CN105117559A - Firearm design scheme evaluation method based on fuzzy decision diagram and gray correlation analysis - Google Patents

Abstract

The invention relates to a firearm design scheme evaluation method based on a fuzzy decision diagram and a gray correlation analysis. The method comprises the steps that 1, an evaluation index system of a firearm design scheme is created; 2, global weights of evaluation indexes are calculated based on the fuzzy decision diagram; 3, by means of the global weights, gray relational degrees of alternative schemes are calculated, and evaluation on the firearm design scheme is achieved according to the gray relational degrees. According to the method, the global weights of the evaluation indexes are obtained through the fuzzy decision diagram; the gray relational analysis serves as an evaluation subject method, the defects that the fuzzy decision diagram does not provide the scheme evaluation subject method, and the gray relational analysis can not evaluate the mutual effect among the evaluation indexes are overcome, advantage complementation between the fuzzy decision diagram and the gray relational analysis is achieved, and therefore a set of complete firearm design scheme evaluation method which can evaluate evaluation index comprehensive influence relationships is formed.

Description

Based on the firearm design schemes evaluation method of fuzzy decision figure and grey correlation analysis

Technical field

The present invention relates to a kind of schemes evaluation method of firearm design field, be specifically related to a kind of firearm design schemes evaluation method based on fuzzy decision figure and grey correlation analysis.

Background technology

Firearms intelligent design system is that the intellectually and automatically of firearm design research and development provides possibility, and the evaluation of firearm design scheme and preferably its important ingredient.Firearm design personnel are intelligent design system In-put design demand, and system can produce multiple alternatives via its reasoning module.But designer often only expects that the scheme of unique a kind of comprehensive optimum is for follow-up simulation analysis and actual production.Therefore, need a kind of schemes evaluation method to realize the evaluation of multinomial alternatives and to sort to draw optimal case.

The evaluation of firearm design scheme needs to consider multinomial evaluation index, and influences each other between evaluation index.In the past popular schemes evaluation method, as analytical hierarchy process (AHP), DEA (DEA) and grey correlation analysis (GRA) etc. all do not consider the problem that influences each other between evaluation index, this can make final evaluation result reliably objective not.

The schemes evaluation method of interact relation between evaluation index can be considered at present and mainly contain Network Analysis Method (ANP) and decision experiments room analytic approach (DEMATEL).But these two kinds of methods still also exist shortcomings.ANP or DEMATEL just have expressed evaluation index direct interact relation between any two.But because evaluation index is interrelated, affecting intensity and will certainly change because of the impact being subject to the 3rd evaluation index originally between two evaluation indexes, and ANP and DEMATEL is difficult to give expression to this deeper combined influence relation.Further, the inferior position of DEMATEL is also that all evaluation indexes are considered as same weight by it, and this does not also meet the primary demand of evaluate alternatives.

Summary of the invention

In view of this, the present invention is directed to the deficiencies in the prior art, a kind of firearm design schemes evaluation method based on fuzzy decision figure and grey correlation analysis is provided.The method considers the relation that influences each other between evaluation index using fuzzy decision figure as the power of tax method, firearm design scheme is evaluated using grey correlation analysis as evaluate alternatives subject method, the sequence of the grey relational grade of each alternatives that last basis calculates carrys out optimum scheme comparison, thus formation complete set, both the combined influence relation between evaluation index can have been expressed, again can reasonably for each evaluation index gives the schemes evaluation method of different weight.

The inventive method is achieved through the following technical solutions:

Based on a firearm design schemes evaluation method for fuzzy decision figure and grey correlation analysis, described method comprises the steps:

(1) assessment indicator system of firearm design scheme is built;

(2) the overall weight of each evaluation index is calculated based on fuzzy decision figure;

(3) utilize described overall weight, calculate the grey relational grade of each alternatives, realize the evaluation to firearm design scheme according to described grey relational grade.

Further, the evaluation index of described step (1) comprising:

1) full rifle quality: full rifle quality refers to the quality of firearms entirety, quantitative target, and unit is kg, is minimal type index;

2) 100m single-shot precision: 100m single-shot precision refers to the order of accuarcy of single-shot projectile hit, quantitative target, unit is cm, is minimal type index;

3) failure rate: failure rate refers to that the probability that firearms break down, quantitative target, unit are % is minimal type index;

4) constructional simplicity: constructional simplicity refers to the simple degree of firearm design structure, qualitative index is large index;

5) maintainability: maintainability refers to the easy care degree of firearms, qualitative index is large index;

6) security: security refers to firearms security performance in use, qualitative index is large index;

7) financial cost: the financial cost that financial cost refers to firearm design, manufactures and safeguard, qualitative index is minimal type index.

Further, described step (2) comprises the steps:

A. eigenvalue method is utilized to obtain the partial weight of each evaluation index;

B. the fuzzy decision figure of Utilization assessment index obtains stable state vector;

C. the overall weight of each evaluation index is obtained according to partial weight and stable state vector.

Wherein, partial weight is defined as: when not considering influencing each other between evaluation index, each evaluation index, for the significance level of general objective, represents with z.

Stable state vector is defined as: in the steady state, the matrix of the state value composition of each node, represents with C* evaluation index fuzzy decision figure.

Overall situation weight is defined as: after considering influencing each other between evaluation index, each evaluation index, for the significance level of general objective, represents with w.

If the evaluation index vector of i-th firearm design scheme is Y=[y _1i, y _2i, y _3i, y _4i, y _5i, y _6i, y _7i], wherein, y _1irepresent full rifle quality, y _2irepresent 100m single-shot precision, y _3irepresenting fault rate, y _4irepresentative structure simplicity, y _5irepresent maintainability, y _6irepresent security, y _7irepresent financial cost.

Further, described steps A comprises:

STEPA1: compare the significance level of each evaluation index for general objective between two, forms partial weight matrix Z;

STEPA2: the proper vector calculating partial weight matrix Z, this proper vector is the partial weight z of each evaluation index _j.

Further, described step B comprises:

STEPB1: the fuzzy decision figure building evaluation index, obtains the interact relation between evaluation index:

Concrete, each evaluation index is considered as the node in fuzzy decision figure, then the interact relation between each evaluation index is considered as the internodal causal structure in fuzzy decision figure, represents with the oriented line of Weight between any two nodes.

STEPB2: interact relation is converted to influence matrix E:

Concrete, if N=is (N ₁, N ₂..., N _n), represent the node in fuzzy decision figure;

E:(N _i, N _j) → e _ijrepresent any two node N _i, N _jbetween the weight of oriented line, the relation that influences each other namely between two evaluation indexes.Special, if i=j, then e _ij=0.Then interact relation is equivalent to matrix (e _ij) ∈ E _{n × n}, this matrix is influence matrix.

STEPB3: obtain stable state vector C* by interative computation:

Concrete, if C _irepresentation node N _istate value, C=(C ₁, C ₂..., C _n);

F represents threshold function table, gets

Interative computation formula is

C ^(t+1)＝f(C ^(t)E),C ⁽⁰⁾＝I _n(1)

In formula, I _nrepresent vector of unit length, C ⁽⁰⁾be called initial vector, C ^(t)represent the C in t generation;

Through iterative computation, system finally also can be got back to point of fixity or be occurred limit cycle, is called stable state.Now, the Matrix C * of the state value composition of each node is stable state vector.

Further, described step C comprises:

STEPC1: calculate overall weight w* by weight equation

$w_j^{*}=z_j+C_j^{*}{z}_j---\left(2\right)$

Wherein, represent the state value corresponding to a jth evaluation index in stable state vector;

STEPC2: overall weight is normalized

$w_j=w_j^{*}/{\mathrm{\Σ}}_{j=1}^m{w}_j^{*}---\left(3\right)$

Finally obtain the overall weight w through normalized _j.

Further, described step (3) comprises the steps:

1.. build evaluation index matrix;

2.. grey correlation generates;

3.. grey incidence coefficient calculates;

4.. grey relational grade calculates;

5.. realize firearm design evaluate alternatives.

Further, 1. step comprises:

If evaluation system has n alternatives, m evaluation index.Then evaluation index matrix can be expressed as

Wherein, x _ijrepresent the evaluation of estimate of i-th alternatives under a jth evaluation index.

Further, 2. step comprises:

Process such as polarization such as grade and normalized are carried out to evaluation index matrix.Object Deng polarization process is that the evaluation index with opposed polarity is all converted to large.The polarity of evaluation index is divided into large (score value is more large more excellent), minimal type (score value is more little more excellent) and moderate type (score value gets moderate value for optimum).Normalized is then the numerical value all score value be converted between [0,1], so that follow-up grey incidence coefficient calculates.Be referred to as grey correlation Deng polarization process generate with normalized.

For large index, its etc. polarization process formula be

$u_{ij}^{\′}\left(x_{ij}\right)=\frac{x_{ij}-{\min }_i\left\{x_{ij}\right\}}{{\max }_i\left\{x_{ij}\right\}-{\min }_i\left\{x_{ij}\right\}}---\left(4\right)$

For minimal type index, its etc. polarization process formula be

$u_{ij}^{\′}\left(x_{ij}\right)=\frac{{\max }_i\left\{x_{ij}\right\}-x_{ij}}{{\max }_i\left\{x_{ij}\right\}-{\min }_i\left\{x_{ij}\right\}}---\left(5\right)$

For moderate type index, its etc. polarization process formula be

$u_{ij}^{\′}\left(x_{ij}\right)=1-\frac{\left|x_{ij}-A\right|}{max\left\{{\max }_i\right\{x_{ij}\}-A,A-{\min }_i\{x_{ij}\left\}\right\}}---\left(6\right)$

In formula, A is moderate value, and general available sequences mean value replaces.

Through etc. after polarization process the matrix that obtains be called and wait the matrix that polarizes:

The matrix of equity polarization is subsequently normalized, and formula is

$u_{ij}=\frac{u_{ij}^{\′}}{{\mathrm{\Σ}}_{i=1}^n{u}_{ij}^{\′}}---\left(7\right)$

The matrix obtained after grey correlation generates is called decision matrix:

Further, 3. step comprises:

First want calculated difference matrix Δ, computing formula is

Δ _ij＝|1-u _ij|(8)

Δ is found out subsequently in matrix of differences Δ _maxand Δ _min:

Δ _max＝Max{Δ _ij,i＝1,2,…,n；j＝1,2,…,m}，

Δ _min＝Min{Δ _ij,i＝1,2,…,n；j＝1,2,…,m}。

Then u _ijand the grey incidence coefficient ε between 1 _ijcan by following formulae discovery

${\mathrm{\ϵ}}_{ij}=\frac{{\mathrm{\Δ}}_{min}+{\mathrm{\ρ\Δ}}_{max}}{{\mathrm{\Δ}}_{ij}+{\mathrm{\ρ\Δ}}_{max}},\mathrm{\ρ}=0.5---\left(9\right)$

In formula, р is resolution ratio, and its effect is the scope of expansion or compression grey incidence coefficient, usually gets р=0.5.

Further, 4. step comprises:

After calculating whole grey incidence coefficient, the grey relational grade of each scheme then draws by following formulae discovery.

$r_i={\mathrm{\Σ}}_{j=1}^m{w}_j{\mathrm{\ϵ}}_{ij}---\left(10\right)$

W in formula _jrepresent the weight of each evaluation index, evaluation personnel can according to needing for evaluation index gives different weights.

Further, 5. step comprises:

After above each step calculates, finally can obtain the grey relational grade result value of each alternatives, numerical value is larger, then prove that the program is more excellent.Therefore, firearm design personnel can sort to final degree of association end value, and the alternatives therefrom selecting numerical value maximum is as optimal case.

Beneficial effect:

The evaluation that fuzzy decision figure combines with grey correlation analysis for realizing firearm design scheme by the present invention, compared with prior art mainly has following beneficial effect:

(1) the method obtains the overall weight of each evaluation index with fuzzy decision figure, and this overall weight carrys out the combined influence relation between indicators by the calculating of partial weight, fuzzy decision figure and weight equation; Take grey correlation analysis as Appraising subject method, compensate for fuzzy decision figure does not provide scheme Appraising subject method and grey correlation analysis cannot consider interactional shortcoming between evaluation index, achieve the mutual supplement with each other's advantages of fuzzy decision figure and grey correlation analysis, thus define the schemes evaluation method can considering evaluation index combined influence relation of complete set.

(2) the method can further improve the confidence level that firearm design schemes synthesis is evaluated.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the firearm design schemes evaluation method based on fuzzy decision figure and grey correlation analysis provided by the invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.

As shown in Figure 1, this example is based on the firearm design schemes evaluation method of fuzzy decision figure and grey correlation analysis, and detailed process is:

Step 1 builds the assessment indicator system of firearm design scheme:

For general objective and the assessment indicator system of particular problem determination evaluate alternatives.

The present invention is applied to firearm design field, therefore, provides 7 evaluation indexes exemplarily in conjunction with concrete background, respectively: full rifle quality, 100m single-shot precision, failure rate, constructional simplicity, maintainability, security, financial cost.

Wherein, full rifle quality refers to the quality of firearms entirety, quantitative target, and unit is kg, is minimal type index;

100m single-shot precision refers to the order of accuarcy of single-shot projectile hit, quantitative target, and unit is cm, is minimal type index;

Failure rate refers to that the probability that firearms break down, quantitative target, unit are %, is minimal type index;

Constructional simplicity refers to the simple degree of firearm design structure, qualitative index, is large index;

Maintainability refers to the easy care degree of firearms, qualitative index, is large index;

Security refers to firearms security performance in use, qualitative index, is large index;

The financial cost that financial cost refers to firearm design, manufactures and safeguard, qualitative index is minimal type index.

Step 2 compares the significance level of each evaluation index for general objective between two, forms partial weight matrix Z:

On the basis of the firearm design evaluating indexesto scheme system set up in step 1, comparing each evaluation index between two for general objective--the significance level of a good firearm design scheme, obtains partial weight matrix as shown in table 1.

Table 1 firearm design evaluating indexesto scheme partial weight matrix

Step 4 builds the fuzzy decision figure of evaluation index, obtains the interact relation between evaluation index:

Relation between evaluation index judged and determines, and being interact relation tax power, obtaining the fuzzy decision figure of firearm design evaluating indexesto scheme.

Interact relation is converted to influence matrix E by step 5:

According to the firearm design evaluating indexesto scheme fuzzy decision figure of step 4 gained, the interact relation between firearms evaluation index is converted to influence matrix.

Step 6 obtains stable state vector by interative computation:

Using vector of unit length as iteration initial vector, i.e. C ⁽⁰⁾=I _n, get threshold function table interative computation is carried out according to interative computation formula.When system reaches stable state, obtain stable state vector C*.

C ^(t+1)＝f(C ^(t)E),C ⁽⁰⁾＝I _n(1)

Step 7 calculates overall weight w* by weight equation:

$w_j^{*}=z_j+C_j^{*}{z}_j---\left(2\right)$

Step 8 is normalized overall weight:

$w_j=w_j^{*}/{\mathrm{\Σ}}_{j=1}^m{w}_j^{*}---\left(3\right)$

Step 9 builds index matrix:

Suppose there is 4 alternativess, A, B, C, D.According to assessment indicator system, for every alternatives is given a mark.If quantitative target, then scoring is concrete numerical value; If index qualitatively, then can be alternatives scoring according to the grading system of 1 ~ 10.Thus set up index matrix, as shown in table 2.

Table 2 index matrix

Step 10 grey correlation generates:

On the basis of index matrix, consider the polarity of each evaluation index, polarization such as grade and normalized are carried out to index matrix, thus obtains decision matrix.

For large index, its etc. polarization process formula be

$u_{ij}^{\′}\left(x_{ij}\right)=\frac{x_{ij}-{\min }_i\left\{x_{ij}\right\}}{{\max }_i\left\{x_{ij}\right\}-{\min }_i\left\{x_{ij}\right\}}---\left(4\right)$

For minimal type index, its etc. polarization process formula be

$u_{ij}^{\′}\left(x_{ij}\right)=\frac{{\max }_i\left\{x_{ij}\right\}-x_{ij}}{{\max }_i\left\{x_{ij}\right\}-{\min }_i\left\{x_{ij}\right\}}---\left(5\right)$

For moderate type index, its etc. polarization process formula be

$u_{ij}^{\′}\left(x_{ij}\right)=1-\frac{\left|x_{ij}-A\right|}{max\left\{{\max }_i\right\{x_{ij}\}-A,A-{\min }_i\{x_{ij}\left\}\right\}}---\left(6\right)$

In formula, A is moderate value, and general available sequences mean value replaces.

Through etc. after polarization process the matrix that obtains be called and wait the matrix that polarizes:

The matrix of equity polarization is subsequently normalized, and formula is

$u_{ij}=\frac{u_{ij}^{\′}}{{\mathrm{\Σ}}_{i=1}^n{u}_{ij}^{\′}}---\left(7\right)$

The matrix obtained after grey correlation generates is called decision matrix:

Step 11 grey incidence coefficient calculates:

On the basis of decision matrix, calculate the grey incidence coefficient of each evaluation of programme.

First want calculated difference matrix Δ, computing formula is

Δ _ij＝|1-u _ij|(8)

Δ is found out subsequently in matrix of differences Δ _maxand Δ _min:

Δ _max＝Max{Δ _ij,i＝1,2,…,n；j＝1,2,…,m}，

Δ _min＝Min{Δ _ij,i＝1,2,…,n；j＝1,2,…,m}。

Then u _ijand the grey incidence coefficient ε between 1 _ijcan by following formulae discovery

${\mathrm{\ϵ}}_{ij}=\frac{{\mathrm{\Δ}}_{\min }+{\mathrm{\ρ\Δ}}_{\max }}{{\mathrm{\Δ}}_{ij}+{\mathrm{\ρ\Δ}}_{\max }},\mathrm{\ρ}=0.5---\left(9\right)$

In formula, р is resolution ratio, and its effect is the scope of expansion or compression grey incidence coefficient, usually gets р=0.5.

Step 12 grey relational grade calculates:

On the common base of overall weight and grey incidence coefficient, grey relational grade computing formula is utilized to calculate the grey relational grade of every alternatives.

$r_i={\mathrm{\Σ}}_{j=1}^m{w}_j{\mathrm{\ϵ}}_{ij}---\left(10\right)$

Step 13 obtains optimal case:

Sort by numerical values recited to the grey relational grade of every alternatives, numerical value the maximum is optimal case.

Claims (8)

1., based on a firearm design schemes evaluation method for fuzzy decision figure and grey correlation analysis, it is characterized in that, comprise the steps:

(1) assessment indicator system of firearm design scheme is built;

(2) the overall weight of each evaluation index is calculated based on fuzzy decision figure;

(3) utilize described overall weight, calculate the grey relational grade of each alternatives, realize the evaluation to firearm design scheme according to described grey relational grade.

2. according to claim 1 based on the firearm design schemes evaluation method of fuzzy decision figure and grey correlation analysis, it is characterized in that, the evaluation index of described step (1) comprising: full rifle quality, 100m single-shot precision, failure rate, constructional simplicity, maintainability, security and financial cost.

3., according to claim 1 based on the firearm design schemes evaluation method of fuzzy decision figure and grey correlation analysis, it is characterized in that, described step (2) comprises the steps:

A. eigenvalue method is utilized to obtain the partial weight of each evaluation index;

B. the fuzzy decision figure of Utilization assessment index obtains stable state vector;

C. the overall weight of each evaluation index is obtained according to partial weight and stable state vector.

4., according to claim 3 based on the firearm design schemes evaluation method of fuzzy decision figure and grey correlation analysis, it is characterized in that, described steps A comprises:

STEPA1: compare the significance level of each evaluation index for general objective between two, forms partial weight matrix;

STEPA2: the proper vector calculating partial weight matrix, this proper vector is the partial weight z of each evaluation index _j, j=1,2 ..., n, n are the sum of evaluation index.

5., according to claim 3 based on the firearm design schemes evaluation method of fuzzy decision figure and grey correlation analysis, it is characterized in that, described step B comprises:

STEPB1: the fuzzy decision figure building evaluation index, obtains the interact relation between evaluation index:

Concrete, each evaluation index is considered as the node in fuzzy decision figure, then the interact relation between each evaluation index is considered as the internodal causal structure in fuzzy decision figure, represents with the oriented line of Weight between any two nodes;

STEPB2: interact relation is converted to influence matrix E:

Concrete, if N=is (N ₁, N ₂..., N _n), represent the node in fuzzy decision figure;

Element in influence matrix E is for e _ijshow any two node N _i, N _jbetween the weight of oriented line, i=1,2 ..., n;

STEPB3: obtain stable state vector C by interative computation ^*:

Concrete, if C _irepresentation node N _istate value, C=(C ₁, C ₂..., C _n);

F represents threshold function table, gets

Interative computation formula is

C ^(t+1)＝f(C ^(t)E),C ⁽⁰⁾＝I _n(1)

In formula, I _nrepresent vector of unit length, C ⁽⁰⁾be called initial vector, C ^(t)represent the C in t generation;

Through iterative computation, obtain the Matrix C of the state value composition of each node during stable state ^*be stable state vector.

6., according to claim 3 based on the firearm design schemes evaluation method of fuzzy decision figure and grey correlation analysis, it is characterized in that, described step C comprises:

STEPC1: calculate overall weight w by weight equation ^*

$w_j^{*}=z_j+C_j^{*}{z}_j---\left(2\right)$

Wherein, represent stable state vector C ^*state value corresponding to a middle jth evaluation index;

STEPC2: overall weight is normalized

$w_j=w_j^{*}/{\Σ}_{j=1}^n{w}_j^{*}---\left(3\right)$

Finally obtain the overall weight w through normalized _j.

7., according to claim 4 based on the firearm design schemes evaluation method of fuzzy decision figure and grey correlation analysis, it is characterized in that, described step (3) comprises the steps:

1. evaluation index matrix is built:

If evaluation system has m alternatives, n evaluation index, then evaluation index matrix can be expressed as

Wherein, x _ijrepresent the evaluation of estimate of i-th alternatives under a jth evaluation index;

2. grey correlation generates:

Process such as polarization such as grade and normalized are carried out to evaluation index matrix X, obtains matrix U;

3. grey incidence coefficient calculates:

First want calculated difference matrix Δ, computing formula is

Δ _ij＝|1-u _ij|(8)

Δ is found out subsequently in matrix of differences Δ _maxand Δ _min

Δ _max＝Max{Δ _ij,i＝1,2,…,m；j＝1,2,…,n}，

Δ _min＝Min{Δ _ij,i＝1,2,…,m；j＝1,2,…,n}，

Then u _ijand the grey incidence coefficient ε between 1 _ijcan by following formulae discovery

${\mathrm{\ϵ}}_{ij}=\frac{{\mathrm{\Δ}}_{min}+{\mathrm{\ρ\Δ}}_{max}}{{\mathrm{\Δ}}_{ij}+{\mathrm{\ρ\Δ}}_{max}}---\left(9\right)$

In formula, ρ is resolution ratio;

4. grey relational grade r _icalculate:

$r_i={\Σ}_{j=1}^n{w}_j{\mathrm{\ϵ}}_{ij}---\left(10\right)$

5. sort to the degree of association end value corresponding to each scheme, the alternatives therefrom selecting numerical value maximum is as optimal case.

8., according to claim 7 based on the firearm design schemes evaluation method of fuzzy decision figure and grey correlation analysis, it is characterized in that, described ρ=0.5.