CN106203778A - Similarity evaluation method between a kind of highway technical specification cloud model - Google Patents

Abstract

The present invention relates to similarity evaluation method between a kind of highway technical specification cloud model, including the Similarity Measure stage between expert opinion cloud generation phase based on cloud model, standard evaluation cloud generation phase based on cloud model and two kinds of clouds.Compared with traditional similarity evaluation method, the method that the present invention proposes improves the deficiency that must strictly mate object properties in tradition similarity-rough set method based on vector, optimizes algorithm, improves the precision of calculating.Meanwhile, decrease the time chosen water dust traditionally, the sequence of water dust and the combination of water dust are consumed, improve the Similarity measures efficiency between cloud model.

Description

Similarity evaluation method between a kind of highway technical specification cloud model

Technical field

The present invention relates to similarity evaluation method between a kind of highway technical specification cloud model, calculate in particular with distance Method to make between two different cloud models similarity calculate thus the key index in highway is made judge.

Background technology

Evaluation to a certain expressway works quality detecting index criticality, is affected by expertise, is had one Fixed randomness, ambiguity and subjectivity, this qualitative judgement giving index the most crucial brings bigger difficulty.

Cloud model is that the description of this randomlikeness, ambiguity and subjectivity quantitatively evaluating data provides important theoretical work Tool, and obtained good application in traffic engineering field.But to having the quantitatively evaluating number of randomness, ambiguity and subjectivity According to the transfer problem of equal value between objective qualitative judgement, also there is no a solution of mature and reliable, therefore it is proposed that a kind of The reference changed as equivalence between quantitatively evaluating data to objective qualitative judgement by the size of similarity between cloud model, for The criticality qualitative evaluation of the key index in qualitative evaluation highway has good practical significance.

Both at home and abroad the main technique methods of Similarity measures between cloud model is had at present:

1, the feature of cloud model is described, to expect Similar Broken Line by the expectation curve of cloud model and maximum boundary curve The similarity degree of degree or the maximum boundary curve quantificational expression to cloud model similarity.

" normal cloud model similarity calculating method " that Li Hailin, Guo Chonghui, Qiu Wangren deliver (" electronic letters, vol ", 2011 Year volume 39 11 phase) propose two kinds of normal cloud model similarity calculating methods, respectively by the expectation curve of normal cloud model and Maximum boundary curve describes the general characteristic of normal cloud model, it is achieved to expect Similar Broken Line degree or maximum boundary curve The similarity degree quantificational expression to normal cloud model similarity.Although producing a desired effect, but computation complexity is higher.

2, for tradition method for measuring similarity exist deficiency, utilize cloud model Qualitative Knowledge represent and qualitative, Function served as bridge during Quantitative Knowledge conversion, proposes a kind of method comparing user's similarity at knowledge level, is analyzing biography comprehensively On the basis of system method, a kind of new Collaborative Filtering Recommendation Algorithm is proposed.

Zhang Guangwei, Li Deyi, Li Peng, " Collaborative Filtering Recommendation Algorithm based on cloud model " of Kang Jianchu, Chen Gui hair growth promoting table (" Journal of Software " 2007, volume 18,10 phases) Collaborative Filtering Recommendation Algorithm based on cloud model is proposed, by special for the numeral of cloud model Levy as vector, and utilize included angle cosine to the similarity problem weighing between cloud model.Although this algorithm is at collaborative filtering Algorithm achieves preferable effect, but a lot of in the case of cloud model numerical characteristic in expected value be far longer than entropy and super Entropy so that the tolerance of included angle cosine easily ignores entropy and the effect of two numerical characteristics of super entropy.

Summary of the invention

The invention aims to solve in above-mentioned prior art the use to cloud model and contribute to the quantitative of object The mathematical description problem of data, does not propose quantitative data and is described to the deficiency of conversion Calculation between qualitative evaluation, propose one The most rational conversion Calculation method.

In order to realize the purpose of the present invention, the invention provides similarity between a kind of highway technical specification cloud model and comment Sentence method, including expert opinion cloud generation phase based on cloud model, standard evaluation cloud generation phase based on cloud model and two Plant the Similarity Measure stage between cloud, specifically include following steps.

1, similarity evaluation method between a kind of highway technical specification cloud model, it is characterised in that comprise the following steps:

Step 1, based on cloud model by expert analysis mode set X_nBeing converted into expert opinion cloud EC, its transformation process includes following Step:

Step 1.1, constitutes expert analysis mode set according to the appraisal result that index a certain in highway is provided by n position expert X_n={ x₁,x₂,...x_i,...,x_n}；Wherein, x₁It is the appraisal result of the 1st expert, x₂It is the appraisal result of the 2nd expert, x_i For the appraisal result of i-th bit expert, x_nBeing the appraisal result of n-th expert, the span of n is [5,50]；

Step 1.2, calculates expert analysis mode set X_nNumerical characteristic, respectively expect E_x, entropy E_nWith super entropy H_e, it calculates Method is respectively as shown in formula (1), (2), (3):

$E_x=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}\left(x_i\right)---\left(1\right)$

$E_n=\sqrt{\frac{\mathrm{\π}}{2}}\×\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}|x_i-E_x|---\left(2\right)$

$H_e=\sqrt{s_k^2-E_n^2}---\left(3\right)$

Wherein,

Step 1.3, with E_nFor expecting,For one normal distribution number N of variance stochastic generation_i, production method such as formula (4) institute Show:

$N_i=Norm(E_n,H_e^2)---\left(4\right)$

Step 1.4, with E_xFor expecting,A normal distribution number s is generated for variance_i, shown in production method such as formula (5):

$s_i=Norm(E_x,N_i^2)---\left(5\right)$

Step 1.5, according to the numerical characteristic of expert analysis mode set, calculates degree of membership u_i, shown in computational methods such as formula (6):

$u_i=e^{-\frac{{(s_i-E_x)}^2}{2N_i^2}}---\left(6\right)$

Step 1.6, as i=1, is generated first water dust of expert opinion cloud EC, is designated as by step 1.3-step 1.5: (s₁,u₁)；

Step 1.7, repeats step 1.3-step 1.5, until producing K water dust, generating expert opinion cloud EC, being designated as: EC ={ (s₁,u₁),(s₂,u₂),...,(s_K,u_K), wherein, K is in the range of [1000,3000]；

Step 2, generates standard evaluation cloud based on cloud model, and its generation process comprises the following steps:

Step 2.1, sets a standard evaluation set, and the element in this set produces at the interval interior of [0, R], and according to This interval is divided into M subinterval by crucial rating scaleThe corresponding qualitative evaluation result in each interval, Wherein, the span of R is [1,10],WithIt is the Lower and upper bounds in m-th interval respectively；M=1,2 ..., M, M value Scope is [2,50]；

Step 2.2, calculates the numerical characteristic of the interval standard evaluation cloud of m-th, respectively expects E'_xm, entropy E'_nmWith super Entropy H'_em, shown in its computational methods such as formula (7), (8), (9):

$E_{xm}^{\&prime;}=\left\{\begin{array}{cc}{R}_m^{\min },& m=1\\ \frac{R_m^{\min }+R_m^{max}}{2},& 1<m<M\\ R_m^{\max },& m=M\end{array}\right.;---\left(7\right)$

$E_{nm}^{\&prime;}=\frac{R_m^{max}-R_m^{\min }}{4};1\&le;m\&le;M---\left(8\right)$

H_em=H_e；1≤m≤M (9)

Step 2.3, with E'_nmFor expectation, H'_emFor one normal distribution number N' of variance stochastic generation_m, production method such as formula (10) shown in:

N'_m=Norm (E'_nmH_e'_m ²) (10)

Step 2.4, with E'_xmFor expectation, N'_m ²For one normal distribution number s' of variance stochastic generation_mi, production method such as formula (11) shown in:

s'_mi=Norm (E'_xm,N'_m ²) (11)

Step 2.5, according to the numerical characteristic of expert analysis mode set, degree of membership u'_miComputational methods such as formula (12) shown in:

$u_{mi}^{\&prime;}=e^{-\frac{{(s_{mi}^{\&prime;}-E_{xm}^{\&prime;})}^2}{2N_{mi}^{\&prime;2}}}---\left(12\right)$

Step 2.6, takes m=1, by the result of calculation of step 2.2 step 2.5, produces the 1st of the 1st the sub-cloud of standard evaluation the Individual water dust is also designated as (s₁'₁,u₁'₁)；

Step 2.7, repeats the process of step 2.2 step 2.5, circulates K the cloud obtaining the 1st the sub-cloud of standard evaluation K time Drip, the 1st the sub-cloud of standard evaluation generated be designated as:

SC₁={ (s₁'₁,u₁'₁),(s₁'₂,u₁'₂),...,(s₁'_K,u₁'_K)}；

Step 2.8, takes m=2 respectively, and 3 ..., M, generate remaining M-1 standard evaluation and drip, there are M The sub-cloud of standard evaluation, constitutes standard evaluation and converges conjunction, be designated as:

SC={SC₁,SC₂,...,SC_m,...,SC_M}；

Wherein, SC_m={ (s'_m1,u'_m1),(s'_m2,u'_m2),...,(s'_mK,u'_mK), m=1,2 ..., M；

Step 3, similarity between each sub-cloud in calculating expert opinion cloud EC and standard evaluation cloud SC set；

All water dusts in expert opinion cloud EC are pressed s_iSize ascending order arrangement, by the arbitrary sub-cloud SC in standard evaluation_mIn All water dusts press s'_miThe arrangement of size ascending order, calculate expert opinion cloud EC and this standard evaluation cloud SC_mBetween correspondence away from From, it is designated as d_m, shown in its computing formula such as formula (13):

$d_m=\underset{i=1}{\overset{K}{\&Sigma;}}\&lsqb;{(u_i-u_{mi}^{\&prime;})}^2+{(s_i-s_{mi}^{\&prime;})}^2\&rsqb;---\left(13\right)$

Wherein, i=1,2 ..., K；

Take m=1,2 ..., M, it is respectively adopted formula (13) and is calculated { d₁,d₂,...,d_M}；

Step 4, compares M tried to achieve respective distances { d₁,d₂,...,d_M, wherein minimum respective distances is designated as d_j, then Show that the criticality of expert opinion cloud EC is evaluated as jth standard evaluation cloud SC_jCorresponding qualitative evaluation.

Compared with prior art, beneficial effects of the present invention is as follows:

1, the present invention propose method improve tradition based on vector similarity-rough set method in must strictly mate right As the deficiency of attribute, optimize algorithm, improve the precision of calculating；

2, the method that the present invention proposes decreases and chooses water dust traditionally, disappeared the sequence of water dust and the combination of water dust The time of consumption, improve the Similarity measures efficiency between cloud model.

Accompanying drawing explanation

Fig. 1 is the basic skills schematic flow sheet of the present invention；

Fig. 2 is embodiment of the present invention Subgrade Compaction index expert opinion cloud EC schematic diagram；

Fig. 3 is that embodiment of the present invention Subgrade Compaction criterion evaluates sub-cloud SC₁Schematic diagram；

Fig. 4 is that embodiment of the present invention Subgrade Compaction criterion evaluates sub-cloud SC₂Schematic diagram；

Fig. 5 is that embodiment of the present invention subgrade and pavement compactness criterion evaluates sub-cloud SC₃Schematic diagram；

Fig. 6 is the big logotype of similarity of embodiment of the present invention compactness index cloud and standard evaluation cloud.

Detailed description of the invention

Fig. 1 is the basic skills schematic flow sheet of the present invention.Below in conjunction with the accompanying drawings 1 and embodiment the present invention is done further Describe in detail.

Step 1, based on cloud model by expert analysis mode set X_nBeing converted into expert opinion cloud EC, its transformation process includes following Step:

Step 1.1, according to 13 experts to Subgrade Compaction index in highway, is given in the range of assigning to 3 points 0 and comments Divide result, form expert analysis mode set: X₁₃={ x₁,x₂,...,x₁₃}={ 3,3,3,3,2,3,3,3,3,3,3,3,3}；

Step 1.2, calculates expert analysis mode set X_nNumerical characteristic, respectively expect E_x, entropy E_nWith super entropy H_e, it calculates Method is respectively as shown in formula (1), (2), (3):

$E_x=\frac{1}{n}\underset{i=1}{\overset{n}{\&Sigma;}}\left(x_i\right)=2.92---\left(1\right)$

$E_n=\sqrt{\frac{\mathrm{\&pi;}}{2}}\&times;\frac{1}{n}\underset{i=1}{\overset{n}{\&Sigma;}}|x_i-E_x|=0.18---\left(2\right)$

$H_e=\sqrt{s_k^2-E_n^2}=0.21---\left(3\right)$

Wherein,

Step 1.3, with E_nFor expecting,For one normal distribution number N of variance stochastic generation_i, production method such as formula (4) institute Show:

$N_i=Norm(E_n,H_e^2)---\left(4\right)$

Step 1.4, with E_xFor expecting,A normal distribution number s is generated for variance_i, shown in production method formula (5):

$s_i=Norm(E_x,N_i^2)---\left(5\right)$

Step 1.5, according to the numerical characteristic of expert analysis mode set, calculates degree of membership u_i, shown in computational methods such as formula (6):

$u_i=e^{-\frac{{(s_i-E_x)}^2}{2N_i^2}}---\left(6\right)$

Step 1.6, as i=1, is generated first water dust (s of expert opinion cloud EC by step 1.3-step 1.5₁,u₁)；

Step 1.7, repeats step 1.3-step 1.5, until producing K water dust, the expert opinion cloud EC of generation is designated as: EC ={ (s₁,u₁),(s₂,u₂),...,(s_K,u_K), wherein, K is in the range of [1000,3000]；

In the present embodiment, K is 1000, so the expert opinion cloud EC generated is designated as:

EC={ (s₁,u₁),(s₂,u₂),...,(s₁₀₀₀,u₁₀₀₀)}

In the present embodiment, Subgrade Compaction expert opinion cloud is as shown in Figure 2.

Step 2, generates standard evaluation cloud based on cloud model, and its generation process comprises the following steps:

Step 2.1, sets a standard evaluation set, and in this set, element produces at the interval interior of [0,3], and according to pass This interval is divided into 3 subintervals, in the present embodiment, the qualitative key corresponding to 3 subintervals by key rating scale qualitatively Degree is respectively as follows: key the most crucial, secondary, crucial three qualitative evaluation grades；

Step 2.2, calculates the numerical characteristic of the interval standard evaluation cloud of m-th, respectively expects E'_xm, entropy E'_nmWith super Entropy H'_em, shown in its computational methods such as formula (7), (8), (9):

$E_{xm}^{\&prime;}=\left\{\begin{array}{cc}0,& m=1\\ \frac{1+2}{2},& m=2\\ 3,& m=3\end{array}\right.---\left(7\right)$

$E_{nm}^{\&prime;}=\left(\begin{array}{cc}\frac{1-0}{3}=0.25,& m=1\\ \frac{2-1}{3}=0.25,& m=2\\ \frac{3-2}{3}=0.25,& m=3\end{array}\right.---\left(8\right)$

H_e'_m=H_e=0.21, m=1,2,3 (9)

Step 2.3, with E'_nmFor expectation, H'_emFor one normal distribution number N' of variance stochastic generation_m, production method such as formula (10) shown in:

N'_m=Norm (E'_nmH'_em ²) (10)

Step 2.4, with E'_xmFor expectation, N'_m ²For one normal distribution number s' of variance stochastic generation_mi, production method such as formula (11) shown in:

s'_mi=Norm (E'_xm,N'_m ²) (11)

Step 2.5, according to the numerical characteristic of expert analysis mode set, degree of membership u'_miComputational methods such as formula (12) shown in:

$u_{mi}^{\&prime;}=e^{-\frac{{(s_{mi}^{\&prime;}-E_{xm}^{\&prime;})}^2}{2N_{mi}^{\&prime;2}}}---\left(12\right)$

Step 2.6, takes m=1, by the result of calculation of step 2.2 step 2.5, produces the 1st of the 1st the sub-cloud of standard evaluation the Individual water dust is also designated as (s₁'₁,u₁'₁)；

Step 2.7, repeats the process of step 2.2 step 2.5, circulate and obtain 1000 water dusts for 1000 times, by the of generation 1 sub-cloud of standard evaluation is designated as:

SC₁={ (s₁'₁,u₁'₁),(s₁'₂,u₁'₂),...,(s₁'₁₀₀₀,u₁'₁₀₀₀)}

Step 2.8, generates the water dust of remaining 2 sub-clouds of standard evaluation respectively, there are 3 sub-clouds of standard evaluation, structure Become standard evaluation cloud, be designated as SC={SC₁,SC₂,SC₃}；3 sub-clouds of standard evaluation of the present embodiment are respectively such as Fig. 3, Fig. 4, Fig. 5 institute Showing, wherein, transverse axis represents the order that water dust number produces, and the longitudinal axis represents degree of membership size；

Step 3, similarity between each sub-cloud in calculating expert opinion cloud EC and standard evaluation cloud SC set；

All water dusts in cloud EC are pressed s_iSize ascending order arrangement i=1,2 ..., 1000, arbitrary by standard evaluation Sub-cloud SC_mInterior all water dusts press s'_miSize ascending order arrangement, m=1,2,3, i=1,2 ..., 1000, calculate expert opinion cloud EC and 3 standard evaluation cloud SC_mBetween respective distances, be designated as d_mShown in its computing formula such as formula (13):

$d_m=\underset{i=1}{\overset{1000}{\&Sigma;}}\&lsqb;{(u_i-u_{mi}^{\&prime;})}^2+{(s_i-s_{mi}^{\&prime;})}^2\&rsqb;---\left(13\right)$

Wherein, i=1,2 ..., 1000

The result that the present embodiment calculates is d₁=8.60, d₂=2.14, d₃=0.10

Step 4, compares tried to achieve 3 distance value { d₁,d₂,d₃In }, minima is d₃=0.10, then draw expert opinion Cloud EC and the 3rd standard evaluation cloud SC₃Similar the highest, therefore, use SC₃Corresponding qualitative evaluation " crucial " index is as specially The final result of family's this index qualitative evaluation of Subgrade Compaction degree.Fig. 5 is that subgrade and pavement compactness criterion evaluates sub-cloud SC₃Schematic diagram.

Claims (1)

1. similarity evaluation method between a highway technical specification cloud model, it is characterised in that comprise the following steps:

Step 1, based on cloud model by expert analysis mode set X_nBeing converted into expert opinion cloud EC, its transformation process comprises the following steps:

Step 1.1, constitutes expert analysis mode set X according to the appraisal result that index a certain in highway is provided by n position expert_n= {x₁,x₂,...x_i,...,x_n}；Wherein, x₁It is the appraisal result of the 1st expert, x₂It is the appraisal result of the 2nd expert, x_iFor The appraisal result of i-th bit expert, x_nBeing the appraisal result of n-th expert, the span of n is [5,50]；

Step 1.2, calculates expert analysis mode set X_nNumerical characteristic, respectively expect E_x, entropy E_nWith super entropy H_e, its computational methods are divided Not as shown in formula (1), (2), (3):

$E_x=\frac{1}{n}\underset{i=1}{\overset{n}{\&Sigma;}}\left(x_i\right)---\left(1\right)$

$E_n=\sqrt{\frac{\mathrm{\&pi;}}{2}}\&times;\frac{1}{n}\underset{i=1}{\overset{n}{\&Sigma;}}|x_i-E_x|---\left(2\right)$

$H_e=\sqrt{s_k^2-E_n^2}---\left(3\right)$

Wherein,

Step 1.3, with E_nFor expecting,For one normal distribution number N of variance stochastic generation_i, shown in production method such as formula (4):

$N_i=Norm(E_n,H_e^2)---\left(4\right)$

Step 1.4, with E_xFor expecting,A normal distribution number s is generated for variance_i, shown in production method such as formula (5):

$s_i=Norm(E_x,N_i^2)---\left(5\right)$

Step 1.5, according to the numerical characteristic of expert analysis mode set, calculates degree of membership u_i, shown in computational methods such as formula (6):

$u_i=e^{-\frac{{(s_i-E_x)}^2}{2N_i^2}}---\left(6\right)$

Step 1.6, as i=1, is generated first water dust of expert opinion cloud EC, is designated as: (s by step 1.3-step 1.5₁, u₁)；

Step 1.7, repeats step 1.3-step 1.5, until producing K water dust, generating expert opinion cloud EC, being designated as: EC= {(s₁,u₁),(s₂,u₂),...,(s_K,u_K), wherein, K is in the range of [1000,3000]；

Step 2, generates standard evaluation cloud based on cloud model, and its generation process comprises the following steps:

Step 2.1, sets a standard evaluation set, and the element in this set produces at the interval interior of [0, R], and according to key This interval is divided into M subinterval by rating scaleThe corresponding qualitative evaluation result in each interval, wherein, The span of R is [1,10],WithIt is the Lower and upper bounds in m-th interval respectively；M=1,2 ..., M, M span For [2,50]；

Step 2.2, calculates the numerical characteristic of the interval standard evaluation cloud of m-th, respectively expects E'_xm, entropy E'_nmWith super entropy H '_em, shown in its computational methods such as formula (7), (8), (9):

$E_{xm}^{\&prime;}=\left\{\begin{array}{cc}{R}_m^{\min },& m=1\\ \frac{R_m^{\min }+R_m^{\max }}{2},& 1<m<M\\ R_m^{\max },& m=M\end{array}\right.;---\left(7\right)$

$E_{nm}^{\&prime;}=\frac{R_m^{max}-R_m^{\min }}{4};1\&le;m\&le;M---\left(8\right)$

H′_em=H_e；1≤m≤M (9)

Step 2.3, with E'_nmFor expectation, H'_emFor one normal distribution number N' of variance stochastic generation_m, production method such as formula (10) institute Show:

$N_m^{\&prime;}=Norm\left(E_{nm}^{\&prime;}{H_{em}^{\&prime;}}^2\right)---\left(10\right)$

Step 2.4, with E'_xmFor expecting,For one normal distribution number s' of variance stochastic generation_mi, production method such as formula (11) Shown in:

$s_{mi}^{\&prime;}=Norm(E_{xm}^{\&prime;},{N_m^{\&prime;}}^2)---\left(11\right)$

Step 2.5, according to the numerical characteristic of expert analysis mode set, degree of membership u'_miComputational methods such as formula (12) shown in:

$u_{mi}^{\&prime;}=e^{-\frac{{(s_{mi}^{\&prime;}-E_{xm}^{\&prime;})}^2}{2N_{mi}^{\&prime;2}}}---\left(12\right)$

Step 2.6, takes m=1, by the result of calculation of step 2.2 step 2.5, produces the 1st cloud of the 1st the sub-cloud of standard evaluation Drip and be designated as (s '₁₁,u′₁₁)；

Step 2.7, repeats the process of step 2.2 step 2.5, circulates K the water dust obtaining the 1st the sub-cloud of standard evaluation K time, The 1st the sub-cloud of standard evaluation generated is designated as:

SC₁={ (s '₁₁,u′₁₁),(s′₁₂,u′₁₂),...,(s′_1K,u′_1K)}；

Step 2.8, takes m=2 respectively, and 3 ..., M, generate remaining M-1 standard evaluation and drip, there are M standard Evaluate sub-cloud, constitute standard evaluation and converge conjunction, be designated as:

SC={SC₁,SC₂,...,SC_m,...,SC_M}；

Wherein, SC_m={ (s'_m1,u'_m1),(s'_m2,u'_m2),...,(s'_mK,u'_mK), m=1,2 ..., M；

Step 3, similarity between each sub-cloud in calculating expert opinion cloud EC and standard evaluation cloud SC set；

All water dusts in expert opinion cloud EC are pressed s_iSize ascending order arrangement, by the arbitrary sub-cloud SC in standard evaluation_mInterior institute There is water dust by s'_miThe arrangement of size ascending order, calculate expert opinion cloud EC and this standard evaluation cloud SC_mBetween respective distances, note For d_m, shown in its computing formula such as formula (13):

$d_m=\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}\&lsqb;{(u_i-u_{mi}^{\&prime;})}^2+{(s_i-s_{mi}^{\&prime;})}^2\&rsqb;---\left(13\right)$

Wherein, i=1,2 ..., K；

Take m=1,2 ..., M, it is respectively adopted formula (13) and is calculated { d₁,d₂,...,d_M}；

Step 4, compares M tried to achieve respective distances { d₁,d₂,...,d_M, wherein minimum respective distances is designated as d_j, then draw specially Family evaluates the criticality of cloud EC and is evaluated as jth standard evaluation cloud SC_jCorresponding qualitative evaluation.