CN107784394A - Consider that the highway route plan of prospect theory does not know more attribute method for optimizing - Google Patents
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Abstract
The invention discloses a kind of highway route plan for considering prospect theory not to know more attribute method for optimizing, first, route plan index is classified by Real-valued, interval type and language type and carries out data standardization processing, secondly the route plan index attribute value after standardization, is converted into prospect decision matrix, then, with entropy weight come the size of description indexes attribute contribution rate in route plan optimization；Finally, the initial attribute value based on index, prospect value and entropy weight, comprehensive optimal evaluation model is established, and schemes ranking, optimum scheme comparison is carried out according to the size of comprehensive preference value；Objectively analyzed the subjective experience of policymaker as an attribute, it is strong to avoid subjectivity, it also avoid preferred process can not combine actual objectively analysis completely, preferably provide a kind of objective, feasible evaluation method for highway geometry, solve the problem that conventional method index can not quantify.
Description
Technical field
The invention belongs to road route scheme comparison field, and in particular to a kind of highway route for considering prospect theory
Scheme does not know more attribute method for optimizing.
Background technology
Highway is as important infrastructure projects, and the choosing of the ratio of route plan is the core of highway geometry scheme optimization.
The comprehensive ratio choosing of expressway construction Decision Making of Line Schemes, is in the highway construction major issue that early stage, needs solved, its basic trend
Scheme Choice whether rationally, can the project of directly influencing meet national economic development needs after building up, and have influence on circuit and set
The quality of the quality of meter, construction costs and operation condition, and finally determine the economic benefit of a highway.Especially in China
Highway transportation carries the prevailing traffic task of national passenger and freight, and politics, economy, national defence and the Highways ' of country are passed through
The politics in region, economy, the development of culture suffer from important function.Therefore, the circuit as expressway construction macro-level policy-making
Schemes synthesis is more very important than selecting work to have the function that.
Route selection be one relate to face is big, be related to that factor is numerous, coverage is wide and complicated system synthesis select it is excellent
Problem.Not only to meet the needs of national and local government politics, economy, culture, health etc., and to consider route
The feasibility of scheme and make selected address routing indicator that there is optimality.Traditional route selection method mainly has two classes：
First, subjectivity is too strong, the economic indicator based on scheme, policymaker is to optimum scheme comparison after the subjective judgements such as society and environment；
Second, too pursuing objectivity, mathematical method is copied mechanically and applied indiscriminately, does not consider actual items feature, it is impossible to which good policymaker is real for many years
Border experience is used in scheme comparison decision-making.
The content of the invention
In view of the shortcomings of the prior art, present invention aims at propose a kind of highway route side for considering prospect theory
Case does not know more attribute method for optimizing, has considered decision-making and has wished subjective experience and influence of the objective condition to route plan, will
Quantitative target changes into different mathematical linguistics from qualitative index in route plan, by prospect theory and Multiple Attribute Decision Making Theory
By route plan preferred process scientific rationalization.
To achieve the above object, the present invention uses following scheme：
Consider that the highway route plan of prospect theory does not know more attribute method for optimizing, comprise the following steps：
First, by scheme collection S={ S1,S2,…,Si,…,SmIn route plan index press Real-valued, interval type and language
Speech type is classified and carries out data standardization processing, and language type state set is L={ L0,L1,…,Lk,…,Lt, attribute value set
For V=[Vij]m×n；Wherein SiFor i-th of alternative, LkFor language type k-th of state value of index, L0…LtFor from difference to it is good by
Walk the state value of change, VijFor j-th of property value of i-th of alternative；
Secondly, route plan Criterion Attribute integrates as A={ A1,A2,…,Aj,…,An, AjFor j-th of attribute；According to decision-making
Preference information P={ P of the person to each Criterion Attribute1,P2,…,Pj,…,Pn, PjFor policymaker according to subjective experience to j-th of attribute
Preference information, the route plan index attribute value after standardization is converted into prospect decision matrix D=[Dij]m×n, DijFor i-th
J-th of attribute decision-making initial value of individual alternative, each attribute are separate；
Then cost function parameter prospect value, is built, the uncertainty occurred based on Criterion Attribute, is retouched with entropy weight
State the size of Criterion Attribute contribution rate in route plan optimization；
Finally, the initial attribute value based on index, prospect value and entropy weight, comprehensive optimal evaluation model is established, and according to comprehensive
The size for closing preference value carries out schemes ranking, optimum scheme comparison.
Further, route plan index is divided into Real-valued (A1), interval type (A2) and language type (A3) three classes, specifically retouch
State as follows：
Real-valued (A1)：The property value of index can be quantified and calculated, and be precise figures, i.e., property value is Vj；
Interval type (A2)：Index can quantitative analysis be difficult to be described with precise figures, state Criterion Attribute with section
Uncertainty, i.e. property value are [Vj -,Vj +]；
Language type (A3)：Index can only qualitative analysis, property value can only use the language description of such as " good, in, poor ", that is, belong to
Property value is [Vj -,Vj 0,Vj +]=(max { (Lk-1)/t,0},Lk/t,max{(Lk+1)/t,0})。
Further, Real-valued, interval type and language type route plan index are subjected to data normalization processing, specifically such as
Under：
Standardization processing is carried out to route scheme Attribute Value data, property value is divided into cost type and profit evaluation model, is denoted as respectively
Aτ,AθThe property value of wherein cost type is the smaller the better, and the property value of profit evaluation model is the bigger the better, and processing mode is as follows：
Real-valued (A1)：If Xj +=max { max { Vij},Pj, Xj -=min { min { Vij},Pj, normalizing is：
Interval type (A2)：IfStandardization is public
Formula is：
Language type (A3)：The determination of language type index attribute value is the process standardized, therefore language type index is standardized
Value directly uses Triangular Fuzzy Number；
Preference vector P '={ P is obtained after data normalization processing1’,P2’,…,Pj’,…,Pn' and decision matrix V '=
[Vij’]m×n。
Further, that the index attribute value after standardization is converted into prospect decision matrix is specific as follows：
Policymaker's subjective experience is determined into preference vector as reference point to weigh " income " of each scheme attribute or " damage
Lose ", to the property value V of each schemeij' and attributes preferred Pj' magnitude relationship weigh scheme attribute, counted using Euclidean distance
Calculate property value and it is attributes preferred between distance, consider subjective experience and the initial attribute of objective reality as different route plans
Value Dij, prospect decision matrix D is built, formula is as follows：
Further, structure cost function parameter prospect value is specially：
Prospect theory assumes that cost function in reference point is convex below reference point, to reflect sensitivity above is recessed
Property decreasing principle；Prospect theory is it is also supposed that cost function is steeper in income region in loss region ratio, to embody loss aversion；
Following cost function C (V are proposed according to above-mentioned hypothesisij‘)：
Wherein, α, β characterize income and lose the concavo-convex degree of region value power function respectively, that is, reflect policymaker's sensitiveness
The speed successively decreased, lambda coefficient are used for characterizing the loss region feature steeper than income region, that is, reflect loss aversion degree.
Further, α=β=0.88；λ=2.25.
Further, the calculation formula of the uncertain agriculture products entropy weight based on Criterion Attribute, entropy and entropy weight is as follows：
K is positive constant, as all piFor any given i it is equal when, pi=1/n, Ei(pl,p2,…,pi,…,
pm) obtain maximum.
Further, the structure of comprehensive optimal evaluation model is specific as follows：
Consider initial attribute value and propose comprehensive optimal evaluation model with prospect value, it is as follows：
Work as UiDuring ＞ 0, evaluation of programme generally " income " state is represented, works as Ui＜ 0 represents evaluation of programme generally " damage
Lose ", the goodness of all schemes is compared, ifThen scheme SrFor optimal case, with policymaker
The degree that preference information deviates integrates optimal with prospect state.
The innovative point of the present invention mainly has following aspect：
1st, reference is regard policymaker's subjective experience as by " prospect theory " that is introduced into economic theory, using objective
Mathematical method carries out preferred to each route plan.
2nd, based on the existing information content of Criterion Attribute, consider entropy and entropy weight, the randomness of unknown thing is being handled from the mankind
With the relative severity of each index of probabilistic analysis of objective world in competition meaning, make highway geometry scheme preferred process
It is more objective reasonable.
3rd, classified for route plan selection indicators, different types of index passes through science, objective mathematical method
United analysis, it is as a result more rationally credible.
4th, the Euclidean distance of decisionmaker's preference and route plan attribute is integrated into prospect decision matrix, as the invention
Data basis.
Advantages of the present invention mainly has following aspect：
1st, objectively analyzed the subjective experience of policymaker as an attribute, it is strong to avoid subjectivity, also avoids
Preferred process can not combine actual objectively analysis completely.
2nd, the thought of prospect theory and entropy weight is introduced into the preferable multiple attributive decision making method of highway geometry scheme, constructed
Comprehensive optimal evaluation model.A kind of objective, feasible evaluation method is preferably provided for highway geometry.
3rd, from mathematical expression, route plan index is divided into Real-valued, interval type and language type.Almost cover road
Line scheme whole index, solves the problem that conventional method index can not quantify.
4th, the present invention is applied to actual items, and preferred scheme it is expected consistent, tool with actual items construction condition, policymaker
There is very strong practicality.
5th, index processing of the present invention is clear, and calculation process is simple, and result of calculation is understandable, is adapted to be widely used in route plan
It is preferred that.
Brief description of the drawings
Fig. 1 is the flow chart of design method of the present invention
Fig. 2 is to carry out Fuzzy processing function with Triangular Fuzzy Number for the language type index corresponding to 7 grades
Fig. 3 is simulation curve of the figure cost function under different parameters in prospect theory
Fig. 4 is the example of highway geometry scheme optimal selection problem
Embodiment
The present invention will be further described below in conjunction with the accompanying drawings.
A kind of highway route plan for considering prospect theory of the present invention does not know more attribute method for optimizing, including once
Step：
First, route plan index is classified and carried out at data normalization by Real-valued, interval type and language type
Reason；
Secondly, is converted into by prospect by the index attribute value after standardization and is determined for the preference of each Criterion Attribute according to policymaker
Plan matrix；
Then the prospect value of accumulation Functional Calculation Criterion Attribute, is established, the uncertainty occurred based on Criterion Attribute, uses entropy
Power carrys out the size of description indexes attribute contribution rate in route plan optimization；
Finally, the initial attribute value based on index, prospect value and entropy weight, comprehensive optimal evaluation model is established, and according to comprehensive
The size for closing preference value carries out schemes ranking, optimum scheme comparison.
Described route plan method for optimizing is described as with mathematical linguistics：If in the presence of a route plan optimal selection problem, its
Scheme collection S={ S1,S2,…,Si,…,Sm, property set is A={ A1,A2,…,Aj,…,An, language type state set is L=
{L0,L1,…,Lk,…,Lt, attribute value set is V=[Vij]m×n, prospect decision matrix is D=[Dij]m×n, decisionmaker's preference letter
Cease P={ P1,P2,…,Pj,…,Pn}.Wherein SiFor i-th of alternative；AjFor j-th of attribute；LkFor language type index kth
Individual state value, L0…LtFor from difference to well stepping state value；VijFor j-th of property value of i-th of alternative, DijFor
J-th of attribute decision-making initial value of i-th of alternative, each attribute are separate；PjFor policymaker according to subjective experience to j-th
The preference information of attribute.
This route plan method for optimizing comprises the following steps that：
Step 1：Evaluation index is classified to be determined with property value
The description feature of calculating, quantitative analysis and qualitative analysis can be quantified according to route plan selection indicators, will preferably be referred to
Mark is divided into Real-valued (A1), interval type (A2) and language type (A3) three classes, it is described in detail below：
(1) Real-valued (A1)：The property value of index can be quantified and calculated, and be precise figures, i.e., property value is Vj.Such as " expense ".
(2) interval type (A2)：Index can quantitative analysis but be difficult described with precise figures, state Criterion Attribute with section
Uncertainty, i.e. property value isSuch as " superelevation ".
(3) language type (A3)：Index can only qualitative analysis, property value can only retouch with the language of such as " good, in, poor " etc
State, i.e., property value isLk/t,max{(Lk+1)/t,0}).As " route plan draws
The geological disaster of hair ".
Step 2：Data normalization processing
In hybrid multi-attribute decision making problems, in order to eliminate influence of the different physical quantities guiding principle to the result of decision, it is necessary to right
Attribute value data carries out standardization processing.Property value is divided into cost type and profit evaluation model, is denoted as A respectivelyτ,AθThe wherein category of cost type
Property value it is the smaller the better, the property value of profit evaluation model is the bigger the better.Processing mode is as follows：
(1) Real-valued (A1)：IfXj -=min { min { Vij},Pj, normalizing
For：
(2) interval type (A2)：IfSpecification
Changing formula is：
(3) language type (A3)：The determination of language type index attribute value is the process standardized, therefore language type index specification
Change value directly uses Triangular Fuzzy Number.
Preference vector P '={ P is obtained after data normalization processing1’,P2’,…,Pj’,…,Pn' and decision matrix V '=
[Vij’]m×n
Step 3：The determination of prospect decision matrix
In prospect theory, policymaker's subjective experience is determined into preference vector as reference point to weigh each scheme attribute
" income " or " loss ", it is therefore desirable to the property value V of each schemeij' and attributes preferred Pj' compare, and according between it
Magnitude relationship weighs scheme attribute.The method for optimizing for above-mentioned three kinds of indexs using Euclidean distance come computation attribute value with it is inclined
Belong to distance between two genders well, consider subjective experience and the initial attribute value D of objective reality as different route plansij, structure
Prospect decision matrix D, formula are as follows：
Step 4：Build cost function parameter prospect value
Prospect theory assume that cost function in reference point above is recessed, be below reference point it is convex, it is quick to reflect
Perceptual decreasing principle；Prospect theory further suppose cost function loss region ratio it is steeper in income region, detest to embody loss
Dislike.Following cost function C (V are proposed according to above-mentioned hypothesisij‘)：
Wherein, α, β characterize income and lose the concavo-convex degree of region value power function respectively, that is, reflect policymaker's sensitiveness
The speed successively decreased, lambda coefficient are used for characterizing the loss region feature steeper than income region, that is, reflect loss aversion degree.
On the other hand, Kahneman and Tversky has drawn decision-making of people when in face of income and loss by experiment
Parameter value, i.e.,：α=β=0.88；λ=2.25, research show above-mentioned value can accurate reaction policymaker sensitiveness with
Loss aversion degree, and a large amount of scholars have also drawn similar parameter and above-mentioned parameter are applied into practical study.
Step 5：Uncertainty based on Criterion Attribute, agriculture products entropy weight
The concept of entropy is initially generated at thermodynamics, is mainly used to what description was likely to occur in a certain one system of given time
There is the uncertainty degree of off status, for describing different evaluation index to the preferable influence degree of route.Based on index AjThere is provided
M objective attribute information V1j,V2j,…,Vij,…,Vmj, it is assumed that these results occur has Probability pl,p2,…,pi,…,pm,
Estimate by informational probability and obtain entropy E (pl,p2,…,pi,…,pm), objectively determine that event occurs not by the size of entropy
Certainty, i.e. entropy weight ω.The calculation formula of entropy and entropy weight is as follows：
K is positive constant, as all piFor any given i it is equal when, pi=1/n, Ei(pl,p2,…,pi,…,
pm) obtain maximum.
As can be seen here, entropy weight represents the index can provide how much degree of useful information content in the problem.Entropy weight is in itself
Not just show the importance on certain index practical significance, also show relative severity of each index in competition meaning.
Entropy weight takes full advantage of the attribute information that oneself knows, reflects the mankind in the randomness for handling unknown thing and the probability of objective world
Property, meet the requirement of highway geometry scheme objective making decision.
Step 6：The structure of comprehensive optimal evaluation model
Initial attribute value DijIt may determine that the degree that the property value of each scheme deviates with decisionmaker's preference information, prospect value
CijThe property value for then judging each scheme is " income " or the degree of " loss ", only when the initial attribute value of scheme is smaller, and
The bigger scheme of prospect value could be optimal, therefore, considers initial attribute value herein and proposes comprehensive optimal evaluation mould with prospect value
Type is as follows：
Work as UiDuring ＞ 0, evaluation of programme generally " income " state is represented, works as Ui＜ 0 represents evaluation of programme generally " damage
Lose ".The goodness of all schemes is compared, ifThen scheme SrFor optimal case, with policymaker
The degree that preference information deviates integrates optimal with prospect state.
Illustrate the present invention program below in conjunction with specific embodiment：
To be contrasted with former scheme, the index chosen in tradition evaluation is chosen first, index is classified and attribute
The determination of value, departure degree, the prospect state of attribute in itself of Criterion Attribute and decisionmaker's preference attribute are considered, with synthesis
Optimal evaluation model is calculated and sorted to each scheme, final according to preference value optimum scheme comparison.
The initial data of this example is In Permafrost Regions of Qinghai-xizang Plateau Xiu Shui rivers to Ya Maer sections route plan data, such as
Fig. 4, the region include 4 route plan S={ S altogether1,S2,S3,S4, evaluation index has averagely every kilometer of peace of building to take A1, bridge tunnel
Ratio A2, unit length ice content A3, geographical environment A4, linear interference A5Deng 5.Fig. 1 is the signal of this exemplary application present invention
Figure, Fig. 2 and Fig. 3 are with the function and parameter wanted in exemplary application.
Step 1：Evaluation index is classified to be determined with property value
Based on above-mentioned data, A1With A2For Real-valued index, A3For interval type index, A4With A5For language type index, if should
Language is denoted as VP, P, MP, M, MG, G respectively for " excessively poor, poor, poor, in, preferable, good, very good " 7 grades in example,
VG, if Language State integrates as L={ 0,1,2,3,4,5,6 }.The report of designer is made an on-the-spot survey through correlation, policymaker proposes expectation
Target, preference vector is converted into as P={ 14000,50, [60,80], M, MG }, scheme initial attribute value such as table 1.
Each scheme index attribute value of table 1
| Scheme | A1 | A2 | A3 | A4 | A5 |
| P | 14000 | 50 | [60,80] | M | MG |
| S1 | 14548 | 61.8 | [64,80] | M | MG |
| S2 | 13526 | 54.7 | [30,50] | MP | VP |
| S3 | 12162 | 51.2 | [48,70] | MP | M |
| S4 | 14026 | 56.3 | [70,98] | M | P |
Step 2：Data normalization processing
Index A1、A2With A3Property value is cost type, i.e., the smaller the better, according to AτNormalizing is handled, and is obtained
Standardize property value, is shown in Table 2.
Property value after each scheme index standardization of table 2
| Scheme | A1 | A2 | A3 | A4 | A5 |
| P | 0.77 | 0 | [0.750,0.625] | (0.333,0.5,0.667) | (0.5,0.667,0.833) |
| S1 | 1 | 1 | [0.850,0.625] | (0.333,0.5,0.667) | (0.5,0.667,0.833) |
| S2 | 0.572 | 0.398 | [0,0] | (0.167,0.333,0.5) | (0,0,0.167) |
| S3 | 0 | 0.102 | [0.450,0.417] | (0.167,0.333,0.5) | (0.333,0.5,0.667) |
| S4 | 0.781 | 0.534 | [1,1] | (0.333,0.5,0.667) | (0,0.167,0.333) |
Step 3：The determination of prospect decision matrix
Using Euclidean distance come computation attribute value and it is attributes preferred between distance, consider subjectivity as different route plans
The initial attribute value of experience and objective reality, prospect decision matrix is built, is shown in Table 3.
The prospect decision matrix of table 3 (initial attribute value)
| Scheme | A1 | A2 | A3 | A4 | A5 |
| S1 | 0.23 | 1 | 0.071 | 0 | 0 |
| S2 | 0.198 | 0.398 | 0.69 | 0.167 | 0.616 |
| S3 | 0.77 | 0.102 | 0.258 | 0.167 | 0.5 |
| S4 | 0.011 | 0.534 | 0.319 | 0 | 0.167 |
Step 4：Build cost function parameter prospect value
According to cost function C (Vij'), wherein decision parameters value take α=β=0.88；λ=2.25, such as Fig. 3.Calculate each
The prospect value of property value, is shown in Table 4.
The prospect value of 4 each property value of table
| Scheme | A1 | A2 | A3 | A4 | A5 |
| S1 | 0.274 | 1 | 0.098 | 0 | 0 |
| S2 | -0.541 | 0.445 | -1.623 | -0.466 | 0.653 |
| S3 | -1.788 | 0.134 | -0.683 | -0.466 | -1.223 |
| S4 | 0.019 | 0.576 | 0.366 | 0 | -0.466 |
Step 5：Uncertainty based on Criterion Attribute, agriculture products entropy weight
The objective attribute information provided based on each scheme, probability measure is calculated, is shown in Table 5.According to entropy weight theoretical calculation entropy weight
For ω=(0.224,0.109,0.116,0.349,0.202)T。
The probability measure of the property value of table 5
| Scheme | A1 | A2 | A3 | A4 | A5 |
| S1 | 0.19 | 0.492 | 0.053 | 0 | 0 |
| S2 | 0.164 | 0.196 | 0.516 | 0.5 | 0.48 |
| S3 | 0.637 | 0.05 | 0.193 | 0.5 | 0.39 |
| S4 | 0.009 | 0.263 | 0.238 | 0 | 0.13 |
Step 6：The structure of comprehensive optimal evaluation model
Result of calculation in step 3~5 is substituted into comprehensive optimal evaluation model, try to achieve goodness for U=(0.12, -0.08, -
0.49,0.05), i.e. U3(- 0.49) ＜ U2(- 0.08) ＜ U4(0.05) ＜ U1(0.12).Evaluation result and traditional evaluation result one
Cause.In addition by result can with it is further seen that：Option A2With option A3State generally " is lost ", with the actual construction condition of scheme
Difference etc. is closely bound up, meets reality.And option A1With option A4For generally " income " state, and option A1While income more
It is expected close to policymaker.Therefore, the present invention has considered the experience and route plan objective reality of policymaker, by preferred process
Scientific rationalization, there is very strong practicality.
Above content is to combine specific preferred embodiment further description made for the present invention, it is impossible to is assert
The embodiment of the present invention is only limitted to this, for general technical staff of the technical field of the invention, is not taking off
On the premise of from present inventive concept, some simple deduction or replace can also be made, should all be considered as belonging to the present invention by institute
Claims of submission determine scope of patent protection.
Claims (8)
1. consider that the highway route plan of prospect theory does not know more attribute method for optimizing, it is characterised in that including following step
Suddenly：
First, by scheme collection S={ S1,S2,…,Si,…,SmIn route plan index press Real-valued, interval type and language type
Classified and carry out data standardization processing, language type state set is L={ L0,L1,…,Lk,…,Lt, attribute value set V
=[Vij]m×n；Wherein SiFor i-th of alternative, LkFor language type k-th of state value of index, L0…LtFor from difference to it is good progressively
The state value of change, VijFor j-th of property value of i-th of alternative；
Secondly, route plan Criterion Attribute integrates as A={ A1,A2,…,Aj,…,An, AjFor j-th of attribute；According to policymaker couple
Preference information P={ the P of each Criterion Attribute1,P2,…,Pj,…,Pn, PjFor policymaker according to subjective experience to the inclined of j-th attribute
Good information, the route plan index attribute value after standardization is converted into prospect decision matrix D=[Dij]m×n, DijIt is standby for i-th
Select j-th of attribute decision-making initial value of scheme, each attribute is separate；
Then cost function parameter prospect value, is built, the uncertainty occurred based on Criterion Attribute, describes to refer to entropy weight
Mark the size of attribute contribution rate in route plan optimization；
Finally, the initial attribute value based on index, prospect value and entropy weight, comprehensive optimal evaluation model is established, and it is excellent according to synthesis
The size of angle value carries out schemes ranking, optimum scheme comparison.
2. the highway route plan according to claim 1 for considering prospect theory does not know more attribute method for optimizing,
It is characterized in that：Route plan index is divided into Real-valued (A1), interval type (A2) and language type (A3) three classes, specifically describe such as
Under：
Real-valued (A1)：The property value of index can be quantified and calculated, and be precise figures, i.e., property value is Vj；
Interval type (A2)：Index can quantitative analysis be difficult to be described with precise figures, state the uncertain of Criterion Attribute with section
Property, i.e., property value is
Language type (A3)：Index can only qualitative analysis, property value can only use the language description of such as " good, in, poor ", i.e. property value
For
3. the highway route plan according to claim 2 for considering prospect theory does not know more attribute method for optimizing,
It is characterized in that：Real-valued, interval type and language type route plan index are subjected to data normalization processing, it is specific as follows：
Standardization processing is carried out to route scheme Attribute Value data, property value is divided into cost type and profit evaluation model, is denoted as A respectivelyτ,Aθ
The property value of wherein cost type is the smaller the better, and the property value of profit evaluation model is the bigger the better, and processing mode is as follows：
Real-valued (A1)：IfNormalizing is：
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Interval type (A2)：IfNormalizing
For：
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</mrow>
Language type (A3)：The determination of language type index attribute value is the process standardized, therefore language type index normative value is direct
Using Triangular Fuzzy Number；
Preference vector P '={ P is obtained after data normalization processing1’,P2’,…,Pj’,…,Pn' and decision matrix V '=
[Vij’]m×n。
4. the highway route plan according to claim 3 for considering prospect theory does not know more attribute method for optimizing,
It is characterized in that：It is specific as follows that index attribute value after standardization is converted into prospect decision matrix：
Policymaker's subjective experience is determined into preference vector as reference point to weigh " income " or " loss " of each scheme attribute,
To the property value V of each schemeij' and attributes preferred Pj' magnitude relationship weigh scheme attribute, category is calculated using Euclidean distance
Property value and it is attributes preferred between distance, the initial attribute value of subjective experience and objective reality is considered as different route plans
Dij, prospect decision matrix D is built, formula is as follows：
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<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
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<mtable>
<mtr>
<mtd>
<mrow>
<mrow>
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<mi>j</mi>
</mrow>
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<mi>j</mi>
<mo>&prime;</mo>
</msubsup>
</mrow>
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</mrow>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>j</mi>
<mo>&Element;</mo>
<msup>
<mi>A</mi>
<mn>1</mn>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msqrt>
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<mrow>
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<mi>V</mi>
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<mi>j</mi>
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</mrow>
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</mrow>
</msqrt>
<mo>,</mo>
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</msup>
</mrow>
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</msup>
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<mn>3</mn>
</mrow>
</msqrt>
<mo>,</mo>
</mrow>
</mtd>
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<mi>j</mi>
<mo>&Element;</mo>
<msup>
<mi>A</mi>
<mn>3</mn>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>.</mo>
</mrow>
5. the highway route plan according to claim 1 for considering prospect theory does not know more attribute method for optimizing,
It is characterized in that：Building cost function parameter prospect value is specially：
Prospect theory assumes that cost function in reference point is convex below reference point, to reflect that sensitiveness is passed above is recessed
Subtract principle；Prospect theory is it is also supposed that cost function is steeper in income region in loss region ratio, to embody loss aversion；
Following cost function C (V are proposed according to above-mentioned hypothesisij‘)：
<mrow>
<mi>C</mi>
<mrow>
<mo>(</mo>
<msup>
<msub>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&prime;</mo>
</msup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mrow>
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<msub>
<mi>D</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>&alpha;</mi>
</msup>
<mo>,</mo>
</mrow>
</mtd>
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<msubsup>
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</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>&lambda;</mi>
<msup>
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<mo>(</mo>
<mo>-</mo>
<msub>
<mi>D</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
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</msub>
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<mi>&beta;</mi>
</msup>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msup>
<msub>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&prime;</mo>
</msup>
<mo>&le;</mo>
<msubsup>
<mi>P</mi>
<mi>j</mi>
<mo>&prime;</mo>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein, α, β characterize income and lose the concavo-convex degree of region value power function respectively, that is, reflect that policymaker's sensitiveness is successively decreased
Speed, lambda coefficient is used for characterizing the loss region feature steeper than income region, that is, reflects loss aversion degree.
6. the highway route plan according to claim 5 for considering prospect theory does not know more attribute method for optimizing,
It is characterized in that：α=β=0.88；λ=2.25.
7. the highway route plan according to claim 1 for considering prospect theory does not know more attribute method for optimizing,
It is characterized in that：The calculation formula of uncertain agriculture products entropy weight based on Criterion Attribute, entropy and entropy weight is as follows：
<mrow>
<msub>
<mi>E</mi>
<mi>i</mi>
</msub>
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<msub>
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</msub>
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<mi>i</mi>
</msub>
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</msub>
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</mrow>
<mo>=</mo>
<mo>-</mo>
<mi>k</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mi>l</mi>
<mi>n</mi>
<mi> </mi>
<msub>
<mi>p</mi>
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</msub>
</mrow>
<mrow>
<msub>
<mi>&omega;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>E</mi>
<mi>i</mi>
</msub>
</mrow>
<mrow>
<mi>m</mi>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msub>
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</msub>
</mrow>
</mfrac>
</mrow>
K is positive constant, as all piFor any given i it is equal when, pi=1/n, Ei(pl,p2,…,pi,…,pm) take
Obtain maximum.
8. the highway route plan according to claim 1 for considering prospect theory does not know more attribute method for optimizing,
It is characterized in that：The structure of comprehensive optimal evaluation model is specific as follows：
Consider initial attribute value and propose comprehensive optimal evaluation model with prospect value, it is as follows：
<mrow>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mrow>
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<munderover>
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<mrow>
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<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&omega;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>D</mi>
<mrow>
<mi>i</mi>
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</mrow>
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<mrow>
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</mrow>
</msub>
<mo>)</mo>
</mrow>
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<msqrt>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<msub>
<mi>D</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mn>2</mn>
</msup>
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</msqrt>
</mrow>
Work as UiDuring ＞ 0, evaluation of programme generally " income " state is represented, works as Ui＜ 0 represents that evaluation of programme generally " loses ", right
The goodness of all schemes is compared, ifThen scheme SrFor optimal case, believe with decisionmaker's preference
Cease the degree deviateed and prospect state synthesis is optimal.
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| CN111913797B (en) * | 2020-07-09 | 2023-01-31 | 烽火通信科技股份有限公司 | Intelligent model distribution method, distribution system and application system |
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