CN108921575A - A kind of Bearing Manufacturing Enterprise green supplier discrimination method not known under incomplete information environment - Google Patents

Abstract

The invention discloses a kind of Bearing Manufacturing Enterprise green supplier discrimination methods not known under incomplete information environment.Initially set up the stratification index system of Bearing Manufacturing Enterprise green supplier identification；Obtain the index value of the potential green supplier of Bearing Manufacturing Enterprise；The index value of potential green supplier is handled using degree of membership；Consider that green supplier recognizes the mutual influence relationship of index at different levels in stratification index system, construct green supplier's identification network analytical framework of Bearing Manufacturing Enterprise, judge of the expert to index importance is indicated using Trapezoid Fuzzy Number, the evaluation result of multidigit expert is integrated using coarse boundary interval, thus the different degree of parameter；Potential green supplier is recognized based on two rank weighted evidence theoretical models, obtains classic green supplier.The present invention is using convenient, it is easy to accomplish, it is provided a method not know the identification of the green supplier under incomplete information environment.

Description

A kind of Bearing Manufacturing Enterprise green supplier not known under incomplete information environment distinguishes Knowledge method

Technical field

The present invention relates to greening supply chain planning field, specially a kind of bearing system not known under incomplete information environment Make enterprise Green supplier discrimination method.

Background technique

Bearing is a kind of important spare part in contemporary mechanical equipment.Its major function is to support mechanical rotary body, is reduced Coefficient of friction in its motion process, and guarantee its rotating accuracy.Bearing mnanufacture plays important angle in entire national economy Color.With the enhancing of global environmental consciousness, Bearing Manufacturing Enterprise is faced with more stringent environmental requirement.Greening supply chain is Inevitable choice as Bearing Manufacturing Enterprise response environment problem.Greening supply chain planning includes green supplier's identification, green The links such as product design, green production, green marketing and waste recovery.Green supplier's identification is in the upper of entire supply chain Trip, the influence to environmental protection and save the cost can be transmitted to each section in downstream by supply chain.

In greening supply chain planning process, various factors becomes the relationship between supplier and Bearing Manufacturing Enterprise It is complicated and fuzzy.The greening supply chain planning of Bearing Manufacturing Enterprise must be continuously improved, to adapt to environment complicated and changeable.? Under this background, green supplier's identification plays extremely important in terms of reducing cost, improving product quality and the market competitiveness Effect.By effective identification to supplier, timely adjustable strategies can promote the green of entire supply chain, develop in a healthy way. As it can be seen that green supplier's identification plays conclusive effect in greening supply chain planning, entire supply chain directly decide Competitiveness.The rise of internet is that the green supplier's identification of Bearing Manufacturing Enterprise implementation is provided convenience, but faces numerous confessions Quotient is answered, Bearing Manufacturing Enterprise still can not quickly select the green supplier for meeting self-demand, how fast and effeciently implement green Color supplier identification becomes the critical issue in Modern Green supply chain planning.

Urgent problem to be solved mainly includes in current green supplier identification：(1) in the reality of green supplier identification In work, the information of supplier is not clear enough, often smudgy, or even loses.Deterministic identification model has been unable to meet The needs of increasingly complicated identification environment.(2) green supplier's identification is a complicated decision problem, and index is mutually closed Connection.In parameter different degree, the core concept of traditional analytic hierarchy process (AHP) is will to establish isolated, level index system. Upper layer element is only considered to the dominating role of bottom element, and the element in same layer is considered mutually independent.So And the relationship between these indexs is often interdependence, also provides feedback effects sometimes.Therefore, traditional step analysis Method can not handle the mutually influence relationship of the complexity between index, and the different degree of acquisition is unscientific.(3) important in solution index When spending, used at present is the judgement that expert is described with perfect number to index relative importance, cannot reflect practical thinking Ambiguity and subjectivity indicate that the judgement of expert is more reasonable with fuzzy number.After introducing fuzzy number and indicating expert judgments, such as What analysis and processing fuzzy number bring inaccuracy and inconsistency are also the problem for needing to solve.

Summary of the invention

For solve Bearing Manufacturing Enterprise in green supplier identification supplier information is indefinite, index mutually influences and special The fuzzy problem of family's thinking, the present invention provides a kind of Bearing Manufacturing Enterprise greens not known under incomplete information environment Supplier's discrimination method.Initially set up the stratification index system of green supplier's identification；Obtain the finger of potential green supplier Scale value；The index value of potential green supplier is handled using degree of membership；Consider that green supplier recognizes in stratification index system The mutual influence relationship of indexs at different levels is constructed the network analysis frame of green supplier's identification, is indicated using Trapezoid Fuzzy Number special Judge of the family to index importance, the evaluation result of multidigit expert is integrated using coarse boundary interval, thus parameter Different degree；Potential green supplier is recognized based on two rank weighted evidence theoretical models, classic green is obtained and supplies Answer quotient.

The technical scheme is that：

A kind of Bearing Manufacturing Enterprise green supplier discrimination method not known under incomplete information environment, feature It is, includes the following steps：

Step 1：Establish the stratification index system of Bearing Manufacturing Enterprise green supplier identification；

Indicate that green supplier recognizes general objective with AO, AO includes four first class index：Product attribute C₁, internal competition power C₂, external competitive power C₃With collaboration capabilities C₄；

C₁Including four two-level index：Monovalent C_1,1, critical size error C_1,2, service C_1,3, degree of flexibility C_1,4；C_1,1、 C_1,2Belong to metered dose, C_1,3、C_1,4Belong to qualitative type；

C₂Including three two-level index：Innovation ability C_2,1, manufacturing capacity C_2,2, adaptability C_2,3；C_2,1、C_2,2、C_2,3Belong to In qualitative type；

C₃Including four two-level index：Economic environment C_3,1, geographical environment C_3,2, social environment C_3,3, legal environment C_3,4； C_3,1、 C_3,2、C_3,3、C_3,4Belong to qualitative type；

C₄Including four two-level index：Technology compatibility C_4,1, culture compatibility C_4,2, information platform compatibility C_4,3, reputation C_4,4；C_4,1、C_4,2、C_4,3、C_4,4Belong to qualitative type；

Step 2：Obtain the index value of the potential green supplier of Bearing Manufacturing Enterprise；

For metered dose index C_1,1、C_1,2, directly acquire the index value of potential green supplier；

For qualitative type index C_1,3、C_1,4、C_2,1、C_2,2、C_2,3、C_3,1、C_3,2、C_3,3、C_3,4、C_4,1、C_4,2、C_4,3、 C_4,4, by After manager investigates the actual conditions of potential green supplier, marking is provided as index value；

If performance of the potential green supplier in certain index is completely specified, index value exact value table Show；If potential performance of the green supplier in certain index be it is uncertain, which is indicated with section；If Potential performance of the green supplier in certain index is totally unknown, then the index value be it is incomplete, with null value table Show；

Step 3：The index value of the potential green supplier of potential Bearing Manufacturing Enterprise is handled using degree of membership；

There is potential green supplier of M family, successively uses x₁,x₂,...,x_MIt indicates；Potential green supplier x_rIn index C_j,lOn Index value v_r,(j,l)It indicates, wherein r=1,2 ..., M, j=1,2 ..., N, l=1,2 ..., n_j；Standardization index value v′_r,(j,l)Calculation method be：If index C_j,lBelong to income class index, then v '_r,(j,l)=v_r,(j,l)/max{v_1,(j,l), v_2,(j,l),...,v_M,(j,l)}；If index C_j,lBelong to cost class index, then v '_r,(j,l)=min { v_1,(j,l),v_2,(j,l),..., v_M,(j,l)}/v_r,(j,l)；C_1,1、C_1,2Belong to cost class index, C_1,3、C_1,4、C_2,1、C_2,2、C_2,3、C_3,1、 C₃,₂、C_3,3、C_3,4、 C_4,1、C_4,2、C_4,3、C_4,4Belong to income class index；

Score value, which is arranged, is：π₁=0.1, π₂=0.3, π₃=0.5, π₄=0.7, π₅=0.9, it is corresponding in turn to comment：It is very poor G₁, difference G₂, medium G₃, good G₄, fine G₅；G₁、G₂、G₃、G₄、G₅Corresponding standardization index value successively uses v '_(j,l)(G₁), v′_(j,l)(G₂),v′_(j,l)(G₃),v′_(j,l)(G₄),v′_(j,l)(G₅) indicate, calculation method is：

v′_(j,l)(G₁)=min { v '_1,(j,l),v′_2,(j,l),...,v′_M,(j,_l),

v′_(j,l)(G₅)=max { v '_1,(j,l),v′_2,(j,l),...,v′_M,(j,l),

Index value belongs to comment G_uDegree of membership β_uIt indicates, using degree of membership β_uTo handle potential green supplier x_r's In index C_j,lOn index value v_r,(j,l), the value of utility τ that is obtained after processing_r,_(j,l)It indicates；If v_r,_(j,l)Equal to accurate Value χ₁Or it is equal to section [χ₁,χ₂], if v '_(j,l)(G_p)≤χ₁≤v′_(j,l)(G_p+1) or v '_(j,l)(G_p)≤χ₁≤χ₂≤v′_(j,l) (G_p+1), wherein p=1,2,3,4, then τ_r,(j,l)=β_pπ_p+β_p+1π_p+1；If v '_(j,l)(G_p)≤χ₁≤v′_(j,l)(G_p+1) and v '_(j,l) (G_p+1)≤χ₂≤v′_(j,l)(G_p+2), wherein p=1,2,3, then τ_r,(j,l)=β_pπ_p+β_p+1π_p+1+β_p+2π_p+2；If v '_(j,l)(G_p)≤ χ₁≤v′_(j,l)(G_p+1) and v '_(j,l)(G_o)≤χ₂≤v′_(j,l)(G_o+1), wherein p=1,2,3,4, o=1,2,3,4, and o > p+1, Then τ_r,(j,l)=β_pπ_p+β_p+1π_p+1+...+β_oπ_o+β_o+1π_o+1；

Step 4：Consider that Bearing Manufacturing Enterprise green supplier recognizes the mutual influence of index at different levels in stratification index system Relationship, the network analysis frame of building Bearing Manufacturing Enterprise green supplier identification；

Control layer element is AO；Network layer includes following element group：C₁,C₂,…,C_N, wherein N=4；Element group C_iIncluding ElementWherein i=1,2 ..., N, n_iIndicate C_iThe element number for being included, then n₁=4, n₂=3, n₃=4, n₄ =4；Each element group mutually influences, and the element for including in each element group also mutually influences；

Step 5：Judge of the expert to index importance is indicated using Trapezoid Fuzzy Number, is collected using coarse boundary interval At the evaluation result of multidigit expert, thus the different degree of parameter；

Step 5.1：Using control layer elements A O as criterion, with element group C_jElements C_j,lFor secondary criterion, wherein j=1, 2 ..., N, l=1,2 ..., n_j, i=1,2 ..., N；

According to element group C_iIncluded element is to C_j,lInfluence degree, carry out element group C_iThe indirect advantage of included element Compare；Q experts are shared, the reciprocal jdgement matrix of Trapezoid Fuzzy Number that wherein expert k is provided isHave：

Here, k=1,2 ..., q,It indicates " to be directed to Elements C_j,l, Elements C_i,hCompared to Elements C_i,gIndirect advantage score ", Wherein g, h=1,2 ..., n_iAnd g ≠ h；It is a Trapezoid Fuzzy Number, is expressed as WithIt is positive real number and satisfaction

To the reciprocal jdgement matrix of Trapezoid Fuzzy NumberIt carries out consistency check and goes to step 5.2 if qualified； If unqualified, by k pairs of expertIt is adjusted；The reciprocal jdgement matrix of the Trapezoid Fuzzy Number of other experts is held The same operation of row, until the reciprocal jdgement matrix of q Trapezoid Fuzzy Number passes through consistency check；

Step 5.2：By E^k,i,(j,l)Dismantling is four matrixes：

Step 5.3：Based on A^1,i,(j,l),A^2,i,(j,l),...,A^q,i,(j,l), construct group decision matrixIts InFor aggregate form,ForIts coarse boundary interval isWhereinForGatheringIn coarse lower limit value and coarse upper limit value；

Step 5.4：Set of computationsCoarse boundary intervalArithmetic average form WhereinFor setCoarse lower limit value and thick Rough upper limit value；

Step 5.5：Construct coarse jdgement matrixBy EA^i,(j,l)Dismantling is coarse lower limit value MatrixWith coarse upper limit value matrix

Step 5.6：For EA^i,(j,l),-And EA^i,(j,l),+, the feature vector for corresponding to maximum eigenvalue is calculated, respectively：WhereinRespectively For VA^i,(j,l),-、VA^i,(j,l),+Value in h dimension, h=1,2 ..., n_i；

Step 5.7：Building setWherein

Step 5.8：Similarly, forIt repeats to walk Rapid 5.3, to step 5.7, are gathered

Step 5.9：Calculate vectorWherein：

Step 5.10：By vectorSwitch toWhereinω^i,(j,l)For C_iMiddle element is to C_j,lStandardization influence degree vector；

Step 5.11：Step 5.1 is repeated to step 5.10, until calculating

Step 5.12：Construct matrixHave：

Wherein, Ω^i,jColumn vector be ω^i,(j,l)；

Step 5.13：Step 5.1 is repeated to step 5.12, calculates all Ω^i,j, wherein j=1,2 ..., N, i= 1,2,...,N；The hypermatrix Ω under control layer elements A O is constructed, is had：

Step 5.14：According to C under control layer elements A O₁,C₂,...,C_NTo C_jInfluence degree, carry out C₁,C₂,...,C_N Indirect advantage compare, using the method as step 5.1 to step 5.11, obtain relative Link Importance matrix Ψ= (ψ^i,j)_N×N, have：

Wherein column vector ψ^,j=[ψ^1,j,ψ^2,j,...,ψ^N,j]^TFor C₁,C₂,...,C_NTo C_jStandardization influence degree to Amount；

Step 5.15：Calculate the weighted type of hypermatrix ΩHaveWherein i=1,2 ..., N, j=1, 2,...,N；

Step 5.16：It is rightSquaring operations are executed, until converging to stable stateI.e.

Step 5.17：It takesAny one column, as network layer all elements Different degree vector, be expressed as：

Step 5.18：Calculate each element group C in network layer₁,C₂,...,C_NDifferent degree, wherein C_jDifferent degree beIt, will under the premise of guaranteeing different degree proportionate relationshipDifferent degreeIt amplifies, makes It is amplifiedMiddle maximum value is 0.95；It is right respectively using same methodDifferent degree Different degreeDifferent degreeC₁, C₂..., C_NDifferent degree θ₁,θ₂,...,θ_NIt amplifies；

Step 6：The potential green supplier of Bearing Manufacturing Enterprise is distinguished based on two rank weighted evidence theoretical models Know, obtains classic green supplier；

Step 6.1：Potential green supplier has M, successively usesIt indicates；Define potential green supply quotient setFor identification framework Θ, i.e.,With power set 2^ΘIndicate the set of all subsets in Θ, hereIt is independent mutually, 2^ΘIn element number be 2^M；For anyDefinition meetsWith's Set function mass:2^Θ→ [0,1] is the basic probability assignment function on identification framework Θ；For anyDefinition meets'sFor burnt member；

In index C_j,lOn, calculate burnt memberWeighting basic probability assignment functional valueWherein s=1, 2 ..., M, M+1, hereCalculation be：

Step 6.2：It is successively calculated by step 6.1It will It is inputted as evidence, carries out evidence fusion：

Wherein

Step 6.3：It is calculated using the method for step 6.2First rank evidence Fusion is completed；

Step 6.4：In index C₁On, calculate burnt memberWeighting basic probability assignment functional value Calculation be：

Step 6.5：It is calculated using the method for step 6.4It will It is inputted as evidence, carries out evidence fusion：

Wherein

Second-order evidence fusion is completed；

Step 6.6：It pressesIt is right from big to smallIt is ranked up, arrange first place is Classic green supplier.

The beneficial effects of the invention are as follows：

(1) index value that potential green supplier is handled using degree of membership, solves the green supply of Bearing Manufacturing Enterprise The indefinite problem of supplier information in quotient's identification；

(2) consider that green supplier recognizes the mutual influence relationship of index at different levels in stratification index system, construct bearing system The green supplier's identification network analytical framework for making enterprise solves the problems, such as that index mutually influences in green supplier's identification；

(3) judge of the expert to index importance is indicated using Trapezoid Fuzzy Number, is integrated using coarse boundary interval The evaluation result of multidigit expert, thus the different degree of parameter, based on two rank weighted evidence theoretical models come to potential green Supplier recognizes, and obtains classic green supplier, solves the ambiguity of expert's thinking in green supplier's identification Problem；

(4) this method is using convenient, it is easy to accomplish.

Detailed description of the invention

Fig. 1 is that a kind of Bearing Manufacturing Enterprise green supplier not known under incomplete information environment provided by the invention distinguishes The flow chart of knowledge method；

Fig. 2 is that a kind of Bearing Manufacturing Enterprise green supplier not known under incomplete information environment provided by the invention distinguishes The green supplier of knowledge method recognizes stratification index system schematic diagram；

Fig. 3 is that a kind of Bearing Manufacturing Enterprise green supplier not known under incomplete information environment provided by the invention distinguishes Green supplier's identification network analytical framework schematic diagram of knowledge method.

Specific embodiment

The description present invention combined with specific embodiments below, so that advantages and features of the invention can be easier to by this field skill Art personnel understanding, so as to make a clearer definition of the protection scope of the present invention.

Embodiment：

To Mr. Yu's Bearing Manufacturing Enterprise, there are three potential bearing retainer suppliersIt is required that being supplied from this three Classic green supplier is picked out in quotient.

Implementation steps are as follows：

Step 1：Establish the stratification index system of green supplier's identification；

Indicate that green supplier recognizes general objective with AO, AO includes four first class index：Product attribute C₁, internal competition power C₂, external competitive power C₃With collaboration capabilities C₄；

C₁Including four two-level index：Monovalent C_1,1, critical size error C_1,2, service C_1,3, degree of flexibility C_1,4；C_1,1、 C_1,2Belong to metered dose, C_1,3、C_1,4Belong to qualitative type；

C₂Including three two-level index：Innovation ability C_2,1, manufacturing capacity C_2,2, adaptability C_2,3；C_2,1、C_2,2、C_2,3Belong to In qualitative type；

C₃Including four two-level index：Economic environment C_3,1, geographical environment C_3,2, social environment C_3,3, legal environment C_3,4； C_3,1、 C_3,2、C_3,3、C_3,4Belong to qualitative type；

C₄Including four two-level index：Technology compatibility C_4,1, culture compatibility C_4,2, information platform compatibility C_4,3, reputation C_4,4；C_4,1、C_4,2、C_4,3、C_4,4Belong to qualitative type；

Step 2：Obtain the index value of potential green supplier；

For metered dose index C_1,1、C_1,2, directly acquire the index value of potential green supplier；

For qualitative type index C_1,3、C_1,4、C_2,1、C_2,2、C_2,3、C_3,1、C_3,2、C_3,3、C_3,4、C_4,1、C_4,2、C_4,3、 C_4,4, by After manager investigates the actual conditions of potential green supplier, marking is provided as index value；

If performance of the potential green supplier in certain index is completely specified, index value exact value table Show；If potential performance of the green supplier in certain index be it is uncertain, which is indicated with section；If Potential performance of the green supplier in certain index is totally unknown, then the index value be it is incomplete, with null value table Show；

The index value of the potential green supplier of three got is as shown in the table：

In C_1,1On the unit of index value be：Member indicates the unit price of supplied retainer；In C_1,2On index value Unit is：Mm indicates the critical dimension errors value of supplied retainer；Index value in remaining index is manager Marking；

Step 3：The index value of potential green supplier is handled using degree of membership；

C_1,1、C_1,2Belong to cost class index, C_1,3、C_1,4、C_2,1、C_2,2、C_2,3、C_3,1、C_3,2、C_3,3、C_3,4、C_4,1、C_4,2、 C_4,3、C_4,4Belong to income class index；The standardization index value of three potential green suppliers is as shown in the table：

Score value, which is arranged, is：π₁=0.1, π₂=0.3, π₃=0.5, π₄=0.7, π₅=0.9, it is corresponding in turn to comment：It is very poor G₁, difference G₂, medium G₃, good G₄, fine G₅；With the index value v ' that standardizes_1,(1,1)=0.0023, v '_2,(1,1)=0.0669, v′_3,(1,1)For=1.0000, calculate： v′_(,1)(G₁)=0.0023, v '_(1,1)(G₅)=1.0000, v '_(1,1)(G₂)= 0.2517, v '_(1,1)(G₃)=0.5011, v '_(1,1)(G₄)=0.7506； π₁=0.1, π₂=0.3, π₃=0.5, π₄=0.7, π₅ =0.9；So for v '_2,(1,1)=0.0669, calculating degree of membership is β₁=0.7410, β₂=0.2590, then τ_2,(1,1) =β₁π₁+β₂π₂=0.1518；

The value of utility of three potential green suppliers calculate for：

Step 4：Consider that green supplier recognizes the mutual influence relationship of index at different levels in stratification index system, building green The network analysis frame of supplier's identification；

Control layer element is AO；Network layer includes following element group：C₁,C₂,…,C_N, wherein N=4；Element group C_iIncluding ElementWherein i=1,2 ..., N, n_iIndicate C_iThe element number for being included, then n₁=4, n₂=3, n₃=4, n₄ =4；Each element group mutually influences, and the element for including in each element group also mutually influences；

Step 5：Judge of the expert to index importance is indicated using Trapezoid Fuzzy Number, is collected using coarse boundary interval At the evaluation result of multidigit expert, thus the different degree of parameter；

Step 5.1：Using control layer elements A O as criterion, with element group C₂Elements C_2,1For secondary criterion, according to element group C₁ Included element is to C_2,1Influence degree, carry out element group C₁The indirect advantage of included element compares；4 experts are shared, The reciprocal jdgement matrix of the Trapezoid Fuzzy Number provided is followed successively by：

Respectively to E^1,1,(2,1),E^2,1,(2,1),E^3,1,(2,1)And E^4,1,(2,1)Consistency check is carried out, is passed through, step is executed 5.2；

Step 5.2：By E^k,1,(2,1)Dismantling is four matrixes： WithWherein k=1,2,3,4；WithFor, have：

Step 5.3：Based on A^1,1,(2,1),A^2,1,(2,1),A^3,1,(2,1),A^4,1,(2,1), construct group decision matrix For：

WithFor, it calculates：

Coarse boundary interval be

Coarse boundary interval be

Coarse boundary interval be

Coarse boundary interval be

Step 5.4：Set of computationsCoarse boundary intervalArithmetic average form be

Step 5.5：Construct coarse jdgement matrixFor：

By EA^1,(2,1)Dismantling is coarse lower limit value matrixWith coarse upper limit value matrix

Step 5.6：ForWithCalculate the feature for corresponding to maximum eigenvalue Vector, respectively：VA^1,(2,1),-=[0.71,0.44,0.45,0.30]^T、VA^1,(2,1),+=[0.65,0.49,0.47, 0.34]^T；

Step 5.7：Construct set GA^1,(2,1)={ 0.68,0.47,0.46,0.32 }；

Step 5.8：Similarly, for：

B^1,1,(2,1),B^2,1,(2,1),B^3,1,(2,1),B^4,1,(2,1),

C^1,1,(2,1),C^2,1,(2,1),C^3,1,(2,1),C^4,1,(2,1),

D^1,1,(2,1),D^2,1,(2,1),D^3,1,(2,1),D^4,1,(2,1),

Step 5.3 is repeated to step 5.7, obtains GB^1,(2,1)={ 0.73,0.51,0.66,0.58 }；GC^1,(2,1)= {0.82,0.67,0.73,0.69}；GD^1,(2,1)={ 0.95,0.77,0.83,0.75 }；

Step 5.9：Calculate outgoing vector ω^1,(2,1)=[0.38,0.29,0.31,0.28]^T；

Step 5.10：By vector ω^1,(2,1)=[0.38,0.29,0.31,0.28]^TSwitch to ω^1,(2,1)=[0.30,0.23, 0.25,0.22]^T；

Step 5.11：Step 5.1 is repeated to step 5.10, is calculated：

ω^1,(2,2)=[0.28,0.41,0.17,0.14]^T,

ω^1,(2,3)=[0.33,0.34,0.13,0.20]^T；

Step 5.12：Construct matrixHave：

Step 5.13：Step 5.1 is repeated to step 5.12, calculates all Ω^i,j, wherein j=1,2,3,4, i=1, 2,3,4；The hypermatrix Ω under control layer elements A O is constructed, is had：

Step 5.14：According to C under control layer elements A O₁,C₂,C₃,C₄To C_jInfluence degree, carry out C₁,C₂,C₃,C₄Between The advantage of connecing compares, wherein j=1, and 2,3,4；Using the method as step 5.1 to step 5.11, relative Link Importance square is obtained Battle array Ψ=(ψ^i,j)_4×4, have：

Step 5.15：Calculate the weighted type of hypermatrix ΩHaveWherein i=1,2,3,4, j=1,2,3, 4；

Step 5.16：It is rightSquaring operations are executed, until converging to stable stateI.e.Here as t=4 Converge to stable state

Step 5.17：It takesAny one column, as network layer all elements C_1,1,C_1,2,C_1,3,C_1,4,C_2,1,C_2,2, C_2,3,C_3,1,C_3,2,C_3,3,C_3,4,C_4,1,C_4,2,C_4,3,C_4,4Different degree vector：

θ=[0.12,0.11,0.10,0.09,0.06,0.06,0.07,0.05,0.04,0.04,0.04,0 .06,0.05, 0.05,0.06]^T；

Step 5.18：Calculate each element group C in network layer₁,C₂,C₃,C₄Different degree θ₁,θ₂,θ₃,θ₄For：0.42,0.19, 0.17,0.22；

Under the premise of guaranteeing different degree proportionate relationship, by C_1,1,C_1,2,C_1,3,C_1,4Different degree θ_1,1,θ_1,2,θ_1,3,θ_1,4 It is enlarged into：0.95,0.87, 0.79,0.71；By C_2,1,C_2,2,C_2,3Different degree θ_2,1,θ_2,2,θ_2,3It is enlarged into：0.95,0.87, 0.79,0.71；By C_3,1,C_3,2,C_3,3,C_3,4Different degree θ_3,1,θ_3,2,θ_3,3,θ_3,4It is enlarged into：0.95,0.87,0.79, 0.71；By C_4,1,C_4,2,C_4,3,C_4,4Different degree θ_4,1,θ_4,2,θ_4,3,θ_4,4It is enlarged into： 0.95,0.87,0.79,0.71；It will C₁,C₂,C₃,C₄Different degree θ₁,θ₂,θ₃,θ₄It is enlarged into：0.95,0.87,0.79,0.71；

Step 6：Potential green supplier is recognized based on two rank weighted evidence theoretical models, is obtained classic Green supplier；

Step 6.1：Potential green supplier has 3, successively usesIt indicates；Define potential green supply quotient setFor identification framework Θ, i.e.,With power set 2^ΘIndicate the set of all subsets in Θ, hereMutually It is mutually independent, 2^ΘIn element number be 2³；For anyDefinition meetsWithSet function mass:2^Θ→ [0,1] is the basic probability assignment function on identification framework Θ；For anyDefinition meets 'sFor burnt member；

In index C_1,1On, calculate burnt memberWeighting basic probability assignment functional valueFor：

Step 6.2：It is successively calculated by step 6.1It obtains：

It willIt is inputted as evidence, carries out evidence fusion, obtain It arrives：

Step 6.3：It is calculated using the method for step 6.2It obtains：

First rank evidence fusion is completed；

Step 6.4：In index C₁On, calculate burnt memberWeighting basic probability assignment functional valueIt obtains：

Step 6.5：It is calculated using the method for step 6.4It obtains：

It willIt is inputted as evidence, carries out evidence fusion, obtain It arrives：

Mass (Θ)=0.5792；

Second-order evidence fusion is completed；

Step 6.6：It pressesIt is right from big to smallIt is ranked up, obtainsAs classic green supplier.

Claims (1)

1. a kind of Bearing Manufacturing Enterprise green supplier discrimination method not known under incomplete information environment, which is characterized in that Include the following steps：

Step 1：Establish the stratification index system of Bearing Manufacturing Enterprise green supplier identification；

Indicate that green supplier recognizes general objective with AO, AO includes four first class index：Product attribute C₁, internal competition power C₂, outside Portion competitiveness C₃With collaboration capabilities C₄；

C₁Including four two-level index：Monovalent C_1,1, critical size error C_1,2, service C_1,3, degree of flexibility C_1,4；C_1,1、C_1,2Belong to Metered dose, C_1,3、C_1,4Belong to qualitative type；

C₂Including three two-level index：Innovation ability C_2,1, manufacturing capacity C_2,2, adaptability C_2,3；C_2,1、C_2,2、C_2,3Belong to qualitative Type；

C₃Including four two-level index：Economic environment C_3,1, geographical environment C_3,2, social environment C_3,3, legal environment C_3,4；C_3,1、 C_3,2、C_3,3、C_3,4Belong to qualitative type；

C₄Including four two-level index：Technology compatibility C_4,1, culture compatibility C_4,2, information platform compatibility C_4,3, reputation C_4,4； C_4,1、C_4,2、C_4,3、C_4,4Belong to qualitative type；

Step 2：Obtain the index value of the potential green supplier of Bearing Manufacturing Enterprise；

For metered dose index C_1,1、C_1,2, directly acquire the index value of potential green supplier；

For qualitative type index C_1,3、C_1,4、C_2,1、C_2,2、C_2,3、C_3,1、C_3,2、C_3,3、C_3,4、C_4,1、C_4,2、C_4,3、C_4,4, by managing After person investigates the actual conditions of potential green supplier, marking is provided as index value；

If potential performance of the green supplier in certain index be it is completely specified, which is indicated with exact value； If potential performance of the green supplier in certain index be it is uncertain, which is indicated with section；If potential Performance of the green supplier in certain index is totally unknown, then the index value be it is incomplete, indicated with null value；

Step 3：The index value of the potential green supplier of potential Bearing Manufacturing Enterprise is handled using degree of membership；

There is potential green supplier of M family, successively uses x₁,x₂,...,x_MIt indicates；Potential green supplier x_rIn index C_j,lOn finger Scale value v_r,(j,l)It indicates, wherein r=1,2 ..., M, j=1,2 ..., N, l=1,2 ..., n_j；Standardization index value v′_r,(j,l)Calculation method be：If index C_j,lBelong to income class index, then v '_r,(j,l)=v_r,(j,l)/max{v_1,(j,l), v_2,(j,l),...,v_M,(j,l)}；If index C_j,lBelong to cost class index, then v '_r,(j,l)=min { v_1,(j,l),v_2,(j,l),..., v_M,(j,l)}/v_r,(j,l)；C_1,1、C_1,2Belong to cost class index, C_1,3、C_1,4、C_2,1、C_2,2、C_2,3、C_3,1、C_3,2、C_3,3、C_3,4、C_4,1、 C_4,2、C_4,3、C_4,4Belong to income class index；

Score value, which is arranged, is：π₁=0.1, π₂=0.3, π₃=0.5, π₄=0.7, π₅=0.9, it is corresponding in turn to comment：Very poor G₁, it is poor G₂, medium G₃, good G₄, fine G₅；G₁、G₂、G₃、G₄、G₅Corresponding standardization index value successively uses v '_(j,l)(G₁),v′_(j,l)(G₂), v′_(j,l)(G₃),v′_(j,l)(G₄),v′_(j,l)(G₅) indicate, calculation method is：

v′_(j,l)(G₁)=min { v '_1,(j,l),v′_2,(j,l),...,v′_M,(j,l),

v′_(j,l)(G₅)=max { v '_1,(j,l),v′_2,(j,l),...,v′_M,(j,l),

Index value belongs to comment G_uDegree of membership β_uIt indicates, using degree of membership β_uTo handle potential green supplier x_rIn index C_j,lOn index value v_r,(j,l), the value of utility τ that is obtained after processing_r,(j,l)It indicates；If v_r,(j,l)Equal to exact value χ₁Or it waits In section [χ₁,χ₂], if v '_(j,l)(G_p)≤χ₁≤v′_(j,l)(G_p+1) or v '_(j,l)(G_p)≤χ₁≤χ₂≤v′_(j,l)(G_p+1), wherein p =1,2,3,4, then τ_r,(j,l)=β_pπ_p+β_p+1π_p+1；If v '_(j,l)(G_p)≤χ₁≤v′_(j,l)(G_p+1) and v '_(j,l)(G_p+1)≤χ₂≤ v′_(j,l)(G_p+2), wherein p=1,2,3, then τ_r,(j,l)=β_pπ_p+β_p+1π_p+1+β_p+2π_p+2；If v '_(j,l)(G_p)≤χ₁≤v′_(j,l) (G_p+1) and v '_(j,l)(G_o)≤χ₂≤v′_(j,l)(G_o+1), wherein p=1,2,3,4, o=1,2,3,4, and o > p+1, then τ_r,(j,l) =β_pπ_p+β_p+1π_p+1+...+β_oπ_o+β_o+1π_o+1；

Step 4：Consider that Bearing Manufacturing Enterprise green supplier recognizes the mutual influence relationship of index at different levels in stratification index system, Construct the network analysis frame of Bearing Manufacturing Enterprise green supplier identification；

Control layer element is AO；Network layer includes following element group：C₁,C₂,…,C_N, wherein N=4；Element group C_iIncluding elementWherein i=1,2 ..., N, n_iIndicate C_iThe element number for being included, then n₁=4, n₂=3, n₃=4, n₄=4；Respectively Element group mutually influences, and the element for including in each element group also mutually influences；

Step 5：Judge of the expert to index importance is indicated using Trapezoid Fuzzy Number, is integrated using coarse boundary interval more The evaluation result of position expert, thus the different degree of parameter；

Step 5.1：Using control layer elements A O as criterion, with element group C_jElements C_j,lFor secondary criterion, wherein j=1,2 ..., N, L=1,2 ..., n_j, i=1,2 ..., N；

According to element group C_iIncluded element is to C_j,lInfluence degree, carry out element group C_iThe indirect odds ratio of included element Compared with；Q experts are shared, the reciprocal jdgement matrix of Trapezoid Fuzzy Number that wherein expert k is provided isHave：

Here, k=1,2 ..., q,It indicates " to be directed to Elements C_j,l, Elements C_i,hCompared to Elements C_i,gIndirect advantage score ", Wherein g, h=1,2 ..., n_iAnd g ≠ h；It is a Trapezoid Fuzzy Number, is expressed as WithIt is positive real number and satisfaction

To the reciprocal jdgement matrix of Trapezoid Fuzzy NumberIt carries out consistency check and goes to step 5.2 if qualified；If no Qualification, by k pairs of expertIt is adjusted；The reciprocal jdgement matrix of the Trapezoid Fuzzy Number of other experts is executed same Sample operation, until the reciprocal jdgement matrix of q Trapezoid Fuzzy Number passes through consistency check；

Step 5.2：By E^k,i,(j,l)Dismantling is four matrixes：

Step 5.3：Based on A^1,i,(j,l),A^2,i,(j,l),...,A^q,i,(j,l), construct group decision matrixWhereinFor aggregate form,ForIts coarse boundary interval isWhereinForGatheringIn coarse lower limit value and coarse upper limit value；

Step 5.4：Set of computationsCoarse boundary intervalArithmetic average form WhereinFor setCoarse lower limit value and thick Rough upper limit value；

Step 5.5：Construct coarse jdgement matrixBy EA^i,(j,l)Dismantling is coarse lower limit value matrixWith coarse upper limit value matrix

Step 5.6：For EA^i,(j,l),-And EA^i,(j,l),+, the feature vector for corresponding to maximum eigenvalue is calculated, respectively：WhereinRespectively For VA^i,(j,l),-、VA^i,(j,l),+Value in h dimension, h=1,2 ..., n_i；

Step 5.7：Building setWherein

Step 5.8：Similarly, forRepeat step 5.3 To step 5.7, gathered

Step 5.9：Calculate vectorWherein：

Step 5.10：By vectorSwitch toWherein ω^i,(j,l)For C_iMiddle element is to C_j,lStandardization influence degree vector；

Step 5.11：Step 5.1 is repeated to step 5.10, until calculating

Step 5.12：Construct matrixHave：

Wherein, Ω^i,jColumn vector be ω^i,(j,l)；

Step 5.13：Step 5.1 is repeated to step 5.12, calculates all Ω^i,j, wherein j=1,2 ..., N, i=1, 2,...,N；The hypermatrix Ω under control layer elements A O is constructed, is had：

Step 5.14：According to C under control layer elements A O₁,C₂,...,C_NTo C_jInfluence degree, carry out C₁,C₂,...,C_NIt is indirect Advantage compares, and using the method as step 5.1 to step 5.11, obtains relative Link Importance matrix Ψ=(ψ^i,j)_N×N, have：

Wherein column vector ψ '^j=[ψ^1,j,ψ^2,j,...,ψ^N,j]^TFor C₁,C₂,...,C_NTo C_jStandardization influence degree vector；

Step 5.15：Calculate the weighted type of hypermatrix ΩHaveWherein i=1,2 ..., N, j=1,2 ..., N；

Step 5.16：It is rightSquaring operations are executed, until converging to stable stateI.e.

Step 5.17：It takesAny one column, as network layer all elements Different degree vector, be expressed as：

Step 5.18：Calculate each element group C in network layer₁,C₂,...,C_NDifferent degree, wherein C_jDifferent degree be It, will under the premise of guaranteeing different degree proportionate relationshipDifferent degreeIt amplifies, makes amplifiedMiddle maximum value is 0.95；It is right respectively using same methodDifferent degree Different degreeDifferent degreeC₁,C₂,...,C_NDifferent degree θ₁,θ₂,...,θ_NIt amplifies；

Step 6：The potential green supplier of Bearing Manufacturing Enterprise is recognized based on two rank weighted evidence theoretical models, is obtained Obtain classic green supplier；

Step 6.1：Potential green supplier has M, successively usesIt indicates；Define potential green supply quotient setFor identification framework Θ, i.e.,With power set 2^ΘIndicate the set of all subsets in Θ, hereIt is independent mutually, 2^ΘIn element number be 2^M；For anyDefinition meetsWith's Set function mass:2^Θ→ [0,1] is the basic probability assignment function on identification framework Θ；For anyDefinition meets'sFor burnt member；

In index C_j,lOn, calculate burnt memberWeighting basic probability assignment functional valueWherein s=1,2 ..., M, M+ 1, hereCalculation be：

Step 6.2：It is successively calculated by step 6.1It will It is inputted as evidence, carries out evidence fusion：

Wherein

Step 6.3：It is calculated using the method for step 6.2First rank evidence fusion is complete At；

Step 6.4：In index C₁On, calculate burnt memberWeighting basic probability assignment functional valueMeter Calculation mode is：

Step 6.5：It is calculated using the method for step 6.4It will It is inputted as evidence, carries out evidence fusion：

Wherein

Second-order evidence fusion is completed.

Step 6.6：It pressesIt is right from big to smallIt is ranked up, arranges the as optimal of first place Elegant green supplier.