CN104680308A - Fuzzy matter element evaluation method for cavability of rock - Google Patents

Abstract

The invention discloses a fuzzy matter element evaluation method for the cavability of a rock. According to the method, fuzzy mathematics is organically combined with matter element analysis together, the cavability of the rock is divided into five grades of no cavability, poor cavability, better cavability, good cavability and excellent cavability as matter elements, an RQD (rock quality designation) value, uniaxial saturated compressive strength, a joint spacing, a primary undermining hydraulic radius and a water characteristic value are selected as evaluation indexes. Through membership grade calculation, correlation degree transformation and preferred membership grade treatment, a correlation coefficient fuzzy matter element for evaluating the cavability of the rock is established. An evaluation index weight is determined by adopting a summation normalization method, the membership grades, relative to different evaluation levels, of each index quantity of the rock are calculated by applying correlation degree calculation and a maximum correlation degree principle, further the membership grade evaluation is carried out on the cavability of the rock, and the problem that a single-factor index and the evaluation of the cavabiliyt of the rock are incompatible is solved. An important reference basis is provided for the evaluation of the cavability of the rock at a mine and the design of a mining method in a spontaneous caving method.

Description

The Fuzzy matter-element evaluation method of a kind of ore deposit collapsing property of rock

Technical field

The invention belongs to mining field of engineering technology, relate to a kind of New Evaluation Method being applicable to natural caving method ore deposit collapsing property of rock.

Background technology

Ore deposit collapsing property of rock is the important indicator whether measurement natural caving method is suitable for, and on the stopping sequence of mining design, the direction that undercuts, the area that undercuts, ore removal way, Oredrawing control, cuts and helps presplitting, safety in production and technical economical index etc. to have conclusive impact.Wherein, R.Kendrick finds to there is obvious linear relationship between rock quality designation (RQD) and collapsing property when carrying out collapsing property to Climax ore deposit and Urad ore deposit and evaluating, and thus proposes and can collapse sex index evaluation method.E.T.Brown and G.A.Ferguson proposes joint plane intensity revised RQD value stage method; D.H.Laubscher proposes geomechanics stage method; L.Obert and A.E.Long proposes seismic wave energy attenuation coefficient evaluation assessment.Above-mentioned collapsing property evaluation method respectively has feature, but all there is a common issue, and namely gradational boundary is stiff, can not reflect the progressive formation of ore deposit lithology matter.In addition, rock collapsing property in ore deposit manages the impact of the factors such as characteristic value by rock quality designation RQD value, saturated uniaxial compressive strength, joint spacing, for the first time undercut hydraulic radius, water.Due to the complicacy of natural ore deposit rock mass, relation between these factors is intricate, with different features, combined influence is produced to ore deposit collapsing property of rock, if evaluate ore deposit collapsing property of rock with single index, its evaluation result usually has paradox, uncertainty and incompatibility, and direct Utilization assessment standard is difficult to make definite evaluation.And due to evaluation criterion be the obvious quantitative criteria of boundary, this will omit some useful information, the conclusion that even can lead to errors.For this reason, the Modern Mathematical Methods such as mathematical statistics, fuzzy mathematics and gray theory have height system, the feature such as non-linear, in solution challenge, have speciality, have had the basis of application in collapsing property of the rock evaluation of ore deposit.As Zhang Zhi's literary composition proposes a kind of capability of orebody assessment of fuzzy math, solve in traditional evaluation method the problem that can not reflect ore deposit lithology matter progressive formation.Lei Xuewen and Xiao Jinfa proposes Artificial Neural Network Method for Quality, describes the nonlinear relationship between ore deposit collapsing property of rock and its influence factor.Estension set combines with cluster analysis by Deng Hongwei etc., successfully predicts ore deposit collapsing property of rock.This illustrates that modern mathematics has good applicability to ore deposit collapsing property of rock evaluation.

Matter Analysis is research matter-element and Changing Pattern thereof, and for solving the effective ways of the inconsistent problem in real world.If the value in matter-element is with ambiguity, just constitute fuzzy inconsistent problem.Fuzzy Matter Element Analysis organically combines fuzzy mathematics and Matter Analysis exactly, the ambiguity have the corresponding value of features and the incompatibility affected between things many factors is analyzed, comprehensively, thus a kind of new method of this kind of fuzzy inconsistent problem that achieves a solution.The present invention is directed to the ambiguity of ore deposit collapsing property of rock evaluation index, on the basis of Matter Analysis, utilize the principle of degree of membership in fuzzy evaluation, calculate the degree of membership of rock each index amount in ore deposit relative to different evaluation rank, set up the compound fuzzy matter element of ore deposit collapsing property of rock, propose ore deposit collapsing property of rock describing method, the collapsing property of ore deposit rock is converted to the matter-element of easier quantitative description to carry out quantitative test, the comprehensive evaluation for natural caving method ore deposit collapsing property of rock provides a new method.

Summary of the invention

This evaluation method organically combines fuzzy mathematics and Matter Analysis, ore deposit collapsing property of rock is divided into can not collapsing property, collapsing property difference, collapsing property better, good, fine 5 grades of collapsing property of collapsing property as matter-element, select ore deposit rock quality index RQD value, saturated uniaxial compressive strength, joint spacing, for the first time undercut hydraulic radius, water to manage characteristic value as evaluation index.Converted by degree of membership calculating, the degree of association and from excellent degree of membership process, set up the correlation coefficient fuzzy matter element that ore deposit collapsing property of rock is evaluated.Adopt summation normalization method determination evaluation criterion weight, use calculation of relationship degree and most relevance degree principle, calculate the degree of membership of rock each index amount in ore deposit relative to different evaluation rank, and then degree of membership evaluation is carried out to ore deposit collapsing property of rock.

Mainly comprise following four steps

Step one: determine matter-element

If ore deposit collapsing property of rock has n evaluation index C ₁, C ₂..., C _nwith corresponding fuzzy value v ₁, v ₂..., v _nbe called that the n of R ties up fuzzy matter element, referred to as R=(n, C, v), combine if the n of m ore deposit collapsing property of rock grade ties up fuzzy matter element, the n dimension just forming m ore deposit collapsing property of rock meets matter-element R _mn

Step 2: set up ore deposit collapsing property of rock fuzzy matter-element model

A () sets up compound fuzzy matter element

By R _mnvalue be rewritten as fuzzy matter element value, be then called that the n of m collapsing property grade ties up composite matter-element, be denoted as:

$R_{\mathrm{mn}}=\left[\begin{array}{cc}& M_i\\ C_k& v_{\mathrm{ik}}\end{array}\right]=\left[\begin{array}{cccc}& M_i& ...& M_m\\ C_1& v_{11}& ...& v_{m1}\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ C_n& v_{1n}& ...& v_{\mathrm{mn}}\end{array}\right]---\left(1\right)$

In formula: R _mnfor the fuzzy matter element of n evaluation index of m ore deposit collapsing property of rock grade; C _kbe K evaluation index, wherein K=1,2 ... n; M _ibe i-th collapsing property grade, wherein i=1,2 ..., m; v _ikbe fuzzy matter element value corresponding to i-th ore deposit collapsing property of rock grade K evaluation index.

B () sets up from excellent degree of membership fuzzy matter element

According to the classification of collapsing property, in collapsing property Fuzzy Matter Element Analysis, in interval, subordinate function adopts osculant, and namely interval end points is in most fringe, and degree of membership is about 0.5; Be clearly in its classification of interval midpoint, degree of membership is 1, builds the subordinate function of boundary.Normal distribution osculant formula has (2), (3) two kinds of method for expressing.

$\mathrm{\μ}\left(x\right)=e^{-{\left(\frac{x-a}{b}\right)}^2}---\left(2\right)$

Or be expressed as follows:

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{ccc}{e}^{-{\left(\frac{x-a_1}{b}\right)}^2}& ,& x<a_1\\ 1& ,& a_1\&le;x\&le;a_2\\ e^{-{\left(\frac{x-a_2}{b}\right)}^2}& ,& x>a_2\end{array}\right\}---\left(3\right)$

Zone line adopts formula (2) to build subordinate function; For borderline region, namely without collapsing property and the good Region dividing of collapsing property, subordinate function is as shown in (3).

In formula (2): a > 0, b > 0, then have x=a, maximal value is got in μ (a)=1, and namely a is the corresponding interval average of evaluation index value.

$a=\frac{x_1+x_2}{2}---\left(4\right)$

In formula: X ₁, X ₂for the upper and lower border of different classification respective segments corresponding index.

And at boundary, boundary value is the transition value being clipped to another kind of rank from a kind of level, is also a kind of smeared out boundary, should belong to two kinds of corresponding ranks, i.e. the equal ≈ 0.5 of the degree of membership of two kinds of ranks, therefore by boundary value X simultaneously ₁, X ₂and formula (4) substitution formula (2) has:

$\mathrm{\&mu;}\left(x_1\right)=\mathrm{\&mu;}\left(x_2\right)=e^{-{\left(\frac{x_1-x_2}{2b}\right)}^2}\&ap;0.5---\left(5\right)$

Abbreviation then can draw:

$b=\frac{x_1-x_2}{1.665}---\left(6\right)$

For the determination of " can not collapsing property " rank with the subordinate function of each index of " collapsing property is fine " borderline region, then need to determine according to formula (3).

Step 3: correlative transformation, be associated coefficient fuzzy matter element

Computing formula different is as follows adopted respectively for different degree of membership:

More large more excellent type:

${\mathrm{\&mu;}}_{\mathrm{ji}}=\frac{X_{\mathrm{ji}}-\min X_{\mathrm{ji}}}{\max X_{\mathrm{ji}}-\min X_{\mathrm{ji}}}---\left(7\right)$

j＝1，2，…，m；i＝1，2，…，n

More little more excellent type:

${\mathrm{\&mu;}}_{\mathrm{ji}}=\frac{{\max X}_{\mathrm{ji}}-X_{\mathrm{ji}}}{\max X_{\mathrm{ji}}-\min X_{\mathrm{ji}}}---\left(8\right)$

j＝1，2，…，m；i＝1，2，…，n

In formula: μ _jirepresent a jth things i-th feature from excellent degree of membership, X _jirepresent the value corresponding to a jth things i-th feature, maxX _ji, minX _jirepresent X respectively _jiin maximal value and minimum value.

M things has several factors of evaluation and corresponding fuzzy value, because correlation coefficient is the numerical value obtained by optimization principles and correlative transformation.Therefore just can be associated coefficient compound fuzzy matter element, is denoted as R _{ξ mn}

$R_{\mathrm{\&xi;mn}}=\left[\begin{array}{cccc}& M_1& ...& M_m\\ C_1& {\mathrm{\&xi;}}_{11}& ...& {\mathrm{\&xi;}}_{m1}\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ C_n& {\mathrm{\&xi;}}_{1n}& ...& {\mathrm{\&xi;}}_{\mathrm{mn}}\end{array}\right]---\left(9\right)$

Wherein: M _jrepresent a jth things; C _irepresent a jth things i-th factor of evaluation, the fuzzy value corresponding with it, with ξ _ij(j=1,2 ..., m; I=1,2 ... n) represent, i.e. the correlation coefficient of a jth things i-th factor of evaluation.

Step 4: the weight of Calculation Estimation index

During Matter Analysis, the determination of feature weight is the key of problem, adopts summation normalization method parameter weight.Namely first obtain each things every feature association coefficient sum, then normalized is done to the correlation coefficient of every feature, just draw the weight of each things various features.Its expression formula is as follows:

$R_w=\left[\begin{array}{ccccc}& C_1& C_2& ...& C_n\\ w_i& w_1& w_2& ...& w_n\end{array}\right]---\left(10\right)$

In formula: R _wrepresent weight composite matter-element, w _irepresent the weighted value of each things i-th feature, represent C _icorrelation coefficient sum, represent various features correlation coefficient sum.

Step 5: judge ownership

The degree of association refers to the tolerance of relevance size between two things, and namely represent the tolerance of ore deposit collapsing property of rock evaluation index value and evaluation criterion relevance size here, it uses K _jrepresent, i.e. the degree of association of a jth things and standard things.In degree of association compound fuzzy matter element, by the size of each degree of association, line up in order, then to the method that things or factor are analyzed, be called fuzzy matter element association analysis.Its object is to the prevailing relationship seeking things, find out the key factor affecting desired value, thus grasp the principal character of things, therefrom determine best things.Structure degree of association compound fuzzy matter element, adopts weighted mean to focus on, then:

R _k＝R _w*R _ξmn(11)

In formula: " * " represents sign of operation, different according to the pattern adopted, the method for computing is also just different, chooses M (× ,+) algorithm herein, namely first takes advantage of the computing added afterwards.

Try to achieve degree of association K _j(j=1,2 ..., m), can according to the concrete outcome evaluating principle determination evaluation object.Comparatively conventional evaluation principle is most relevance degree principle: from the degree of association of each things, determine its maximal value K ^*, as Evaluation principle, shown in (12):

K ^*＝max(K ₁，K ₂，…，K _m) (12)

The invention has the beneficial effects as follows: the method adopts summation normalization method determination evaluation criterion weight, use calculation of relationship degree and most relevance degree principle, calculate the degree of membership of rock each index amount in ore deposit relative to different evaluation rank, and then degree of membership evaluation is carried out to ore deposit collapsing property of rock.The present invention and single factor test metrics evaluation compare, and solve single factor test index and evaluate inconsistent problem to ore deposit collapsing property of rock.For collapsing property of the rock evaluation of ore deposit, natural caving method mine and Mining method design provide important reference frame.

Embodiment

Below in conjunction with specific embodiment, technical scheme of the present invention is described further.

Embodiment:

This technique is applied at Yunnan copper-molybdenum, according to certain copper-molybdenum engineering geological data and ore deposit rock mechanics parameter measuring result, calculates each evaluation index value.Meanwhile, according to collapsing property of single index grade scale, utilize single index to evaluate collapsing property, result shows, there is notable difference, even occur inconsistent situation according to collapsing property of single index evaluation conclusion.Utilize fuzzy matter element to evaluate ore deposit collapsing property of rock thus, and contrast with the lumpiness monitoring result that stope bottom structure goes out mine mouth, both match.

Step one: determine matter-element

Collapsing property grade classification is: can not collapsing property, collapsing property difference, collapsing property better, good, fine five ranks of collapsing property of collapsing property.

Collapsing property evaluation index: rock quality designation RQD value, saturated uniaxial compressive strength R _c, joint spacing J _d, to undercut hydraulic radius R, water reason characteristic value K for the first time _w.Evaluation index magnitude calculation result is as shown in table 1.

The each evaluation index calculated value of certain collapsing property of copper-molybdenum of table 1

Step 2: set up compound fuzzy matter element

1. determine subordinate function

For the determination of " can not collapsing property " rank with the subordinate function of each index of " collapsing property is fine " borderline region, then need to determine according to formula (2).

The subordinate function of " can not collapsing property " each index of rank is as follows:

(1) rock quality designation RQD value:

During " can not collapsing property " rank, borderline region scope 90 ~ 100, if X ₁=100, X ₂=90; A, b value is calculated according to (4), (6):

$a=\frac{x_1+x_2}{2}\frac{100+90}{2}$

$b=\frac{x_1-x_2}{1.665}\frac{100-95}{1.665}$

The value of a, b substituted in (4), the expression formula of computation bound subordinate function is as follows:

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{ccc}{e}^{-{\left(\frac{x-95}{6.01}\right)}^2}& ,& x<95\\ 1& ,& x\&GreaterEqual;95\end{array}\right\}---\left(13\right)$

In like manner, single-revolution compressive strength R _c, joint spacing J _d, to undercut hydraulic radius R, water reason characteristic value K for the first time _wsubordinate function as follows:

(2) saturated uniaxial compressive strength R _c

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{ccc}{e}^{-{\left(\frac{x-250}{60.1}\right)}^2}& ,& x<250\\ 1& ,& x\&GreaterEqual;250\end{array}\right\}---\left(14\right)$

(3) joint spacing J _d:

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{ccc}{e}^{-{\left(\frac{x-250}{60.1}\right)}^2}& ,& x<250\\ 1& ,& x\&GreaterEqual;250\end{array}\right\}---\left(15\right)$

(4) undercut hydraulic radius R for the first time

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{ccc}{e}^{-{\left(\frac{x-90}{12.0}\right)}^2}& ,& x<90\\ 1& ,& x\&GreaterEqual;90\end{array}\right\}---\left(16\right)$

(5) water reason characteristic value K _w

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{ccc}{e}^{-{\left(\frac{x-90}{0.120}\right)}^2}& ,& x<0.9\\ 1& ,& x\&GreaterEqual;0.9\end{array}\right\}---\left(17\right)$

The subordinate function of each index of " collapsing property is fine " rank is as follows:

(1) rock quality designation RQD value:

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{ccc}1& ,& x\&le;12.5\\ e^{-{\left(\frac{x-12.5}{15.0}\right)}^2}& ,& x>12.5\end{array}\right\}---\left(18\right)$

(2) saturated uniaxial compressive strength R _c

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{ccc}1& ,& x\&le;12.5\\ e^{-{\left(\frac{x-12.5}{15.0}\right)}^2}& ,& x>12.5\end{array}\right\}---\left(19\right)$

(3) joint spacing J _d

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{ccc}1& ,& x\&le;3\\ e^{-{\left(\frac{x-3}{3.60}\right)}^2}& ,& x>3\end{array}\right\}---\left(20\right)$

(4) undercut hydraulic radius R for the first time

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{ccc}1& ,& x\&le;4\\ e^{-{\left(\frac{x-4}{2.40}\right)}^2}& ,& x>4\end{array}\right\}---\left(21\right)$

(5) water reason characteristic value K _w

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{ccc}1& ,& x\&le;0.1\\ e^{-{\left(\frac{x-0.1}{0.120}\right)}^2}& ,& x>0.1\end{array}\right\}---\left(22\right)$

The subordinate function of metrics evaluation zone line is as formula (3), and computing method are the same, and the value of a, b parameter is as shown in table 2, the subordinate function of borderline region such as formula shown in (13) ~ (22), specifically in table 2:

Table 2 ore deposit collapsing property of rock grading evaluation index subordinate function parameter

2. set up and evaluate fuzzy matter element

Collapsing property evaluation index sees things C as _n, the collapsing property evaluation index of ore deposit rock sees feature M as _i, μ (x), for each index value is relative to the degree of membership of different evaluation rank, sets up the fuzzy matter element R that ore deposit, nine mountains collapsing property of different lithology rock is evaluated _{5 × 5}.

Alteration horn stone:

Alteration granite porphyry:

Fine and close granite porphyry:

Step 3: correlative transformation, be associated coefficient fuzzy matter element

Correlative transformation is carried out to fuzzy matter element and from excellent degree of membership process.In optimizing process, defer to more large more excellent principle (such as formula 22), set up the correlation coefficient fuzzy matter element R that ore deposit collapsing property of rock is evaluated thus _{ξ 5 × 5}.

Alteration horn stone:

Alteration granite porphyry:

Fine and close granite porphyry:

Step 4: the weight of Calculation Estimation index

The weight of each ore deposit rock index is determined according to summation normalization method, namely the correlation coefficient sum of each things every feature is first obtained, then normalized is done to the correlation coefficient of various features, shown in (10), just obtain the weight composite matter-element R between the rock evaluation index of each ore deposit _w.

R _w1＝[0.1741，0.1650，0.2088，0.2628，0.1892]

Alteration granite porphyry:

R _w2＝[0.1581，0.2393，0.2532，0.1968，0.1525]

Fine and close granite porphyry:

R _w3＝[0.1830，0.1683，0.1951，0.1510，0.3026]

Step 5: judge ownership

By the weight composite matter-element R of different lithology _wwith correlation coefficient fuzzy matter element R _{ξ 5 × 5}substitution formula (11), can obtain corresponding degree of association fuzzy matter element R _k.

Alteration horn stone:

Alteration granite porphyry:

Fine and close granite porphyry:

Judge degree of association fuzzy matter element according to most relevance degree principle (see formula 12), result of calculation is as shown in table 3:

Certain copper-molybdenum ore deposit collapsing property of rock rank result of determination of table 3

Analyzing and associating degree fuzzy matter element, known for alteration horn stone k ₃, k ₄all close to 0.5, show: the collapsing property of alteration horn stone close to the fuzzyyest place, border, due to k ₃> 0.5 > k ₄, therefore the collapsing property of alteration horn stone is between better becoming reconciled, and is partial to that the former is more.Finally can show that the collapsing property of alteration horn stone, alteration granite porphyry, fine and close granite porphyry in certain copper-molybdenum ore deposit rock is respectively better, fine, poor conclusion.Compared with the lumpiness monitoring result going out mine mouth with stope bottom structure, the goodness of fit is higher.

Claims (2)

1. the Fuzzy matter-element evaluation method of ore deposit a collapsing property of rock, it is characterized in that: the method organically combines fuzzy mathematics and Matter Analysis, ore deposit collapsing property of rock is divided into can not collapsing property, collapsing property difference, collapsing property better, good, fine 5 grades of collapsing property of collapsing property as matter-element, select ore deposit rock quality index RQD value, saturated uniaxial compressive strength, joint spacing, for the first time undercut hydraulic radius, water to manage characteristic value as evaluation index.Converted by degree of membership calculating, the degree of association and from excellent degree of membership process, set up the correlation coefficient fuzzy matter element that ore deposit collapsing property of rock is evaluated.Adopt summation normalization method determination evaluation criterion weight, use calculation of relationship degree and most relevance degree principle, calculate the degree of membership of rock each index amount in ore deposit relative to different evaluation rank, and then degree of membership evaluation is carried out to ore deposit collapsing property of rock.

2. the Fuzzy matter-element evaluation method of ore deposit as claimed in claim 1 collapsing property of rock, it is characterized in that, its evaluation procedure is as follows:

Step one: determine matter-element

If ore deposit collapsing property of rock has n evaluation index C ₁, C ₂..., C _nwith corresponding fuzzy value v ₁, v ₂..., v _nbe called that the n of R ties up fuzzy matter element, referred to as R=(n, C, v), combine if the n of m ore deposit collapsing property of rock grade ties up fuzzy matter element, the n dimension just forming m ore deposit collapsing property of rock meets matter-element R _mn;

Step 2: set up ore deposit collapsing property of rock fuzzy matter-element model

A () sets up compound fuzzy matter element

If by R _mnvalue be rewritten as fuzzy matter element value, be then called that the n of m collapsing property grade ties up composite matter-element, be denoted as:

$R_{\mathrm{mn}}=\left[\begin{array}{cc}& M_i\\ C_k& v_{\mathrm{ik}}\end{array}\right]=\left[\begin{array}{cccc}& M_i& ...& M_m\\ C_1& v_{11}& ...& v_{m1}\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ C_n& v_{1n}& ...& v_{\mathrm{mn}}\end{array}\right]---\left(1\right)$

In formula: R _mnfor the fuzzy matter element of n evaluation index of m ore deposit collapsing property of rock grade; C _kbe K evaluation index, wherein K=1,2 ... n; M _ibe i-th collapsing property grade, wherein i=1,2 ..., m; v _ikbe fuzzy matter element value corresponding to i-th ore deposit collapsing property of rock grade K evaluation index;

B () sets up from excellent degree of membership fuzzy matter element

According to the classification of collapsing property, in collapsing property Fuzzy Matter Element Analysis, in interval, subordinate function adopts osculant, and namely interval end points is in most fringe, and degree of membership ≈ 0.5, then build the expression formula of the subordinate function of boundary as shown in (2):

$\mathrm{\&mu;}\left(x\right)=e^{-{\left(\frac{x-a}{b}\right)}^2}---\left(2\right)$

For borderline region, namely without collapsing property and the good Region dividing of collapsing property, degree of membership is 1, then build the expression formula of the subordinate function of boundary as shown in (3):

$\mathrm{\&mu;}\left(x\right)=\left\{\begin{array}{cc}{e}^{-{\left(\frac{x-a_1}{b}\right)}^2},& x<a_1\\ 1,& a_1\&le;x\&le;a_2\\ e^{-{\left(\frac{x-a_2}{b}\right)}^2},& x>a_2\end{array}\right\}---\left(3\right)$

In formula (1): a>0, b>0, then have x=a, and maximal value is got in μ (a)=1, namely a is the corresponding interval average of evaluation index value;

Step 3: correlative transformation, be associated coefficient fuzzy matter element

Computing formula different is as follows adopted respectively for different degree of membership:

More large more excellent type:

${\mathrm{\&mu;}}_{\mathrm{ji}}=\frac{X_{\mathrm{ji}}-\min X_{\mathrm{ji}}}{\max X_{\mathrm{ji}}-{\min }_X\mathrm{ji}}---\left(4\right)$

j＝1,2,…,m；i＝1,2,…,n

More little more excellent type:

${\mathrm{\&mu;}}_{\mathrm{ji}}=\frac{\max X_{\mathrm{ji}}-X_{\mathrm{ji}}}{\max X_{\mathrm{ji}}-{\min }_X\mathrm{ji}}---\left(5\right)$

j＝1,2,…,m；i＝1,2,…,n

In formula: μ _jirepresent a jth things i-th feature from excellent degree of membership, X _jirepresent the value corresponding to a jth things i-th feature, maxX _ji, minX _jirepresent X respectively _jiin maximal value and minimum value;

M things has several factors of evaluation and corresponding fuzzy value, because correlation coefficient is the numerical value obtained by optimization principles and correlative transformation; Therefore just can be associated coefficient compound fuzzy matter element, is denoted as R _{ξ mn}

$R_{\mathrm{\&xi;mn}}=\left[\begin{array}{cccc}& M_1& ...& M_m\\ C_1& {\mathrm{\&xi;}}_{11}& ...& {\mathrm{\&xi;}}_{m1}\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ C_n& {\mathrm{\&xi;}}_{1n}& ...& {\mathrm{\&xi;}}_{\mathrm{mn}}\end{array}\right]---\left(6\right)$

Wherein: M _jrepresent a jth things; C _irepresent a jth things i-th factor of evaluation, the fuzzy value corresponding with it, with ξ _ij(j=1,2 ..., m; I=1,2 ... n) represent, i.e. the correlation coefficient of a jth things i-th factor of evaluation;

Step 4: the weight of Calculation Estimation index

During Matter Analysis, the determination of feature weight is the key of problem, adopts summation normalization method parameter weight, namely each things every feature association coefficient sum is first obtained, then make normalized to the correlation coefficient of every feature, just draw the weight of each things various features, its expression formula is as follows:

$R_w=\left[\begin{array}{ccccc}& C_1& C_2& ...& C_n\\ w_i& w_1& w_2& ...& w_n\end{array}\right]---\left(7\right)$

In formula: R _wrepresent weight composite matter-element, w _irepresent the weighted value of each things i-th feature, represent C _icorrelation coefficient sum, represent various features correlation coefficient sum;

Step 5: judge ownership

The degree of association refers to the tolerance of relevance size between two things, and namely represent the tolerance of ore deposit collapsing property of rock evaluation index value and evaluation criterion relevance size here, it uses K _jrepresent, i.e. the degree of association of a jth things and standard things.In degree of association compound fuzzy matter element, by the size of each degree of association, line up in order, then to the method that things or factor are analyzed, be called fuzzy matter element association analysis, its object is to the prevailing relationship seeking things, find out the key factor affecting desired value, thus grasp the principal character of things, therefrom determine best things, structure degree of association compound fuzzy matter element, adopts weighted mean to focus on, then:

R _k＝R _w*R _ξmn(8)

In formula: " * " represents sign of operation, different according to the pattern adopted, the method for computing is also just different, chooses M (× ,+) algorithm herein, namely first takes advantage of the computing added afterwards;

Try to achieve degree of association K _j(j=1,2 ..., m), can according to the concrete outcome evaluating principle determination evaluation object, comparatively conventional evaluation principle is most relevance degree principle: from the degree of association of each things, determine its maximal value K ^*, as Evaluation principle, shown in (9):

K ^*＝max(K ₁,K ₂,…,K _m) (9)。