CN104809235B - A kind of program evaluation system and method - Google Patents
A kind of program evaluation system and method Download PDFInfo
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Abstract
The present invention provides a kind of program evaluation system and method, including：Input block, for inputting tax power method, program to be evaluated and evaluation index；Program Criterion Attribute space construction unit, decision matrix is obtained according to program to be evaluated and evaluation index calculation formula；Power index space construction unit is assigned, right vector is obtained according to the Linearly Representation multiplication for assigning weight and each tax power method that power method calculates each program evaluation index；Program evaluation model construction unit, objective optimization model is built using decision matrix and right vector according to evaluation method；Optimal solution determining unit, program evaluation model optimal solution is solved using method of Lagrange multipliers；Obtaining unit, the optimum linearity table that each evaluation index of each program is obtained according to the audience information of program to be evaluated and optimal solution go out coefficient vector and optimum combination weight vector, obtain the comprehensive evaluation value of each program.The present invention reflects subjective and objective making decision simultaneously, realizes that the science of evaluation index assigns power, improves evaluation accuracy.
Description
Technical field
The present invention relates to field of broadcast televisions, more specifically, is related to a kind of program evaluation system and method.
Background technology
In field of broadcast televisions, the multiple metrics evaluation users of generally use are to the preference of program, to evaluation criterion weight
Assignment is an important step of multiobjective decision-making.The weight of index refers to be marked on the anti-of different significance levels in evaluation procedure
Reflect, be a kind of subjective assessment of index relative importance and the comprehensive measurement objectively responded in decision-making (or assessment) problem.Power
Whether reasonable the assignment of weight is, and vital effect is played to the scientific rationality of evaluation result；If the weight hair of a certain factor
Changing, it will influence whole evaluation result.Therefore, the assignment of weight must accomplish science and objective, and this requires to seek to close
Suitable Weight Determination.
The determination method both at home and abroad on evaluation index weight coefficient has many kinds at present, according to original number when calculating weight coefficient
According to source and the difference of calculating process, these methods can substantially be divided to subjective weighting method and the major class of objective weighted model two.Subjectivity is assigned
Power Evaluation Method takes qualitatively method, rule of thumb carries out subjective judgement by expert and obtains flexible strategy, and then index is carried out again
Comprehensive assessment, such as analytic hierarchy process (AHP), expert survey, Fuzzy Analysis Method, binomial coefficient method, wherein, analytic hierarchy process (AHP) is real
Most methods for using in the application of border, it is by challenge stratification, by qualitative question quantification.Objective Weight assesses rule
Comprehensive assessment is carried out according to the dependency relation between historical data research index or the relation of index and assessment result, mainly had
The methods of Information Entropy, PCA, average variance method, VC Method, wherein, more, this enabling legislation of Information Entropy
Used data are decision matrixs, and identified attribute weight reflects the dispersion degree of property value.Subjective weighting method can be with
The micro-judgment of policymaker is embodied, the relative importance of attribute will not typically violate the general knowledge of people.But its randomness is larger,
Accuracy of determination and less reliable.Be present entitled objective standard in objective weighted model, using certain mathematical modeling, pass through
The weight coefficient of attribute is calculated.Its shortcoming is to ignore the subjective preference informations such as Subjective Knowledge and the experience of policymaker, is had
When the irrational phenomenon of weight coefficient occurs.
The content of the invention
In view of the above problems, it is an object of the invention to provide one kind reflection subjective decision and objective making decision, TV Festival is realized
The entitled program evaluation system of mesh evaluation index science and method.
According to an aspect of the present invention, there is provided a kind of program evaluation system, including：Input block, for inputting the power of tax
Method, program to be evaluated and evaluation index, wherein, the tax power method includes subjective weights method and Objective Weighting；Section
Mesh Criterion Attribute space construction unit, the program to be evaluated and the calculation formula of evaluation index inputted according to input block obtain respectively
The decision matrix of each evaluation index composition of program, i.e. program Criterion Attribute space；Power index space construction unit is assigned, according to defeated
Enter the weight of each evaluation index of each program of taxs power method calculating of unit input and with the Linearly Representation coefficient of each tax power method,
Multiplication obtains right vector, that is, assigns power index space, wherein, determined according to the weight vectors that Objective Weighting obtains with described
Plan matrix correlation, right vector F,
F=W Θ=[F1 F2 … Fn]T
Fn=wn,1θ1+wn,2θ2+…+wn,lθl
Wherein, the weight vectors matrix that matrix W obtains for every evaluation index of each program according to various tax power methods, Θ
For the Linearly Representation coefficient vector of each tax power method, wn,lThe weight of n-th of evaluation index is obtained to assign power method according to l kinds,
Weight not less than zero, n be evaluation index number, l be tax power method number, wlObtained respectively to assign power method according to l kinds
The weight vectors of the weight composition of evaluation index, and weight sum is equal to 1, θ in each weight vectorslPower side is assigned for l kinds
The Linearly Representation coefficient of method,FnFor the combining weights of n-th of evaluation index；Program is commented
Valency model construction unit, objective optimization model is built using decision matrix and right vector according at least two evaluation methods,
That is program evaluation model, wherein, the objective optimization model is double-goal optimal model or Model for Multi-Objective Optimization；Optimal solution
Determining unit, the optimal solution of above-mentioned program evaluation model is solved using method of Lagrange multipliers；Obtaining unit, according to section to be evaluated
The optimum linearity table that purpose audience information and the optimal solution obtain each evaluation index of each program goes out coefficient vector and optimal set
Weight vector is closed, so as to obtain the comprehensive evaluation value of each program.
According to another aspect of the present invention, there is provided a kind of program evaluation method, including：Select tax power method, to be evaluated
Program and evaluation index, wherein, the tax power method includes subjective weights method and Objective Weighting；Build program index category
Property space, i.e., the program to be evaluated and the calculation formula of evaluation index inputted according to input block obtain each evaluation of each program and refer to
Mark the decision matrix of composition, i.e. program Criterion Attribute space；Structure assigns power index space, i.e. is calculated according to the tax power method
The weight vectors of each evaluation index of each program simultaneously obtain right vector with the Linearly Representation coefficient of each tax power method, multiplication,
Assign power index space；Program evaluation model is built, decision matrix and right vector are utilized according at least two evaluation methods
Build Bi-objective or Model for Multi-Objective Optimization, i.e. program evaluation model；Above-mentioned program is solved using method of Lagrange multipliers to comment
The optimal solution of valency model；Each evaluation index of each program is obtained most according to the audience information of program to be evaluated and the optimal solution
Excellent Linearly Representation coefficient vector and optimal weights vector, obtain the comprehensive evaluation value of each program.
Program evaluation system and method for the present invention, which realize, considers a variety of subjective weights methods and Objective Weight
The combination weighting of method, and using at least two evaluation methods structure Bi-objective or Model for Multi-Objective Optimization, can be simultaneously anti-
Reflect subjective decision and objective making decision, realize TV programme evaluation index science assign power, improve program evaluation accuracy and
Reliability.
Brief description of the drawings
By reference to the explanation and the content of claims below in conjunction with accompanying drawing, and with to the present invention more comprehensively
Understand, other purposes and result of the invention will be more apparent and should be readily appreciated that.In the accompanying drawings：
Fig. 1 is the composition block diagram of program evaluation system of the present invention；
Fig. 2 is the flow chart of program evaluation method of the present invention；
Fig. 3 is the flow chart of program evaluation model construction method of the present invention；
Fig. 4 is the construction method of double-goal optimal model of the present invention based on discrete maximization and unitization constraints
Flow chart；
Fig. 5 is the flow chart of the method for solving of program evaluation model optimal solution of the present invention.
Identical label indicates similar or corresponding feature or function in all of the figs.
Embodiment
In the following description, for purposes of illustration, in order to provide the comprehensive understanding to one or more embodiments, explain
Many details are stated.It may be evident, however, that these embodiments can also be realized in the case of these no details.
The specific embodiment of the present invention is described in detail below with reference to accompanying drawing.
The specific embodiment of the present invention is described in detail below with reference to accompanying drawing.
Fig. 1 is the composition block diagram of program evaluation system of the present invention, as shown in figure 1, program evaluation system bag of the present invention
Include：
Input block 110, for selecting tax power method, program to be evaluated and evaluation index, wherein, the tax power method bag
Subjective weights method and Objective Weighting are included, for example, input block 110 can be touch-screen, computer, keyboard, mouse etc., its
Upper display tax power method, program to be evaluated and evaluation index select for user, and user can select m programs to be evaluated, be designated as S
={ S1,S2,…,Sm, n evaluation index, it is designated as P={ P1,P2,…,Pn, assigning power method includes such as analytic hierarchy process (AHP), specially
Family's investigation method, Fuzzy Analysis Method, the subjective weights method of binomial coefficient method and such as Information Entropy, PCA, mean square deviation
The Objective Weighting of method, VC Method.
Program Criterion Attribute space construction unit 120, the program to be evaluated inputted according to input block 110 and evaluation index
Calculation formula obtain each program each evaluation index composition decision matrix, i.e. program Criterion Attribute space, it is preferable that described
Program Criterion Attribute space also includes the specified decision matrix after the decision matrix standardization processing, for example, i-th of section
Mesh SiTo j-th of evaluation index PjProperty value be designated as aij, A=(aij)m×nReferred to as decision matrix, wherein, i=1,2 ..., m, j
=1,2 ..., n；The matrix B of normalized processing=(bij)m×nThe decision matrix referred to as to standardize, bijRepresent i-th of program Si
To j-th of evaluation index PjStandardization property value, then matrix B the i-th row represent i-th of program SiTo the category of n evaluation index
The normal value of property value, and for example, evaluation index PjFor audience ratings, then
Power index space construction unit 130 is assigned, the tax power method inputted according to input block 110 calculates respectively commenting for each program
The weight of valency index simultaneously obtains right vector with the Linearly Representation coefficient of each tax power method, multiplication, that is, assigns power index space, its
In, the weight of each evaluation index obtained according to Objective Weighting is related to the decision matrix, right vector F,
F=W Θ=[F1 F2 … Fn]T
Fn=wn,1θ1+wn,2θ2+…+wn,lθl
Wherein, the weight vectors matrix that matrix W obtains for every evaluation index of each program according to various tax power methods, Θ
For the Linearly Representation coefficient vector of each tax power method, wn,lThe weight of n-th of evaluation index is obtained to assign power method according to l kinds,
Weight not less than zero, n be evaluation index number, l be tax power method number, wlObtained respectively to assign power method according to l kinds
The weight vectors of the weight composition of evaluation index, and weight sum is equal to 1, θ in each weight vectorslPower side is assigned for l kinds
The Linearly Representation coefficient of method,FnFor the combining weights of n-th of evaluation index.
Program evaluation model construction unit 140, decision matrix and right vector are utilized according at least two evaluation methods
Bi-objective or Model for Multi-Objective Optimization, i.e. program evaluation model are built, for example, according to deviation maximization and unitization constraints
The double-goal optimal model that two kinds of evaluation methods are built using decision matrix and right vector.
Optimal solution determining unit 150, the optimal solution of above-mentioned program evaluation model is solved using method of Lagrange multipliers.
Obtaining unit 160, each evaluation that each program is obtained according to the audience information of program to be evaluated and the optimal solution refer to
Target optimum linearity table goes out coefficient vector and optimal optimum combination weight vector, so as to obtain the comprehensive evaluation value of each program.
Preferably, program evaluation model construction unit 140 includes：First single object optimization model construction unit, according to one
Kind evaluation method builds a kind of single object optimization model using decision matrix and right vector；Second single object optimization model structure
Unit is built, another single object optimization model is built using decision matrix and right vector according to another evaluation method；It is double
Objective optimization model construction unit, the linear combination of above two single object optimization model is built into binocular using linear weight sum method
Mark Optimized model.
Foregoing description shows the program evaluation model construction unit 140 of structure double-goal optimal model, but of the invention
This is not limited to, program evaluation model construction unit 140 can include multiple single object optimization model construction units, using linear
Method of weighting obtains Model for Multi-Objective Optimization.
The program evaluation model of above-mentioned program evaluation system is to the comprehensive of program evaluation index subjective weights and Objective Weight
Program evaluation model is closed, several evaluation methods can be integrated above-mentioned model is evaluated, both embody the micro-judgment of policymaker,
The dispersion degree of property value is reflected again, has been reached and has been carried out the entitled purpose of science for broadcast TV program index system.
Fig. 2 is the flow chart of program evaluation method of the present invention, as shown in Fig. 2 program evaluation method of the present invention includes：
First, in step S210, tax power method, program to be evaluated and evaluation index are selected, wherein, the tax power method
Including subjective weights method and Objective Weighting；
In step S220, build program Criterion Attribute space, i.e. i.e. according to the program to be evaluated that input block inputs with
The calculation formula of evaluation index obtains the decision matrix of each evaluation index composition of each program, i.e. program Criterion Attribute space；
In step S230, structure assigns power index space, i.e. each evaluation that each program is calculated according to the tax power method refers to
Target weight simultaneously obtains right vector with the Linearly Representation coefficient of each tax power method, multiplication, that is, assigns power index space；
In step S240, program evaluation model is built, decision matrix and right vector structure are utilized according to evaluation method
Objective optimization model, i.e. program evaluation model are built, specific building process will describe in figures 3 and 4；
In step s 250, the optimal solution of above-mentioned program evaluation model is solved using method of Lagrange multipliers, is specifically asked
Solution preocess will be described in Figure 5；
In step S260, each evaluation that each program is obtained according to the audience information of program to be evaluated and the optimal solution refers to
Target optimum linearity table goes out coefficient vector and optimum combination weight vector, so as to obtain each program comprehensive evaluation value.
Preferably, in step S220, in addition to standardization processing is carried out to the decision matrix.
Fig. 3 is the flow chart of program evaluation model construction method of the present invention, as shown in figure 3, the program evaluation model structure
Construction method includes：
First, in step S310, a kind of list is built using decision matrix and right vector according to a kind of evaluation method
Objective optimization model；
In step s 320, another monocular is built using decision matrix and right vector according to another evaluation method
Mark Optimized model；
In step S330, the linear combination of above two single object optimization model is built into binocular using linear weight sum method
Mark Optimized model.
Above-mentioned flow chart only gives the flow chart of the building method of double-goal optimal model, but the present invention is not limited to
This, when structure Model for Multi-Objective Optimization makes, it is only necessary to it is again that its is linear to build multiple single object optimization models according to the method described above
Combination.
Fig. 4 is the construction method of double-goal optimal model of the present invention based on discrete maximization and unitization constraints
Flow chart, as shown in figure 4, the construction method bag of the double-goal optimal model based on discrete maximization and unitization constraints
Include：
First, in step S410, the evaluation method based on deviation maximization utilizes decision matrix or specified decision square
Battle array structure single object optimization model, specifically, utilizes standardization property value of each program in specified decision matrix to each index
Difference structure mean dispersion error matrix J1,Then, exist
In step S320, the single object optimization model based on deviation maximization is built using mean dispersion error matrix and right vector, i.e. M1
(F)=J1F=J1W Θ,
In the step s 420, the evaluation method based on unitization constraints utilizes decision matrix or specified decision matrix
Build single object optimization model, specifically, using standardization property value of each program in specified decision matrix to each index it
With structure decision-making synthetical matrix J2,Then, decision-making synthetical matrix and right vector structure are utilized
Build the single object optimization model based on unitization constraints, i.e. M2(F)=J2F=J2W Θ,
In step S430, using weigthed sums approach by the linear combination of above two single object optimization model structure be based on from
Difference maximizes and the double-goal optimal model of unitization constraints, and the double-goal optimal model is M3(F)=J3F=J3W
Θ,Wherein, J3For biobjective scheduling coefficient matrix, aJ1+bJ2=J3, a and b are linear weighted function system
Number, a+b=1.Preferably, a=b=0.5.
Program evaluation method of the present invention builds the combination weights method based on deviation maximization and unitization constraints, not only
The comprehensive evaluation value of each program is widened the difference between different grades as far as possible, even if the comprehensive evaluation value of each program is as scattered as possible, also make each section
Purpose comprehensive evaluation value maximizes as far as possible, realizes science and assigns power, ensure that the accuracy and reliability of program evaluation.
Fig. 5 is the flow chart of the method for solving of program evaluation model optimal solution of the present invention, as shown in figure 5, program evaluates mould
The method for solving of type optimal solution includes：
First, in step S510, Lagrangian conversion is carried out to program evaluation model, for example, construction is based on deviation most
The Lagrangian of the double-goal optimal model of bigization and unitization constraints
In step S520, to the program evaluation model derivation by Lagrange conversion, it is zero to find first derivative
Linearly Representation coefficient, carry it into constraints and obtain optimal solution, wherein, constraints ΘTΘ=1, and meet Θ simultaneously
>=0, such as the first derivative of upper example function is solved, find the Linearly Representation coefficient that first derivative is zero, i.e. orderTry to achieve θk=-J3Wk/ 2 λ, k=1,2 ..., l, carry it into ΘTΘ=1, and meet Θ >=0 simultaneously, try to achieveSo the optimal solution of the double-goal optimal model is
Preferably, in step S520, the optimal solution of program evaluation model is normalized, for example, rightEnter
Row normalized, i.e.So that the weighting of program index to
Amount meets normalization constraints.
Furthermore it is preferred that according in upper example, the double-goal optimal model based on deviation maximization and unitization constraints
Optimal solution, obtain the optimum combination weight vector F of the double-goal optimal modelj **=wj,1θ1 **+wj,2θ2 **+…+wj,lθl **, profit
The comprehensive evaluation value for obtaining each program with two kinds of evaluation methods of deviation maximization and unitization constraints is
In summary, it has been described by way of example with reference to according to program evaluation system proposed by the present invention and side
Method.It will be understood by those skilled in the art, however, that the system and method proposed for the invention described above, can also not take off
From making various improvement on the basis of present invention.Therefore, protection scope of the present invention should be by appended claims
Content determine.
Claims (6)
1. a kind of program evaluation system, including：
Input block, for inputting tax power method, program to be evaluated and evaluation index, wherein, the tax power method includes subjectivity
Tax power method and Objective Weighting；
Program Criterion Attribute space construction unit, the program to be evaluated and the calculation formula of evaluation index inputted according to input block
Obtain the decision matrix of each evaluation index composition of each program, i.e. program Criterion Attribute space；
Power index space construction unit is assigned, the tax power method inputted according to input block calculates the power of each evaluation index of each program
Weight simultaneously obtains right vector with the Linearly Representation multiplication of each tax power method, that is, assigns power index space, wherein, according to objective
The weight vectors that tax power method obtains are related to the decision matrix, right vector F,
F=W Θ=[F1 F2 … Fn]T
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Fn=wn,1θ1+wn,2θ2+…+wn,lθl
Wherein, the weight vectors matrix that matrix W obtains for every evaluation index of each program according to various tax power methods, Θ is each
The Linearly Representation coefficient vector of tax power method, wn,lThe weight of n-th of evaluation index, weight are obtained to assign power method according to l kinds
Not less than zero, n be evaluation index number, l be tax power method number, wlEach evaluation is obtained to assign power method according to l kinds
The weight vectors of the weight composition of index, and weight sum is equal to 1, θ in each weight vectorslPower method is assigned for l kinds
Linearly Representation coefficient, θk>=0, k=1,2 ..., l,FnFor the combining weights of n-th of evaluation index；
Program evaluation model construction unit, target is built using decision matrix and right vector according at least two evaluation methods
Optimized model, i.e. program evaluation model, wherein, the objective optimization model is double-goal optimal model or multiple-objection optimization mould
Type；
Optimal solution determining unit, the optimal solution of above-mentioned program evaluation model is solved using method of Lagrange multipliers；
Obtaining unit, obtained according to the audience information of program to be evaluated and the optimal solution each program each evaluation index it is optimal
Linearly Representation coefficient vector and optimum combination weight vector, so as to obtain the comprehensive evaluation value of each program,
Wherein, the program evaluation model construction unit includes：
First single object optimization model construction unit, the evaluation method based on deviation maximization using decision matrix and combined weights to
Single object optimization model of the amount structure based on deviation maximization, the single object optimization model based on deviation maximization is M1
(F)=J1F=J1W Θ,Wherein, J1For mean dispersion error matrix,bijRepresent i-th of program SiJ-th is commented
Valency index PjStandardization property value, i=1,2 ..., m, m be program to be evaluated number, j=1,2 ..., n；
Second single object optimization model construction unit, the evaluation method based on unitization constraints utilize decision matrix and combination
Weight vector builds the single object optimization model of unitization constraints, the single object optimization mould based on unitization constraints
Type is M2(F)=J2F=J2W Θ,Wherein, J2For decision-making synthetical matrix,
Double-goal optimal model construction unit, using linear weight sum method by above-mentioned two single object optimization model linear combination structure
The double-goal optimal model based on deviation maximization and unitization constraints is built, the double-goal optimal model is M3(F)=
J3F=J3W Θ,Wherein, J3For biobjective scheduling coefficient matrix, aJ1+bJ2=J3, a and b are line
Property weight coefficient, a+b=1.
2. program evaluation system according to claim 1, wherein, the program Criterion Attribute space also includes described determining
Specified decision matrix after plan matrix standardization processing.
3. a kind of program evaluation method, including：
Tax power method, program to be evaluated and evaluation index are selected, wherein, the tax power method includes subjective weights method and objective
Tax power method；
Program Criterion Attribute space is built, i.e., the program to be evaluated and the calculation formula of evaluation index inputted according to input block obtains
The decision matrix formed to each evaluation index of each program, i.e. program Criterion Attribute space；
Structure assigns power index space, i.e. calculated according to the tax power method weight vectors of each evaluation index of each program and with
Each Linearly Representation multiplication for assigning power method obtains right vector, that is, assigns power index space, wherein, according to Objective Weight side
The weight vectors that method obtains are related to the decision matrix, right vector F,
F=W Θ=[F1 F2 … Fn]T
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Fn=wn,1θ1+wn,2θ2+…+wn,lθl
Wherein, the weight vectors matrix that matrix W obtains for every evaluation index of each program according to various tax power methods, Θ is each
The Linearly Representation coefficient vector of tax power method, wn,lThe weight of n-th of evaluation index, weight are obtained to assign power method according to l kinds
Not less than zero, n be evaluation index number, l be tax power method number, wlEach evaluation is obtained to assign power method according to l kinds
The weight vectors of the weight composition of index, and weight sum is equal to 1, θ in each weight vectorslPower method is assigned for l kinds
Linearly Representation coefficient, θk>=0, k=1,2 ..., l,FnFor the combining weights of n-th of evaluation index；
Build program evaluation model, according at least two evaluation methods using decision matrix and right vector build Bi-objective or
Person's Model for Multi-Objective Optimization, i.e. program evaluation model；
The optimal solution of above-mentioned program evaluation model is solved using method of Lagrange multipliers；
The optimum linearity table that each evaluation index of each program is obtained according to the audience information of program to be evaluated and the optimal solution goes out
Coefficient vector and optimal weights vector, the comprehensive evaluation value of each program is obtained,
Wherein, the structure program evaluation model includes：
Evaluation method based on deviation maximization monocular based on deviation maximization using decision matrix and right vector structure
Optimized model is marked, wherein, the single object optimization model based on deviation maximization is M1(F)=J1F=J1W Θ,Wherein, J1For mean dispersion error matrix,bijRepresent i-th of program SiJ-th is commented
Valency index PjStandardization property value, i=1,2 ..., m, m be program to be evaluated number, j=1,2 ..., n；
Evaluation method based on unitization constraints builds unitization constraints using decision matrix and right vector
Single object optimization model, the single object optimization model based on unitization constraints are M2(F)=J2F=J2W Θ,Wherein, J2For decision-making synthetical matrix,
Above-mentioned two single object optimization model linear combination structure is based on deviation maximization and unit using linear weight sum method
Change the double-goal optimal model of constraints, the double-goal optimal model is M3(F)=J3F=J3W Θ,Wherein, J3For biobjective scheduling coefficient matrix, aJ1+bJ2=J3, a and b are linear weighted function coefficient, a
+ b=1.
4. program evaluation method according to claim 3, wherein, the structure program Criterion Attribute space is included to described
Decision matrix carries out standardization processing.
5. program evaluation method according to claim 3, wherein, it is described to be based on deviation maximization and unitization constraints
The method for solving of optimal solution of double-goal optimal model include：
Biobjective scheduling program evaluation model based on deviation maximization and unitization constraints is subjected to Lagrangian conversion
Derivation is carried out to the program evaluation model by Lagrange conversion, finds the Linearly Representation coefficient that first derivative is zero,
Carry it into constraints and obtain optimal solution, wherein, constraints ΘTΘ=1, and meet Θ >=0 simultaneously, the Bi-objective is excellent
Change model optimal solution be
To optimal solutionIt is normalized, obtains normalizing optimal solution, i.e.
6. program evaluation method according to claim 5, wherein, it is described to be based on deviation maximization and unitization constraints
Double-goal optimal model optimum combination weight vector Fj **=wj,1θ1 **+wj,2θ2 **+…+wj,lθl **, the overall merit of each program
It is worth and is
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