CN104408522A - A fuzzy AHP-TOPSIS based environmental awareness machinery designing scheme relative green degree evaluation method - Google Patents

Abstract

A fuzzy AHP-TOPSIS based environmental awareness machinery designing scheme relative green degree evaluation method includes the following steps: step 1, hierarchy index optimization ranking based on the fuzzy AHP, 1.1) establishing a table of a semantic variable and triangle fuzzy number of importance comparisons between two indexes, and 1.2) using the fuzzy AHP to calculate a hierarchy total ranking result; and step 2, optimal scheme solving based on the fuzzy TOPSIS, 2.1) differently processing a qualitative index and a quantitative index, and 2.2) obtaining the optimal scheme using the fuzzy TOPSIS. The present invention provides a fuzzy AHP-TOPSIS based environmental awareness machinery designing scheme relative green degree evaluation method which takes the environmental awareness into account, and effectively performs the green degree evaluation.

Description

A kind of relative Green Degree Evaluation of environmental consciousness scheme of machine design based on fuzzy AHP-TOPSIS

Technical field

The present invention relates to Green design schemes evaluation method, especially a kind of relative Green Degree Evaluation of environmental consciousness scheme of machine design considering profit evaluation model, cost type qualitative index and quantitative target.

Background technology

Increasingly serious shortage of resources and ecological degeneration are one of the subject matter of 21 century facing mankind, the shortage of the energy will directly affect the sustainable development of various countries' economy, excessive exploitation then more exacerbates this trend with waste, various environmental pollution such as atmospheric pollution, water pollutions etc. then directly threaten health and the existence of the mankind, and just towards intensification, globalize, diversified future development, the mankind need a kind of method radical cure resources and environment problems badly, make it and industrialization harmonious coexistence; In the tide of economic globalization; green barrier problem is more outstanding in international trade; due to the green standard disunity of various countries and the difference to green standard understanding; create problems such as trade cost to increase; developed country protects domestic firms etc. whereby; be unfavorable for global economic integration, the engineering goods of China affect by this deeply.But then; improving and setting up along with environmental protection relevant laws and regulations; the enhancing of CSR consciousness and the mankind are to the self-examination of self-growth; environmental consciousness Machine Design is arisen at the historic moment, and becomes the Strategic Thought solved the problem and the important channel promoting the sustainable development of socio-economy.Environmental consciousness Machine Design is emphasized to reduce its impact on human and environment from the angle of product lifecycle, is the combination of each side such as technical advance, environment friendly and economy.As the foundation of product improvement and optimization, the important ring that comprehensive analysis and inspection is Environmental Consciousness Design is carried out to the green intensity of Environmental Consciousness Design engineering goods, and field involved by machinery industry is extensive, product complexity is various, according to the knowledge of oneself, different understanding is had for green product different industries people, although green product concept proposes the history of existing two more than ten years, but up to the present also do not formed one generally acknowledged, the definition of authority, green product assessment system is caused " to let a hundred schools contend thus, a hundred flowers blossom " situation, this hinders the design and development of green machine product to a certain extent, so evaluate in the right perspective green machine product, significant for environmental consciousness Machine Design, being both also is Focal point and difficult point problem urgently to be resolved hurrily at present.

AHP (Analytic Hierarchy Process, analytical hierarchy process) a kind of combine as important qualitative and quantitative analysis the method for solution Multiple-criteria Decision Problems is also often applied in green product assessment, easy by means of it, flexible and practical feature obtains extensive research, but green product assessment index comprises quantitative and qualitative analysis index, and both have cost type and profit evaluation model point, but tradition stratum fractional analysis does not consider cost type and profit evaluation model is qualitative and quantitative target, have impact on reliability and the objectivity of evaluation result simultaneously.TOPSIS (similarity to ideal solution ranking method) can sort according to the degree of closeness of limited cost type and profit evaluation model qualitative and quantitative index and idealized target, thus reduce evaluation result because of the difference of estimator and preference thereof difference, the possibility that changes because of estimator and preference change thereof, but its deficiency is exactly decision matrix and index weights vector to be needed to provide in advance.

Summary of the invention

In order to the deficiency of environmental consciousness is evaluated, lacked to the redgreen degree overcoming existing scheme of machine design evaluation method, the invention provides a kind of relative Green Degree Evaluation of environmental consciousness scheme of machine design based on fuzzy AHP-TOPSIS considered environmental consciousness, effectively carry out Enterprises ' Green Degree.

In order to the technical scheme solving the problems of the technologies described above proposition is:

Based on the relative Green Degree Evaluation of environmental consciousness scheme of machine design of fuzzy AHP-TOPSIS, described method comprises the steps:

The first step, the target layers carried out based on fuzzy AHP always sorts

Target layers always sorts and refers to the ranking value of described bottom Index element relative to the relative importance of general objective.

1.1 couples of kth layer n being under the jurisdiction of kth-1 layer of certain index _kwhen individual index is evaluated, in the comparator matrix between two of metrics evaluation, Triangular Fuzzy Number M1, M3, M5, M7, M9 is used to replace traditional 1,3,5,7,9, and M2, M4, M6, M8 are intermediate values, be on average integrated into a fuzzy value when there being multiple expert with formula (1);

$M_{\mathrm{ij}}^k=\frac{1}{T}\⊕(a_{\mathrm{ij}}^1+a_{\mathrm{ij}}^2+...+a_{\mathrm{ij}}^T)---\left(1\right)$

Wherein, t=1,2 ..., T represents that a common T expert gives Triangular Fuzzy Number i, j=1,2 ..., n _k;

1.2 list the k layer n being under the jurisdiction of k-1 layer index _kthe Synthetic Judgement Matrix of individual index, then obtain fuzzy set according to formula (2) they represent the k layer n being under the jurisdiction of k-1 layer index _kthe fuzzy synthesis degree of individual index:

$S_i^k=\underset{j=1}{\overset{n_k}{\mathrm{\Σ}}}{M}_{\mathrm{ij}}^k\⊗{\left(\underset{i=1}{\overset{n_k}{\mathrm{\Σ}}}\underset{j=1}{\overset{n_k}{\mathrm{\Σ}}}{M}_{\mathrm{ij}}^k\right)}^{-1}---\left(2\right)$

i,j＝1,2,...,n _k

1.3 de-fuzzies, obtain the kth layer n being under the jurisdiction of kth-1 layer of certain index _kindividual index finally determine weight

If M ₁and M ₂convex Fuzzy number, fuzzy number M ₁>=M ₂probability level be defined as:

$V(M_1\≥M_2)=\left\{\begin{array}{cc}1& m_1\≥m_2\\ \frac{l_1-u_2}{(m_2-u_2)-(m_1-l_1)}& m_1\≤m_2,u_1\≥l_2\\ 0& \mathrm{otherwise}\end{array}\right.---\left(3\right)$

M>=M ₁, M>=..., M>=M _kprobability level be defined as:

$\begin{array}{c}V(M\≥M_1,...,M_{n_k})\\ =V[(M\≥M_1)\mathrm{and}(M\≥M_2)\mathrm{and}...\mathrm{and}(M\≥M_{n_k})]\\ =\min V(M\≥M_i),i=\mathrm{1,2},...,n_k\end{array}---\left(4\right)$

The final normalization of 1.4 each index weights

Suppose

m(P _i)＝minV(M ₁≥M _k)k＝1,2,...,n _k；k≠i (5)

Then be under the jurisdiction of the kth layer n of kth-1 layer of certain index _kthe weight vectors of individual index is:

$W^{\′}={(m\left(P_1\right),m\left(P_2\right),...,m\left(P_{n_k}\right))}^T---\left(6\right)$

To this vectorial normalization, then proper vector and weight are:

$W={(w\left(P_1\right),w\left(P_2\right),...,w\left(P_{n_k}\right))}^T---\left(7\right)$

Wherein W is non-fuzzy number, gives the weight of influence factor to object effects;

1.5 calculate the total ranking results of level;

Suppose m _nit is Rn that institute is subordinate to index, and the index that Rn is subordinate to is Cn, and the index that Cn is subordinate to is O, then

$w_{m_n}^O=w_{\mathrm{Cn}}^O\×w_{\mathrm{Rn}}^{\mathrm{Cn}}\×w_{m_n}^{\mathrm{Rn}}---\left(8\right)$

Wherein, for detailed layer index m _nabout the weight of destination layer O, for detailed layer index m _nabout the weight of be subordinate to indicator layer index Rn, for indicator layer index Rn is about the weight of be subordinate to rule layer index Cn, for rule layer index Cn is about the weight of destination layer;

Second step, the optimal case carried out based on fuzzy TOPSIS solves

The 2.1 Comprehensive Evaluation index systems setting up each scheme;

Set up fuzzy evaluating matrix according to formula (8), for qualitative index, adopt semanteme to judge, be divided into the classification standard of setting number, semantic variant Triangular Fuzzy Number describes; For quantitative target, corresponding concrete value is brought into initial fuzzy matrix for assessment correspondence position.

$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1m}\\ x_{21}& x_{22}& ...& x_{2m}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_{k1}& x_{k2}& ...& x_{\mathrm{km}}\end{array}\right],$ i＝1,2,...,k；j＝1,2,...,m (9)

Wherein x _ijthe fuzzy value of i-th scheme to a detailed layer jth evaluation index;

Matrix X is standardized as by 2.2:

R＝[r _ij] _k×m,i＝1,2,...,k；j＝1,2,...,m (10)

Wherein,

Quantitative target:

$r_{\mathrm{ij}}=\left\{\begin{array}{c}\frac{x_{\mathrm{ij}}-x_j^{-}}{x_j^{+}-x_j^{-}},x_{\mathrm{ij}}\∈I^{\′},i=\mathrm{1,2},...,k\\ \frac{x_j^{+}+x_{\mathrm{ij}}}{x_j^{+}-x_j^{-}},x_{\mathrm{ij}}\∈I^{\′\′},i=\mathrm{1,2},...,k\end{array}\right.---\left(11\right)$

Wherein, for x in canonical matrix X _ijthe maximal value of column, for x in canonical matrix X _ijthe minimum value of column.

Qualitative index:

$r_{\mathrm{ij}}=\left\{\begin{array}{c}(\frac{a_{\mathrm{ij}}}{c_j^{+}},\frac{b_{\mathrm{ij}}}{c_j^{+}},\frac{c_{\mathrm{ij}}}{c_j^{+}}),c_j^{+}=\max \{a_{\mathrm{ij}},b_{\mathrm{ij}},c_{\mathrm{ij}}\},x_{\mathrm{ij}}\∈I^{\′};i=\mathrm{1,2},...,k\\ (\frac{a_j^{-}}{c_{\mathrm{ij}}},\frac{a_j^{-}}{b_{\mathrm{ij}}},\frac{a_j^{-}}{a_{\mathrm{ij}}}),a_j^{-}=\min \{a_{\mathrm{ij}},b_{\mathrm{ij}},c_{\mathrm{ij}}\},x_{\mathrm{ij}}\∈I^{\′\′};i=\mathrm{1,2},...,k\end{array}\right.---\left(12\right)$

Wherein, for qualitative index (a _ij, b _ij, c _ij), when it is gain-type index, for a _ij, b _ij, c _ijin maximal value, for a _ij, b _ij, c _ijminimum value.

I' is incremental index; I " is cost-effectivenes index.

2.3 according to the weight of evaluation index and standardization fuzzy matrix, and setting up Weighted Fuzzy matrix is:

V＝[v _ij] _k×m,i＝1,2,...,k；j＝1,2,...,m (13)

Wherein $v_{\mathrm{ij}}=r_{\mathrm{ij}}\×w_j^{*}$

2.4 build fuzzy positive ideal solution A+ and fuzzy minus ideal result A-is respectively:

$A^{+}=\{v_1^{+},v_2^{+},...,v_j^{+}\},$ i＝1,2,...,m；j＝1,2,...,n (14)

$A^{-}=\{v_1^{-},v_2^{-},...,v_j^{-}\},$ i＝1,2,...,m；j＝1,2,...,n (15)

Wherein,

$v_j^{+}=\left\{\begin{array}{c}\max v_{\mathrm{ij}},j\∈I^{\′},j=\mathrm{1,2},...,m\\ \min v_{\mathrm{ij}},j\∈I^{\′\′},j=\mathrm{1,2},...,m\end{array}\right.$

$v_j^{-}=\left\{\begin{array}{c}\min v_{\mathrm{ij}},j\∈I^{\′},j=\mathrm{1,2},...,m\\ \max v_{\mathrm{ij}},j\∈I^{\′\′},j=\mathrm{1,2},...,m\end{array}\right.$

2.5 distances calculating each alternatives and positive ideal solution and minus ideal result are respectively:

$d_i^{+}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}d(v_{\mathrm{ij}},v_j^{+}),$ j＝1,2,...,n (16)

$d_i^{-}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}d(v_{\mathrm{ij}},v_j^{-}),$ j＝1,2,...,n (17)

If there are 2 Triangular Fuzzy Number a=(a ₁, a ₂, a ₃), b=(b ₁, b ₂, b ₃), then the distance between them is:

$d(a,b)=\sqrt{\frac{1}{3}[{(a_1-b_1)}^2+{(a_2-b_2)}^2+{(a_3-b_3)}^2]}---\left(18\right)$

2.6 approach degrees calculating each scheme and ideal solution are:

$C_i=\frac{d_i^{-}}{d_i^{+}+d_i^{-}}---\left(19\right)$

C _ilarger, option A _imore close to ideal value, each scheme is according to C _isize carries out trap queuing.

Technical conceive of the present invention is: herein first according to principle and the system of the Green Evaluation of achievement in research Erecting and improving science both domestic and external, and strictly distinguished profit evaluation model and cost type qualitative index, profit evaluation model and cost type quantitative target, then according to this principle and system, utilize principle and the method for fuzzy AHP and fuzzy TOPSIS, propose the relative Comprehensive evaluation on green degree method of Environmental Consciousness Design engineering goods based on fuzzy AHP-TOPSIS, research has cost type and profit evaluation model is qualitative and the Green Evaluation system of quantitative target, sets up the evaluation procedure of concrete norm.The method has science in theory, has operability in practice, is a kind of effective ways.

Beneficial effect of the present invention is mainly manifested in: carried out strict differentiation to the principle of the Environmental Consciousness Design engineering goods metrics evaluation based on Life cycle and system profit evaluation model and cost type qualitative index, profit evaluation model and cost type quantitative target.For this situation, propose the relative Comprehensive evaluation on green degree method of Environmental Consciousness Design engineering goods based on fuzzy AHP-TOPSIS, the method is fully in conjunction with both advantages, first use fuzzy AHP that each index factor is divided into orderly level, science determines each level weight, build fuzzy AHP--TOPSIS Model for Comprehensive in conjunction with fuzzy TOPSIS again, the degree of closeness according to limited cost type and profit evaluation model qualitative and quantitative index and idealized target carries out sequence optimum scheme comparison.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of the Comprehensive evaluation on green degree index system of engineering goods.

Fig. 2 is the process flow diagram of the relative Green Degree Evaluation of environmental consciousness Machine Design of fuzzy AHP-TOPSIS.

Fig. 3 is the schematic diagram of the assessment indicator system of chain saw.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described.

With reference to Fig. 1 ~ Fig. 3, a kind of relative Green Degree Evaluation of environmental consciousness scheme of machine design based on fuzzy AHP-TOPSIS, described method comprises the steps:

The first step, the target layers carried out based on fuzzy AHP always sorts

Target layers always sorts and refers to the ranking value of described bottom Index element relative to the relative importance of general objective.

1.1 couples of kth layer n being under the jurisdiction of kth-1 layer of certain index _kwhen individual index is evaluated, in the comparator matrix between two of metrics evaluation, Triangular Fuzzy Number M1, M3, M5, M7, M9 are used to replace traditional 1,3,5,7,9, and M2, M4, M6, M8 are intermediate values, as shown in table 1.A fuzzy value can be on average integrated into formula (1) when there being multiple expert.

$M_{\mathrm{ij}}^k=\frac{1}{T}\⊕(a_{\mathrm{ij}}^1+a_{\mathrm{ij}}^2+...+a_{\mathrm{ij}}^T)---\left(1\right)$

Wherein, t=1,2 ..., T represents that a common T expert gives Triangular Fuzzy Number i, j=1,2 ..., n _k;

Table 1 index is important ratio comparatively semantic variant and Triangular Fuzzy Number table between two

1.2 list the k layer n being under the jurisdiction of k-1 layer index _kthe Synthetic Judgement Matrix of individual index, then obtain fuzzy set according to formula (2) they represent the k layer n being under the jurisdiction of k-1 layer index _kthe fuzzy synthesis degree of individual index:

$S_i^k=\underset{j=1}{\overset{n_k}{\mathrm{\Σ}}}{M}_{\mathrm{ij}}^k\⊗{\left(\underset{i=1}{\overset{n_k}{\mathrm{\Σ}}}\underset{j=1}{\overset{n_k}{\mathrm{\Σ}}}{M}_{\mathrm{ij}}^k\right)}^{-1}---\left(2\right)$

i,j＝1,2,...,n _k

1.3 de-fuzzies, obtain the kth layer n being under the jurisdiction of kth-1 layer of certain index _kindividual index finally determine weight

If M ₁and M ₂convex Fuzzy number, fuzzy number M ₁>=M ₂probability level be defined as:

$V(M_1\≥M_2)=\left\{\begin{array}{cc}1& m_1\≥m_2\\ \frac{l_1-u_2}{(m_2-u_2)-(m_1-l_1)}& m_1\≤m_2,u_1\≥l_2\\ 0& \mathrm{otherwise}\end{array}\right.---\left(4\right)$

M>=M ₁, M>=..., M>=M _kprobability level be defined as:

$\begin{array}{c}V(M\≥M_1,...,M_{n_k})\\ =V[(M\≥M_1)\mathrm{and}(M\≥M_2)\mathrm{and}...\mathrm{and}(M\≥M_{n_k})]\\ =\min V(M\≥M_i),i=\mathrm{1,2},...,n_k\end{array}---\left(5\right)$

The final normalization of 1.4 each index weights

Suppose

m(P _i)＝minV(M ₁≥M _k)k＝1,2,...,n _k；k≠i (6)

Then be under the jurisdiction of the kth layer n of kth-1 layer of certain index _kthe weight vectors of individual index is:

$W^{\′}={(m\left(P_1\right),m\left(P_2\right),...,m\left(P_{n_k}\right))}^T---\left(7\right)$

To this vectorial normalization, then proper vector and weight are:

$W={(w\left(P_1\right),w\left(P_2\right),...,w\left(P_{n_k}\right))}^T---\left(8\right)$

Wherein W is non-fuzzy number, gives the weight of influence factor to object effects;

1.5 calculate the total ranking results of level

Suppose m _nit is Rn that institute is subordinate to index, and the index that Rn is subordinate to is Cn, and the index that Cn is subordinate to is O, then

$w_{m_n}^O=w_{\mathrm{Cn}}^O\×w_{\mathrm{Rn}}^{\mathrm{Cn}}\×w_{m_n}^{\mathrm{Rn}}---\left(9\right)$

Wherein, for detailed layer index m _nabout the weight of destination layer O, for detailed layer index m _nabout the weight of be subordinate to indicator layer index Rn, for indicator layer index Rn is about the weight of be subordinate to rule layer index Cn, for rule layer index Cn is about the weight of destination layer.

Second step, the optimal case carried out based on fuzzy TOPSIS solves

2.1 set up schemes synthesis judgment index system,

Set up fuzzy evaluating matrix according to formula (8), for qualitative index, adopt semanteme to judge, be divided into the classification standard of setting number, semantic variant Triangular Fuzzy Number describes; For quantitative target, corresponding concrete value is brought into initial fuzzy matrix for assessment correspondence position.

$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1m}\\ x_{21}& x_{22}& ...& x_{2m}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_{k1}& x_{k2}& ...& x_{\mathrm{km}}\end{array}\right],$ i＝1,2,...,k；j＝1,2,...,m (10)

Wherein x _ijthe fuzzy value of i-th scheme to a detailed layer jth evaluation index;

Matrix X is standardized as by 2.2:

R＝[r _ij] _k×m,i＝1,2,...,k；j＝1,2,...,m (11)

Wherein,

Quantitative target:

$r_{\mathrm{ij}}=\left\{\begin{array}{c}\frac{x_{\mathrm{ij}}-x_j^{-}}{x_j^{+}-x_j^{-}},x_{\mathrm{ij}}\∈I^{\′},i=\mathrm{1,2},...,k\\ \frac{x_j^{+}+x_{\mathrm{ij}}}{x_j^{+}-x_j^{-}},x_{\mathrm{ij}}\∈I^{\′\′},i=\mathrm{1,2},...,k\end{array}\right.---\left(12\right)$

Wherein, for x in canonical matrix X _ijthe maximal value of column, for x in canonical matrix X _ijthe minimum value of column.

Qualitative index:

$r_{\mathrm{ij}}=\left\{\begin{array}{c}(\frac{a_{\mathrm{ij}}}{c_j^{+}},\frac{b_{\mathrm{ij}}}{c_j^{+}},\frac{c_{\mathrm{ij}}}{c_j^{+}}),c_j^{+}=\max \{a_{\mathrm{ij}},b_{\mathrm{ij}},c_{\mathrm{ij}}\},x_{\mathrm{ij}}\∈I^{\′};i=\mathrm{1,2},...,k\\ (\frac{a_j^{-}}{c_{\mathrm{ij}}},\frac{a_j^{-}}{b_{\mathrm{ij}}},\frac{a_j^{-}}{a_{\mathrm{ij}}}),a_j^{-}=\min \{a_{\mathrm{ij}},b_{\mathrm{ij}},c_{\mathrm{ij}}\},x_{\mathrm{ij}}\∈I^{\′\′};i=\mathrm{1,2},...,k\end{array}\right.---\left(13\right)$

Wherein, for qualitative index (a _ij, b _ij, c _ij), when it is gain-type index, for a _ij, b _ij, c _ijin maximal value, for a _ij, b _ij, c _ijminimum value.

I' is incremental index; I " is cost-effectivenes index.

2.3 according to the weight of evaluation index and standardization fuzzy matrix, and setting up Weighted Fuzzy matrix is:

V＝[v _ij] _k×m,i＝1,2,...,k；j＝1,2,...,m (14)

Wherein $v_{\mathrm{ij}}=r_{\mathrm{ij}}\×w_j^{*}$

2.4 build fuzzy positive ideal solution A ⁺with fuzzy minus ideal result A ^-be respectively:

$A^{+}=\{v_1^{+},v_2^{+},...,v_j^{+}\},$ i＝1,2,...,m；j＝1,2,...,n (15)

$A^{-}=\{v_1^{-},v_2^{-},...,v_j^{-}\},$ i＝1,2,...,m；j＝1,2,...,n (16)

Wherein,

$v_j^{+}=\left\{\begin{array}{c}\max v_{\mathrm{ij}},j\∈I^{\′},j=\mathrm{1,2},...,m\\ \min v_{\mathrm{ij}},j\∈I^{\′\′},j=\mathrm{1,2},...,m\end{array}\right.$

$v_j^{-}=\left\{\begin{array}{c}\min v_{\mathrm{ij}},j\∈I^{\′},j=\mathrm{1,2},...,m\\ \max v_{\mathrm{ij}},j\∈I^{\′\′},j=\mathrm{1,2},...,m\end{array}\right.$

2.5 distances calculating each alternatives and positive ideal solution and minus ideal result are respectively:

$d_i^{+}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}d(v_{\mathrm{ij}},v_j^{+}),$ j＝1,2,...,n (17)

$d_i^{-}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}d(v_{\mathrm{ij}},v_j^{-}),$ j＝1,2,...,n (18)

If there are 2 Triangular Fuzzy Number a=(a ₁, a ₂, a ₃), b=(b ₁, b ₂, b ₃), then the distance between them is:

$d(a,b)=\sqrt{\frac{1}{3}[{(a_1-b_1)}^2+{(a_2-b_2)}^2+{(a_3-b_3)}^2]}---\left(19\right)$

2.6 approach degrees calculating each scheme and ideal solution are:

$C_i=\frac{d_i^{-}}{d_i^{+}+d_i^{-}}---\left(19\right)$

C _ilarger, option A _imore close to ideal value, each scheme is according to C _isize carries out trap queuing.

Example: consider specific object, sets up the assessment indicator system of chain saw, as shown in Figure 3.

1) total hierarchial sorting result is asked by fuzzy AHP

Step 1 asks each layering index relative to the weight of last layer, sets up assessment fuzzy Judgment by expert, for rule layer, the index of all the other each layers ask method consistent with it.

A) set up O-C and judge fuzzy judgment matrix, as shown in table 2.

Table 2 judges fuzzy judgment matrix

B) C1, C2, C3 fuzzy weighted values is calculated according to formula (2)

$S_1^2=\left(\mathrm{0.206,0.385,0.659}\right)$

$S_2^2=\left(\mathrm{0.175,0.296,0.549}\right)$

$S_3^2=\left(\mathrm{0.181,0.319,0.571}\right)$

C) de-fuzzy, obtains C1 according to formula (3), (4), the weight of C2 and C3

$V(S_1^2\≥S_2^2)=1$

$V(S_1^2\≥S_3^2)=1$

$V(S_2^2\≥S_1^2)=\frac{0.206-0.549}{(0.296-0.549)-(0.385-0.206)}=0.794$

$V(S_2^2\≥S_3^2)=\frac{0.181-0.549}{(0.296-0.549)-(0.319-0.181)}=0.941$

$V(S_3^2\≥S_1^2)=\frac{0.206-0.571}{(0.319-0.571)-(0.385-0.206)}=0.847$

$V(S_3^2\≥S_2^2)=1$

$m\left(C1\right)=\min V(S_1^2\≥S_2^2,S_3^2)=1$

$m\left(C2\right)=\min V(S_2^2\≥S_1^2,S_3^2)=0.794$

$m\left(C3\right)=\min V(S_3^2\≥S_1^2,S_2^2)=0.847$

According to formula (5), (6),

W'＝(1,0.794,0.847)

D) by above weight normalization, the final weight of each index of rule layer is obtained according to formula (7)

$W=(w_{C1}^O,w_{C2}^O,w_{C3}^O)=\left(\mathrm{0.379,0.300,0.321}\right)$

Step 2 calculates the total ranking results of level.

According to formula (8), be example in the hope of m1, m2-m11 is in Table.

$\begin{array}{c}{w}_{m1}^O=w_{C1}^O\×w_{R1}^{C1}\×w_{m1}^{R1}\\ =0.379\×0.652\×0.153\\ =0.038\end{array}$

Table 3 total hierarchial sorting result

2) ask the weight of each scheme with fuzzy TOPSIS, namely choose the best alternatives.

Step 1 sets up the Comprehensive Evaluation index system of each scheme, and it is as shown in the table.

The Comprehensive Evaluation index system of each scheme of table 4

Step 2 sets up fuzzy evaluating matrix according to formula (9).

$\begin{array}{c}X=\left[\begin{array}{ccccccc}20.3& 83.5& 120& 81& 76.5& 20.8& 3.6\\ 15.7& 96.1& 110& 82.3& 82.3& 15.2& 7.1\\ 18.2& 91.5& 100& 79.9& 79.9& 23.3& 5.3\end{array}\right.\\ \left.\begin{array}{ccccc}81.6& 40.3& \left(\mathrm{0.3,0.5,0.7}\right)& \left(\mathrm{0.5,0.7,0.9}\right)& 75.3\\ 76.8& 46.7& \left(\mathrm{0.5,0.7,0.9}\right)& 0.5,\mathrm{0.7,0.9}& 80.2\\ 73.9& 41.1& \left(\mathrm{0.1,0.3,0.5}\right)& \mathrm{0.7,0.9,1}& 85.1\end{array}\right]\end{array}$

Step 3 carries out standardization according to formula (10) (11) (12) to X.

$\begin{array}{c}R=\left[\begin{array}{ccccccc}0& 1& 0& 0.6& 0& 0.691& 1\\ 1& 0& 0.5& 1& 1& 0& 0\\ 0.457& 0.380& 1& 0& 0.586& 1& 0.514\end{array}\right.\\ \left.\begin{array}{ccccc}1& 0& \left(\mathrm{0.333,0.556,0.778}\right)& \left(\mathrm{0.5,0.7,0.9}\right)& 0\\ 0.377& 1& \left(\mathrm{0.556,0.778,1}\right)& \left(\mathrm{0.5,0.7,0.9}\right)& 0.5\\ 0& 0.125& \left(\mathrm{0.111,0.333,0.556}\right)& \left(\mathrm{0.7,0.9,1}\right)& 1\end{array}\right]\end{array}$

Step 4 builds Weighted Fuzzy Evaluations matrix according to formula (13).

$\begin{array}{c}V=\left[\begin{array}{ccccccc}0& 0.209& 0& 0& 0.124& 0.037& 0.01\\ \mathrm{0.0.38}& 0& 0.034& 0.064& 0& 0& 0\\ 0.017& 0.079& 0.068& 0.038& 0.179& 0.054& 0.05\end{array}\right.\\ \left.\begin{array}{ccccc}0.037& 0& \left(\mathrm{0.031,0.052,0.072}\right)& \left(\mathrm{0.02,0.027,0.035}\right)& 0\\ 0.014& 0.02& \left(\mathrm{0.052,0.072,0.093}\right)& \left(\mathrm{0.02,0.027,0.035}\right)& 0.095\\ 0& 0.003& \left(\mathrm{0.01,0.031,0.052}\right)& \left(\mathrm{0.027,0.035,0.039}\right)& 0.189\end{array}\right]\end{array}$

Step 5 builds positive and negative ideal solution according to formula (14) (15).

$\begin{array}{c}\left[\begin{array}{ccccccc}A+& 0.38& 0.209& 0.068& 0.064& 0.179& 0.054\\ A-& 0& 0& 0& 0& 0& 0\end{array}\right.\\ \left.\begin{array}{cccccc}0.01& 0.037& 0.02& \left(\mathrm{0.052,0.072,0.093}\right)& \left(\mathrm{0.027,0.035,0.039}\right)& 0.189\\ 0& 0& 0& \left(\mathrm{0.01,0.031,0.052}\right)& \left(\mathrm{0.02,0.027,0.035}\right)& 0\end{array}\right]\end{array}$

Step 6 calculates the distance of each scheme and positive and negative ideal solution according to formula (16) (17) (18).

$\begin{array}{c}{d}_1^{+}=\sqrt{\begin{array}{c}{(0.038-0)}^2+{(0.209-0.209)}^2+\·\·\·\\ +\frac{1}{3}[{(0.052-0.031)}^2+{(0.072-0.052)}^2+{(0.039-0.072)}^2]\\ +\·\·\·+{(0.189-0)}^2\end{array}}\\ =0.224\end{array}$

$d_1^{-}=0.228$

$d_2^{+}=0.255$

$d_2^{-}=0.055$

$d_3^{+}=0.042$

$d_3^{-}=0.254$

Step 7 calculates the relative similarity degree of each scheme and ideal solution according to formula (19).

C ₁＝0.504；C ₂＝0.177；C ₃＝0.858

Due to C ₃> C ₁> C ₂, so scheme 3 is optimal case.

Claims (1)

1., based on the relative Green Degree Evaluation of environmental consciousness scheme of machine design of fuzzy AHP-TOPSIS, it is characterized in that, comprise the steps:

The first step, the target layers carried out based on fuzzy AHP always sorts

Target layers always sorts and refers to the ranking value of described bottom Index element relative to the relative importance of general objective;

1.1 couples of kth layer n being under the jurisdiction of kth-1 layer of certain index _kwhen individual index is evaluated, in the comparator matrix between two of metrics evaluation, Triangular Fuzzy Number M1, M3, M5, M7, M9 is used to replace traditional 1,3,5,7,9, and M2, M4, M6, M8 are intermediate values, be on average integrated into a fuzzy value when there being multiple expert opinion with formula (1);

$M_{\mathrm{ij}}^k=\frac{1}{T}\⊕(a_{\mathrm{ij}}^1+a_{\mathrm{ij}}^2+...+a_{\mathrm{ij}}^T)---\left(1\right)$

Wherein, t=1,2 ..., T represents that a common T expert gives Triangular Fuzzy Number $a_{\mathrm{ij}}^t=(l_{\mathrm{ij}}^t,m_{\mathrm{ij}}^t,n_{\mathrm{ij}}^t),i,j=\mathrm{1,2},...,n_k;$

1.2 list the k layer n being under the jurisdiction of k-1 layer index _kthe Synthetic Judgement Matrix of individual index, then according to formula (2), obtain fuzzy set they represent the k layer n being under the jurisdiction of k-1 layer index _kthe fuzzy synthesis degree of individual index:

$S_i^k=\underset{j=1}{\overset{n_k}{\mathrm{\Σ}}}{M}_{\mathrm{ij}}^k\⊗{\left(\underset{i=1}{\overset{n_k}{\mathrm{\Σ}}}\underset{j=1}{\overset{n_k}{\mathrm{\Σ}}}{M}_{\mathrm{ij}}^k\right)}^{-1}---\left(2\right)$

i,j＝1,2,...,n _k

1.3 de-fuzzies, obtain the kth layer n being under the jurisdiction of kth-1 layer of certain index _kindividual index finally determine weight

If M ₁and M ₂convex Fuzzy number, fuzzy number M ₁>=M ₂probability level be defined as:

$V(M_1\≥M_2)=\left\{\begin{array}{cc}1& m_1\≥m_2\\ \frac{l_1-u_2}{(m_2-u_2)-(m_1-l_1)}& m_1\≤m_2,u_1\≥l_2\\ 0& \mathrm{otherwise}\end{array}\right.---\left(3\right)$

M>=M ₁, M>=..., M>=M _kprobability level be defined as:

$\begin{array}{c}V(M\≥M_1,...,M_{n_k})\\ =V[(M\≥M_1)\mathrm{and}(M\≥M_2)\mathrm{and}...\mathrm{and}(M\≥M_{n_k})]\\ =\min V(M\≥M_i),i=\mathrm{1,2},...,n_k\end{array}---\left(4\right)$

The final normalization of 1.4 each index weights

Suppose

m(P _i)＝min V(M ₁≥M _k) k＝1,2,...,n _k；k≠i (5)

Then be under the jurisdiction of the kth layer n of kth-1 layer of certain index _kthe weight vectors of individual index is:

$W^{\′}={(m\left(P_1\right),m\left(P_2\right),...,m\left(P_{n_k}\right))}^T---\left(6\right)$

To this vectorial normalization, then proper vector and weight are:

$W={(w\left(P_1\right),w\left(P_2\right),...,w\left(P_{n_k}\right))}^T---\left(7\right)$

Wherein W is non-fuzzy number, gives the weight of influence factor to object effects;

1.5 calculate the total ranking results of level

Suppose m _nit is Rn that institute is subordinate to index, and the index that Rn is subordinate to is Cn, and the index that Cn is subordinate to is O, then

$w_{m_n}^O=w_{\mathrm{Cn}}^O\×w_{\mathrm{Rn}}^{\mathrm{Cn}}\×w_{m_n}^{\mathrm{Rn}}---\left(8\right)$

Wherein, for detailed layer index m _nabout the weight of destination layer O, for detailed layer index m _nabout the weight of be subordinate to indicator layer index Rn, for indicator layer index Rn is about the weight of be subordinate to rule layer index Cn, for rule layer index Cn is about the weight of destination layer;

Second step, the optimal case carried out based on fuzzy TOPSIS solves

The 2.1 Comprehensive Evaluation index systems setting up each scheme;

Set up fuzzy evaluating matrix according to formula (8), for qualitative index, adopt semanteme to judge, be divided into the classification standard of setting number, semantic variant Triangular Fuzzy Number describes; For quantitative target, corresponding concrete value is brought into initial fuzzy matrix for assessment correspondence position;

$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1m}\\ x_{21}& x_{22}& ...& x_{2m}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_{k1}& x_{k2}& ...& x_{\mathrm{km}}\end{array}\right],i=\mathrm{1,2},...,k;j=\mathrm{1,2},...,m---\left(9\right)$

Wherein x _ijthe fuzzy value of i-th scheme to a detailed layer jth evaluation index;

Matrix X is standardized as by 2.2:

R＝[r _ij] _k×m,i＝1,2,...,k；j＝1,2,...,m (10)

Wherein, quantitative target:

$r_{\mathrm{ij}}=\left\{\begin{array}{c}\frac{x_{\mathrm{ij}}-x_j^{-}}{x_j^{+}-x_j^{-}},x_{\mathrm{ij}}\∈I^{\′},i=\mathrm{1,2},...,k\\ \frac{x_j^{+}-x_{\mathrm{ij}}}{x_j^{+}-x_j^{-}},x_{\mathrm{ij}}\∈I^{\′\′},i=\mathrm{1,2},...,k\end{array}\right.---\left(11\right)$

Wherein, for x in canonical matrix X _ijthe maximal value of column, for x in canonical matrix X _ijthe minimum value of column;

Qualitative index:

$r_{\mathrm{ij}}=\left\{\begin{array}{c}(\frac{a_{\mathrm{ij}}}{c_j^{+}},\frac{b_{\mathrm{ij}}}{c_j^{+}},\frac{c_{\mathrm{ij}}}{c_j^{+}}),c_j^{+}=\max \{a_{\mathrm{ij}},b_{\mathrm{ij}},c_{\mathrm{ij}}\},x_{\mathrm{ij}}\∈I^{\′};i=\mathrm{1,2},...,k\\ (\frac{a_j^{-}}{c_{\mathrm{ij}}},\frac{a_j^{-}}{b_{\mathrm{ij}}},\frac{a_j^{-}}{a_{\mathrm{ij}}}),a_j^{-}=\min \{a_{\mathrm{ij}},b_{\mathrm{ij}},c_{\mathrm{ij}}\},x_{\mathrm{ij}}\∈I^{\′\′};i=\mathrm{1,2},...,k\end{array}\right.---\left(12\right)$

Wherein, for qualitative index (a _ij, b _ij, c _ij), when it is gain-type index, for a _ij, b _ij, c _ijin maximal value, for a _ij, b _ij, c _ijminimum value;

I ' is incremental index; I " is cost-effectivenes index;

2.3 according to the weight of evaluation index and standardization fuzzy matrix, and setting up Weighted Fuzzy matrix is:

V＝[v _ij] _k×m,i＝1,2,...,k；j＝1,2,...,m (13)

Wherein $v_{\mathrm{ij}}=r_{\mathrm{ij}}\×w_j^{*}$

2.4 build fuzzy positive ideal solution A ⁺with fuzzy minus ideal result A ^-be respectively:

$A^{+}=\{v_1^{+},v_2^{+},...,v_j^{+}\},i=\mathrm{1,2},...,m;j=\mathrm{1,2},...,n---\left(14\right)$

$A^{-}=\{v_1^{-},v_2^{-},...,v_j^{-}\},i=\mathrm{1,2},...,m;j=\mathrm{1,2},...,n---\left(15\right)$

Wherein,

$v_j^{+}=\left\{\begin{array}{c}\max v_{\mathrm{ij}},j\∈I^{\′},j=\mathrm{1,2},...,m\\ \min v_{\mathrm{ij}},j\∈I^{\′\′},j=\mathrm{1,2},...,m\end{array}\right.$

$v_j^{-}=\left\{\begin{array}{c}\min v_{\mathrm{ij}},j\∈I^{\′},j=\mathrm{1,2},...,m\\ \max v_{\mathrm{ij}},j\∈I^{\′\′},j=\mathrm{1,2},...,m\end{array}\right.$

2.5 distances calculating each alternatives and positive ideal solution and minus ideal result are respectively:

$d_i^{+}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}d(v_{\mathrm{ij}},v_j^{+}),j=\mathrm{1,2},...,n---\left(16\right)$

$d_i^{-}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}d(v_{\mathrm{ij}},v_j^{-}),j=\mathrm{1,2},...,n---\left(17\right)$

If there are 2 Triangular Fuzzy Number a=(a ₁, a ₂, a ₃), b=(b ₁, b ₂, b ₃), then the distance between them is:

$d(a,b)=\sqrt{\frac{1}{3}[{(a_1-b_1)}^2+{(a_2-b_2)}^2+{(a_3-b_3)}^2]}---\left(18\right)$

2.6 approach degrees calculating each scheme and ideal solution are:

$C_i=\frac{d_i^{-}}{d_i^{+}+d_i^{-}}---\left(19\right)$

Each scheme is according to C _isize carries out trap queuing, C _ilarger, option A _imore close to ideal value.