang are the cluster object, functional department's management index, dust control by ventilation equipment control index, operating environment management index, worker health management index are the cluster index, and cluster albefaction number sees Table 3.

The management index in each ore deposit of table 3

(2) bring cluster albefaction number into write universal program

(3) carry out grey evaluation according to the result

1. technique of estimation result

ans＝

0.8785 0.4375 0.1294

0.8785 0.4375 0.1294

0.2312 0.2500 0.7267

0.6250 0.7371 0.2339

0.2409 0.6250 0.7387

0.8844 0.4375 0.1367

0.5299 0.2500 0.5371

The ore deposit that dust control by ventilation work is good is: length of bow Ling Kuang, Long Yankuang, Da Yekuang

The medium ore deposit of dust control by ventilation work is: Mei Shankuang

The ore deposit of dust control by ventilation work difference is: Orebody in Jingtieshan ore deposit, Cheng Chaokuang, Kingsoft Dian Kuang

2. technique of estimation result

ans＝

0.7571 0.2063 0.0905

0.6779 0.3965 0.0553

0.2312 0 0.7267

0.4239 0.4566 0.3486

0.0597 0.6591 0.7020

0.7464 0.2390 0.1657

0.4154 0.2464 0.5371

The ore deposit that dust control by ventilation work is good is: length of bow Ling Kuang, Long Yankuang, Da Yekuang

The medium ore deposit of dust control by ventilation work is: Mei Shankuang

The ore deposit of dust control by ventilation work difference is: Orebody in Jingtieshan ore deposit, Cheng Chaokuang, Kingsoft Dian Kuang

Embodiment 4

The present invention is applicable to environmental science, with the present invention monitoring point well water water quality is done comprehensive evaluation.

(1) chooses a Mitsui, Ai You two wells, five wells, clear many companies, clear vertical, foundation well as cluster object, total hardness SO ₄ ^2-, Cl ^-, total dissolved solid, permanganate index, nitrate nitrogen, salinity concentration be as the cluster index.

Cluster albefaction number sees Table 4.

Table 4 monitoring point well water water quality monitoring result unit: mg/L

(2) bring cluster albefaction number into write universal program

(3) carry out grey evaluation according to the result

The result of technique of estimation is:

ans＝

0.6929 0.4643 0.2499

0.3173 0.2500 0.7670

0.7617 0.3571 0.1741

0.2099 0.3571 0.7785

0.3585 0.7857 0.6451

0.4291 0.8929 0.5723

Water quality is that the well of one-level is: door Mitsui, Ai You two wells

Water quality is that the well of secondary is: five wells, clear many companies

Water quality is that three grades well is: clear vertical, foundation well

The result of method of interpolation is:

ans＝

0.6147 0.1941 0.1319

0.3173 0.0194 0.7474

0.6613 0.1408 0.1371

0.1603 0.1333 0.6942

0.1054 0.5940 0.3180

0.1036 0.5390 0.3260

Water quality is that the well of one-level is: door Mitsui, Ai You two wells

Water quality is that the well of secondary is: five wells, clear many companies

Water quality is that three grades well is: clear vertical, foundation well

The foregoing description shows that the result of technique of estimation and method of interpolation has very big similarity.In actual applications in general, when cluster object cluster index number more for a long time, but method of interpolation is than result's property degree height of technique of estimation.The present invention can be applied to the comprehensive evaluation of the gray system performance of industry-by-industry every field in addition.

Claims (4)

1. a grey clustering analysis method is characterized in that: comprise the following steps:

(1) provides cluster albefaction number: choose n cluster object, obtain m cluster index, construct a n * m table;

(2) with cluster albefaction number input computing machine, carry out the algorithm that grey clustering analysis is estimated, comprise that cluster albefaction number is carried out the equalization nondimensionalization to be handled; Determine the grey class that each cluster desired value of each cluster object is affiliated; Adopt technique of estimation or method of interpolation to obtain the albefaction weight function value of each grey class; Demarcate cluster and weigh grey matrix number; Structure cluster matrix;

(3) result according to step (2) carries out grey evaluation.

2. a kind of grey clustering analysis method according to claim 1 is characterized in that: described cluster object is that bamboo fibre, cotton fiber, viscose rayon, terylene, Model, Tencel, male silk are as the cluster object; Described cluster index is that fracture strength and elastic recovery rate represent that the index of fibre machinery performance and regain and mass specific resistance represent that the index of fiber comfort property is as the cluster index.

3. a kind of grey clustering analysis method according to claim 1, it is characterized in that: described cluster object is the Coolmax yarn for choosing warp thread, weft yarn is that fabric, the warp thread of Coolmax yarn is the Coolmax yarn, weft yarn be bamboo former/fabric of cotton 55/45 yarn and the cotton textiles of same specification, pure bamboo is former and wash/bafta is the cluster object; Described cluster index is Air permenbility, vapor transfer rate, measure wicking height, leads wet overall target as the cluster index.

4. a kind of grey clustering analysis method according to claim 1 is characterized in that: described cluster object for choose length of bow Ling Kuang, Long Yankuang, Orebody in Jingtieshan ore deposit, Mei Shankuang, Cheng Chaokuang, Da Yekuang, Kingsoft Dian Kuang are the cluster object; Described cluster index is that functional department's management index, dust control by ventilation equipment control index, operating environment management index, worker health management index are the cluster index.