CN110046204A - Consider the building of the section hesitation fuzzy graph decision-making technique of relevance and dominance relation - Google Patents
Consider the building of the section hesitation fuzzy graph decision-making technique of relevance and dominance relation Download PDFInfo
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Abstract
The invention discloses the buildings of a kind of consideration relevance and the section hesitation fuzzy graph decision-making technique of dominance relation, model foundation and model including the section hesitation fuzzy graph multiple attributive decision making method for considering relevance and dominance relation, which calculate, to be studied, pass through input interval hesitation fuzzy decision matrix, linear precedence relationship between attribute describes the section hesitation fuzzy graph of relevance between attribute；Export optimal alternative；Specific calculate includes the attribute a with relevance for calculating alternative decision making schemeiAnd ajBetween section hesitation fuzzy message energy coefficient ψij；Utilize the linear precedence relationship computation attribute weights omega between attributej；Calculate alternative decision making scheme pkThe bulk properties value of (k=1,2 ..., m)Calculate alternative decision making scheme pkThe score value of corresponding bulk properties valueDetermine optimal alternative decision making schemeThe present invention utilizes the characteristics of section hesitation fuzzy graph and advantage, provides a kind of effective solution scheme to be provided simultaneously with the complicated uncertain multi-attribute decision-making problem of relevance and dominance relation.
Description
Technical field
The present invention relates to multiple attributive decision making method technical fields, and in particular to a kind of area for considering relevance and dominance relation
Between hesitation fuzzy graph decision-making technique building.
Background technique
As the important branch of modern decision science, multiple attribute decision making (MADM) is intended to the angle to limited scheme from multiple attributes
Analysis of Policy Making is carried out, and then is made a choice by way of information integration to alternative, theory has been answered extensively with method
For numerous areas, the development of social economy has effectively been pushed.Since the cognitive presence of policymaker is uncertain and decision is asked
The complexity of topic such as is continuously increased at the reasons, and policymaker is caused to be difficult to accurately handle decision information.And fuzzy set reason is proposed from Zadeh
Since, Fuzzy Multiple Attribute Decision Making problem has become the important directions of multiple attribute decision making (MADM) research.In recent years, in order to from inaccurate
Ipsilateral does not describe uncertain information efficiently further for property, inconsistency, incompleteness, ambiquity and hesitation etc., Duo Zhongmo
The popularizing form of paste collection is suggested.The needs of policymaker's hesitation degree, Torra are embodied during wherein indicating for decision data
The value of degree of membership is generalized to the set that multiple values are constituted by single value, thereby establishes hesitation fuzzy set theory.It examines later
Consider hesitation fuzzy set and only focused on the case where evaluation information is perfect number, if replacing perfect number that can more effectively handle with interval number
The incompleteness that decision information is contained, then Chen et al. combines the advantage of interval number and hesitation fuzzy set, has developed section
The concept of hesitation fuzzy set.In view of section hesitation fuzzy set proposition can flexibly describe incompleteness that uncertain information has with
Hesitation, section hesitation Fuzzy Multiple Attribute Decision Making problem have obtained extensive research.
So far, most of multiple attributive decision making methods are that there are ground on the basis of mutually indepedent relationship between attribute
Study carefully.However as the increasingly complicated of modern policy setting, the case where there are relevance and dominance relations between attribute, is in reality
Generally existing is for example, institution of higher learning are in talent introduction, and human resources expert is often from moral character, the capacity of scientific research, teaching energy
Power, education background etc. make an appraisal to applicant.Usually possess well educated and elite school's education background applicant's scientific research energy
Power is also relatively strong, i.e., there are relevances between talent evaluation attribute, while expert can preferentially carry out the investigation of moral character and be regarded
For most important attribute, the capacity of scientific research, teaching ability, education background, i.e. talent evaluation attribute are successively investigated by importance later
Between there are dominance relation therefore, it is necessary to system research consider relevance and dominance relation multiple attributive decision making method.
In recent years, there is relevance between attribute, the relationship between attribute usually is indicated using fuzzy mearue, it
Information integration is carried out by way of Choquet is integrated afterwards；There is dominance relation between attribute, by establishing a system
Preferential Integrated Operator is arranged rationally to be solved to the Multiple Attribute Decision Problems of consideration dominance relation；It is existed simultaneously between attribute
The problem of relevance and dominance relation, Chen et al. are integrated using Choquet, and successively proposing generalized precedence, to estimate guidance integrated
Operator and weak order preferentially estimate guidance Integrated Operator.
The relevance between attribute can be efficiently indicated by the side between vertex in view of fuzzy graph, and then utilizes the concept of fuzzy graph
Study influence of the relevance between attribute to the result of decision, so as to form multiple attributive decision making method based on fuzzy graph its
Middle Yu et al. first proposed the decision-making technique based on graph theory and fuzzy graph theory, then set up alliance's decision based on digraph
Method.Open the solution that superfine people proposes the concept of hesitation fuzzy graph and is used for Multiple Attribute Decision Problems.Recently, towards actually answering
Many challenges based on data-driven, the popularizing form of multi-Fuzzy figure present in are suggested, and are in respective background
Uncertain expression based on Graph-theoretical Approach provides theory support.
However, for the multiple attributive decision making method for existing simultaneously relevance and dominance relation between attribute in hesitation blurred background
Research is also fewer, and has the section hesitation Fuzzy Multiple Attribute Decision Making problem of relevance and dominance relation existing simultaneously between attribute
It is again generally existing in reality.For the demand for solving above-mentioned decision problem, it is contemplated that fuzzy graph modeling method belongs in indicating decision
Flexibility and intuitive between property when relationship, i.e., many Fuzzy Multiple Attribute Decision Making problems for having correlation between complex properties are all
It is represented by the structure of fuzzy graph, it is necessary to carry out with advantage in conjunction with the characteristics of fuzzy graph to considering relevance and dominance relation
The system research of section hesitation fuzzy graph multiple attributive decision making method.
In conclusion solving the problems, such as that section hesitation Fuzzy Multiple Attribute Decision Making, the present invention are main to efficiently use fuzzy graph
Simultaneously there is the multiple attribute decision making (MADM) of relevance and dominance relation to ask based on the concept of section hesitation fuzzy graph, and between Attribute Oriented
Topic constructs the multiple attributive decision making method based on section hesitation fuzzy graph.
Summary of the invention
The technical problem to be solved by the present invention is to overcoming above-mentioned deficiency, a kind of consideration relevance and dominance relation are provided
Hesitation fuzzy graph decision-making technique in section considers relevance and preferential using constructing the characteristics of the hesitation fuzzy graph of section and advantage
The section hesitation fuzzy graph multiple attributive decision making method of relationship.
Technical scheme is as follows:
A kind of building for the section hesitation fuzzy graph decision-making technique considering relevance and dominance relation, includes the following steps:
Step 1. considers the model foundation of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation
The foundation and expression of 1.1 decision informations: being directed to a Multiple Attribute Decision Problems, firstly, determining the multiple attribute decision making (MADM)
There is relevance and dominance relation simultaneously between the attribute of problem；Then, alternative collection, property set and attribute weight are established；It enables
The alternative decision making scheme of the Multiple Attribute Decision Problems integrates as P, P={ p1,p2,...,pm, property set V, V={ a1,a2,...,
an, attribute weight ω, ω=(ω1,ω2,...,ωn)T；Policymaker is to alternative pk(k=1,2 ..., m) utilize category
Property aj(j=1,2 ..., n) it is evaluated；
The building of 1.2 section hesitation fuzzy decision matrixes and section hesitation fuzzy graph: 1.1 decisions in step 1 are completed
After the foundation and expression of information, policymaker is to alternative pk(k=1,2 ..., m) utilize attribute aj(j=1,2 ..., n) into
Row evaluation；Using the theory of section hesitation fuzzy set, evaluation result d is provided with the form of section hesitation fuzzy numberkj, to constitute
Section hesitation fuzzy decision matrix D, D=(dkj)m×n；Fuzzy network theory is recycled to construct section hesitation fuzzy graph；
The selection of the integrated analysis and optimal case of 1.3 section hesitation fuzzy messages: the multiple of alternative decision making scheme are integrated
After section hesitation fuzzy message under attribute, to alternative decision making scheme p1,p2,...,pmCorresponding bulk properties value is analyzed
And it chooses the best alternatives；
Step 2. considers that the model of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation calculates
Input: section hesitation fuzzy decision matrix D=(dkj)m×n, linear precedence relationship between attribute describes to close between attribute
The section hesitation fuzzy graph of connection property；
Output: optimal alternative；
It is required according to the input information of model and output, by the attribute a with relevance for calculating alternative decision making schemei
And ajBetween section hesitation fuzzy message energy coefficient, attribute weight ωj, alternative decision making scheme pk(k=1,2 ..., m)
Bulk properties value, and to alternative decision making scheme pk(k=1,2 ..., bulk properties value comparative analysis m), finally determine excellent standby
Select decision scheme.
Further, the step 1 considers the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation
Model foundation 1.1 decision informations foundation and expression, establish alternative collection, property set and attribute weight；Enable more categories
The alternative decision making scheme of property decision problem integrates as P, P={ p1,p2,...,pm, property set V, V={ a1,a2,...,an, belong to
Property weight be ω, ω=(ω1,ω2,...,ωn)T；And between attribute there is linear precedence relationship be a1> a2> ... > an,
Middle a1> a2Indicate attribute a1Compared to a2It is more important, higher priority is possessed in multiple attribute decision making (MADM)；Policymaker is to alternative
pk(k=1,2 ..., m) utilize attribute aj(j=1,2 ..., n) it is evaluated.Still further, the step 1 considers association
1.2 section hesitation fuzzy decision matrixes of the model foundation of the section hesitation fuzzy graph multiple attributive decision making method of property and dominance relation
With the building of section hesitation fuzzy graph:
After the foundation and expression for completing 1.1 decision informations in step 1, policymaker is to alternative pk(k=1,
2 ..., m) utilize attribute aj(j=1,2 ..., n) it is evaluated；Using the theory of section hesitation fuzzy set, hesitated with section
The form of fuzzy number provides evaluation result dkj, to constitute section hesitation fuzzy decision matrix D, D=(dkj)m×n；Recycle mould
The theoretical building section hesitation fuzzy graph of paste figure；Section hesitation fuzzy decision matrix is completed especially by following steps and section hesitates
The building of fuzzy graph；
Firstly, interval of definition hesitation fuzzy set is as follows:
If V is a nonempty finite domain, int [0,1] represents all set for closing subinterval composition on [0,1], on V
1 section hesitation fuzzy set be represented by function h, which, which is applied on V, can return to 1 subset on int [0,1],
Claim
For 1 section hesitation fuzzy set on V,It is the set of several possibility interval numbers in int [0,1], indicates V
In element x belong toDegree of membership, claimIt hesitates fuzzy first, is expressed as sectionIts
Middle γ=[γL,γU] it is 1 interval number, the lower bound of the interval number and the upper bound are denoted as γL=inf γ and γU=sup γ, this
Outside, section hesitation fuzzy set all on V is denoted as IVHF (V)；
After the foundation and expression for completing 1.1 decision informations in step 1, policymaker is to alternative pk(k=1,
2 ..., m) utilize attribute aj(j=1,2 ..., n) it is evaluated；Using the definition of section hesitation fuzzy set, hesitated with section
The form of fuzzy number provides evaluation result dkj, to constitute section hesitation fuzzy decision matrix D, D=(dkj)m×n；
Secondly, ambiguity in definition figure is as follows:
If V is 1 nonempty finite set, the equivalence relation being defined on V × V~{ (x, x): x ∈ V } is following form:
(x1,y1)~(x2,y2)Or (x1,y1)=(x2,y2) or x1=y2, y1=x2；ClaimFor the quotient obtained by this equivalence relation
Collection, and xy, yx or [(x, y)] they are referred to as the equivalence class comprising (x, y)；If it existsThen claiming ordered pair (V, E) is 1 undirected
Simple graph,
If V is 1 nonempty finite set, ambiguity in definition figure G is following form:
G=(μ, ρ),
Wherein μ: V → [0,1], ρ: V × V → [0,1], and for all x, y ∈ V, have ρ (xy)≤μ (x) ∧ μ (y) at
Vertical, G=(μ, ρ) is figure G at this time*The fuzzy graph μ of=(V, E) is referred to as the fuzzy vertex set about fuzzy graph G, and ρ is about fuzzy
Scheme the fuzzy side collection of G；
Again, interval of definition hesitation fuzzy graph:
If V is 1 nonempty finite set, interval of definition hesitation fuzzy graph G is following form:
WhereinIt is 1 section hesitation fuzzy set on V, meets It is 1 section on V × V
Hesitation fuzzy set meetsAnd have for all x, y ∈ VAt
It is vertical, at this timeIt is figure G*The section hesitation fuzzy graph of=(V, E) claimsFor the area about section hesitation fuzzy graph G
Between hesitate fuzzy vertex set,Side collection is obscured to hesitate about the section of section hesitation fuzzy graph G；
Finally, building section hesitation fuzzy graph:
It enablesIt is 1 section hesitation fuzzy set on property set V, meets It is 1 on V × V
Hesitation fuzzy set in section meetsFor any aiAnd aj, have
It sets up, thus gives figure G*The section hesitation fuzzy graph of=(V, E)ClaimFor about section hesitation fuzzy graph G
Section hesitate fuzzy vertex set,Side collection is obscured to hesitate about the section of section hesitation fuzzy graph G, whereinGeneration
Table section, which hesitates, obscures side collectionCorresponding section, which hesitates, obscures member,WithRepresent the fuzzy vertex set of section hesitationCorresponding section hesitates fuzzy first.
Further, the step 2 considers the section hesitation fuzzy graph multiple attribute decision making (MADM) side of relevance and dominance relation
During the model of method calculates,
Input: section hesitation fuzzy decision matrix D=(dkj)m×n, linear precedence relationship between attribute describes to close between attribute
The section hesitation fuzzy graph of connection property；
Output: optimal alternative；
It is required according to the input information of model and output, by the attribute a with relevance for calculating alternative decision making schemei
And ajBetween section hesitation fuzzy message energy coefficient, attribute weight ωj, alternative decision making scheme pk(k=1,2 ..., m)
Bulk properties value, and to alternative decision making scheme pk(k=1,2 ..., bulk properties value comparative analysis m), finally determine excellent standby
Select decision scheme；Specific step is as follows:
The attribute a with relevance of step 2.1 calculating alternative decision making schemeiAnd ajBetween section hesitation fuzzy message
Energy coefficient ψij；
Step 2.2 utilizes the linear precedence relationship computation attribute weights omega between attributej；
Step 2.3 calculates alternative decision making scheme pkThe bulk properties value of (k=1,2 ..., m)
Step 2.4 calculates alternative decision making scheme pkThe score value of corresponding bulk properties value
Step 2.5 determines optimal alternative decision making scheme
Further, the step 2 considers the section hesitation fuzzy graph multiple attribute decision making (MADM) side of relevance and dominance relation
The model of method is followed in the calculating of step 2.1 to 2.3 in calculating as given a definition and operation principle:
It defines 1. and sets a=[aL,aU] and b=[bL,bU] it is interval number, there is following operation rule:
1. if aL=bLAnd aU=bU, then a=b；
2. a+b=[aL+bL,aU+bU], a-b=[min (aL-bL,aU-bU),max(aL-bL,aU-bU)]；
3. working as aLAnd bLWhen being all larger than 0, ab=[aLbL,aUbU],
It defines 2. and sets a=[aL,aU] and b=[bL,bU] it is interval number, the possibility degree of a >=b and a≤b are defined as shape
Formula:
In order to improve the operation efficiency of section hesitation fuzzy set, in conjunction with it is assumed hereinafter that giving the letter of section hesitation fuzzy set
Change operation rule:
1. for 1 section hesitation fuzzy setIt enables whereinIn interval number by ascending order arrange, claimForIn the big number of t, the lower bound of the interval number and the upper bound are denoted asWith
2. for 2 section hesitation fuzzy setsWithIf whereinWithIn interval number number it is different,
It then hesitates to the section containing less interval number and obscures member supplement wherein maximum interval number, finally makeWithIn
Interval number number it is identical；
It defines 3. and sets V as a nonempty finite domain, there are section hesitation fuzzy setsIt is defined as follows
Operation rule:
①
②
③
④
⑤
⑥
The step 2 considers that the model of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation calculates
In, step 2.4 and 2.5 calculating in follow as given a definition and operation principle:
4. are defined to setIt hesitates for 1 section fuzzy first,It representsThe number of middle interval number claims
ForScoring function for 2 section hesitation fuzzy setsWithIf
Then
Further, the step 2 considers the section hesitation fuzzy graph multiple attribute decision making (MADM) side of relevance and dominance relation
During the model of method calculates,
The attribute a with relevance of step 2.1 calculating alternative decision making schemeiAnd ajBetween section hesitation fuzzy message
Energy coefficient ψij；Circular are as follows:
For 2 attribute a with relevanceiAnd aj(i, j=1,2 ..., n), section hesitation fuzzy message energy coefficient
It is expressed asHesitation fuzzy message energy coefficient in section represents aiFor ajInfluence each other journey
Degree, whereinIt representsThe number of middle interval number.
Further, the step 2 considers the section hesitation fuzzy graph multiple attribute decision making (MADM) side of relevance and dominance relation
During the model of method calculates,
The attribute a with relevance of step 2.1 calculating alternative decision making schemeiAnd ajBetween section hesitation fuzzy message
Energy coefficient ψij；Wherein, calculated section hesitation fuzzy message energy coefficient is between [0,0] and [1,1], when section still
When the maximum value of Henan fuzzy message energy coefficient reaches [1,1], relevance is maximum between indicating attribute, when section hesitation fuzzy message
Energy coefficient reaches minimum value for [0,0], between expression attribute independently of each other.
Further, the step 2 considers the section hesitation fuzzy graph multiple attribute decision making (MADM) side of relevance and dominance relation
During the model of method calculates,
The attribute a with relevance of step 2.1 calculation alternative decision making schemeiAnd ajBetween section hesitation fuzzy message energy
Coefficient of discharge ψij；Including calculating the section hesitation fuzzy message energy coefficient in alternative decision making scheme between all any two attributes
ψij。
Further, the step 2 considers the section hesitation fuzzy graph multiple attribute decision making (MADM) side of relevance and dominance relation
During the model of method calculates,
Step 2.2 utilizes the linear precedence relationship computation attribute weights omega between attributej；Specifically:
The eccentricity of vertex correspondence is obscured firstly, calculating each section and hesitating, ifIt is figure G*=(V, E's)
Hesitation fuzzy graph in section hesitates there are n+1 section and obscures vertex u=a0,a1,...,an-1,an=v, then section hesitates fuzzy
Eccentricity is
Secondly, seeking eccentricity e (a to each attribute of property set V in the Multiple Attribute Decision Problems described in step 1j)(j
=1,2 ..., n), and be normalizedUtilize the linear precedence relationship between attribute, meter
Calculate attribute weight ωj；
When there is linear precedence relationship a between attribute1> a2> ... > an, then attribute weight ωjIt can be used to normalization area
Between the fuzzy eccentricity that hesitates obtain, i.e.,Wherein as j ≠ 0,As j=0, Sj=[1,1].
Compared with prior art, the invention has the following beneficial effects:
1, the present invention combines section hesitation fuzzy set and fuzzy graph to propose the concept of section hesitation fuzzy graph, and to section
The operation rule of hesitation fuzzy graph is provided.
2, hesitation fuzzy graph in section is applied in the Multiple Attribute Decision Problems for considering relevance and dominance relation, invention one
For the multiple attributive decision making method for existing simultaneously relevance and dominance relation between attribute in kind section hesitation blurred background, thus side
Exist simultaneously between attribute relevance and dominance relation more attribute questions decision.
3, the present invention takes full advantage of the characteristics of fuzzy graph and advantage, can not only effectively indicate that multiple attribute decision making (MADM) information has
Standby incompleteness and hesitation, and existing relevance and preferential can be handled in section hesitation fuzzy enviroment between attribute simultaneously
Relationship.The characteristics of utilizing section hesitation fuzzy graph and advantage have relevance and preferential while being generally existing in reality
The complicated uncertain multi-attribute decision-making problem of relationship provides a kind of effective solution scheme, and has further highlighted section still
Henan fuzzy graph is modeled in important scientific meaning and potential using value in complicated multiple attribute decision making (MADM).
Detailed description of the invention
Fig. 1 is the section hesitation fuzzy graph decision-making technique decision model of consideration relevance and dominance relation of the invention；
Fig. 2 is the section hesitation fuzzy graph decision-making technique model calculation block of consideration relevance and dominance relation of the invention
Figure；
Fig. 3 is the section hesitation fuzzy graph of relevance between describing attribute in embodiment.
Specific embodiment
The present invention is described in detail below with reference to the accompanying drawings and embodiments.
According to universities talents team foundation is reinforced, talent in demand is attracted to be effectively improved talent team's knot into teaching body
The demand of structure, certain Chinese Universities ' management college have carried out the introduction work of overseas outstanding personnel, by the first of human resources expert
Step audit, has 5 applicants to enter interview program.It is asked for the multiple attribute decision making (MADM) in the overseas outstanding personnel's introduction of the colleges and universities
Topic, will further be described in detail method of the invention.
As shown in Figures 1 to 3, a kind of section hesitation fuzzy graph decision considering relevance and dominance relation provided by the invention
The building of method includes the following steps: that decision model is as shown in Figure 1.
Step 1. considers the model foundation of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation
The foundation and expression of 1.1 decision informations: being directed to a Multiple Attribute Decision Problems, firstly, determining the multiple attribute decision making (MADM)
There is relevance and dominance relation simultaneously between the attribute of problem, then establish alternative collection, property set and attribute weight, enabling should
The alternative decision making scheme of Multiple Attribute Decision Problems integrates as P, P={ p1,p2,...,pm, property set V, V={ a1,a2,...,
an, attribute weight ω, ω=(ω1,ω2,...,ωn)T；And there is linear precedence relationship a between attribute1> a2> ... >
an, wherein a1> a2Indicate attribute a1Compared to a2It is more important, higher priority is possessed in multiple attribute decision making (MADM)；Policymaker is to alternative
Scheme pk(k=1,2 ..., m) utilize attribute aj(j=1,2 ..., n) it is evaluated；
Multiple Attribute Decision Problems in the present embodiment are that the overseas outstanding personnel of colleges and universities introduces, and applicant's set expression is P=
{p1,p2,p3,p4,p5, University Human Resources expert has uniformly formulated the property set V={ a to 5 applicants evaluation1,a2,
a3,a4, wherein a1Represent moral character, a2Represent the capacity of scientific research, a3Represent teaching ability, a4Education background is represented, this 4 categories
The weight vectors of property are expressed as ω=(ω1,ω2,ω3,ω4)T, wherein there are dominance relations between talent evaluation attribute in interview
a1> a2> a3> a4, i.e. the human resources expert investigation that preferentially carries out moral character successively investigated scientific research energy by importance later
Power, teaching ability, education background；
The building of 1.2 section hesitation fuzzy decision matrixes and section hesitation fuzzy graph: section hesitation fuzzy set and mould are utilized
Paste figure is theoretical, completes the building of section hesitation fuzzy decision matrix and section hesitation fuzzy graph as follows；
Firstly, interval of definition hesitation fuzzy set is as follows:
If V is a nonempty finite domain, int [0,1] represents all set for closing subinterval composition on [0,1].On V
1 section hesitation fuzzy set be represented by function h, which, which is applied on V, can return to 1 subset on int [0,1],
Claim
For 1 section hesitation fuzzy set on V,It is the set of several possibility interval numbers in int [0,1], indicates V
In element x belong toDegree of membership, claimIt hesitates fuzzy first, is expressed as sectionIts
Middle γ=[γL,γU] it is 1 interval number, the lower bound of the interval number and the upper bound are denoted as γL=inf γ and γU=sup γ, this
Outside, section hesitation fuzzy set all on V is denoted as IVHF (V)；
In completing step 1 after the foundation and expression of 1.1 decision informations, policymaker is to alternative pk(k=1,2 ...,
M) attribute a is utilizedj(j=1,2 ..., n) it is evaluated；Using the definition of section hesitation fuzzy set, with section hesitation fuzzy number
Form provide evaluation result dkj, to constitute section hesitation fuzzy decision matrix D, D=(dkj)m×n；
Rationally to describe the incompleteness and hesitation that uncertain information in talent evaluation has, human resources expert is established
Section hesitation fuzzy decision matrix D=(dkj)5×4, as shown in table 1:
1 section hesitation fuzzy decision matrix of table
Secondly, ambiguity in definition figure is as follows:
If V is 1 nonempty finite set, the equivalence relation being defined on V × V~{ (x, x): x ∈ V } is following form:
(x1,y1)~(x2,y2)Or (x1,y1)=(x2,y2) or x1=y2, y1=x2；ClaimFor the quotient obtained by this equivalence relation
Collection, and xy, yx or [(x, y)] they are referred to as the equivalence class comprising (x, y)；If it existsThen claiming ordered pair (V, E) is 1 undirected
Simple graph,
If V is 1 nonempty finite set, ambiguity in definition figure G is following form:
G=(μ, ρ),
Wherein μ: V → [0,1], ρ: V × V → [0,1], and for all x, y ∈ V, have ρ (xy)≤μ (x) ∧ μ (y) at
Vertical, G=(μ, ρ) is figure G at this time*The fuzzy graph μ of=(V, E) is referred to as the fuzzy vertex set about fuzzy graph G, and ρ is about fuzzy
Scheme the fuzzy side collection of G；
Again, interval of definition hesitation fuzzy graph:
If V is 1 nonempty finite set, interval of definition hesitation fuzzy graph G is following form:
WhereinIt is 1 section hesitation fuzzy set on V, meets It is 1 section on V × V
Hesitation fuzzy set meetsAnd have for all x, y ∈ VAt
It is vertical, at this timeIt is figure G*The section hesitation fuzzy graph of=(V, E) claimsFor the section about section hesitation fuzzy graph G
Hesitate fuzzy vertex set,Side collection is obscured to hesitate about the section of section hesitation fuzzy graph G；
Finally, building section hesitation fuzzy graph:
It enablesIt is 1 section hesitation fuzzy set on property set V, meets It is 1 on V × V
Hesitation fuzzy set in section meetsFor any aiAnd aj, have
It sets up, thus gives figure G*The section hesitation fuzzy graph G of=(V, E),ClaimIt is fuzzy to hesitate about section
The section for scheming G, which hesitates, obscures vertex set,Side collection is obscured to hesitate about the section of section hesitation fuzzy graph G, wherein
Represent the fuzzy side collection of section hesitationCorresponding section, which hesitates, obscures member,WithRepresent the fuzzy vertex of section hesitation
CollectionCorresponding section hesitates fuzzy first.
In view of often there is relevance between talent evaluation attribute in the present embodiment, such as possess the application of outstanding education background
Person's capacity of scientific research is generally also relatively strong, establishes figure G*The section hesitation fuzzy graph of=(V, E)To describe the pass between attribute
Connection property, wherein E={ a1a2,a1a3,a1a4,a2a3,a2a4,a3a4, the section hesitation fuzzy graph is as shown in Figure 3.
The selection of the integrated analysis and optimal case of 1.3 section hesitation fuzzy messages: the multiple of alternative decision making scheme are integrated
After section hesitation fuzzy message under attribute, to alternative decision making scheme p1,p2,...,pmCorresponding bulk properties value is analyzed
And it chooses the best alternatives；
Next, using considering that it is best that the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation determines
Apply for person.It integrates after the section hesitation fuzzy message under multiple attributes to decision scheme p1,p2,p3,p4,p5Corresponding overall category
Property value analyzed and chosen the best alternatives, that is, determine best application person.
Step 2 considers the model construction of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation
The block diagram of model construction is as shown in Figure 2.
Input: section hesitation fuzzy decision matrix D=(dkj)m×n, linear precedence relationship a between attribute1> a2> ... >
an, the section hesitation fuzzy graph of relevance between attribute is described
Output: optimal alternative；
The attribute a with relevance of step 2.1 calculating alternative decision making schemeiAnd ajBetween section hesitation fuzzy message
Energy coefficient ψij；Circular are as follows: for 2 attribute a with relevanceiAnd aj(i, j=1,2 ..., n), section
Hesitation fuzzy message energy coefficient is expressed asSection hesitation fuzzy message energy coefficient generation
Table aiFor ajInfluence each other degree,It representsThe number of middle interval number；Wherein, calculated section
Hesitation fuzzy message energy coefficient is between [0,0] and [1,1], when the maximum value of section hesitation fuzzy message energy coefficient reaches
When to [1,1], relevance is maximum between indicating attribute, is [0,0], table when hesitation fuzzy message energy coefficient in section reaches minimum value
Show mutually indepedent between attribute.
Calculate the attribute a with relevance of alternative decision making schemeiAnd ajBetween section hesitation fuzzy message energy coefficient
ψijIncluding calculating the section hesitation fuzzy message energy coefficient ψ in alternative decision making scheme between all any two attributesij；
Step 2.2 utilizes the linear precedence relationship computation attribute weights omega between attributej；Circular are as follows:
The eccentricity of vertex correspondence is obscured firstly, calculating each section and hesitating, ifIt is figure G*=(V, E's)
Hesitation fuzzy graph in section hesitates there are n+1 section and obscures vertex u=a0,a1,...,an-1,an=v, then section hesitates fuzzy
Eccentricity is
Secondly, seeking eccentricity e (a to each attribute of property set V in the Multiple Attribute Decision Problems described in step 1.1j)
(j=1,2 ..., n), and be normalizedUsing the linear precedence relationship between attribute,
Computation attribute weights omegaj；
When there is linear precedence relationship a between attribute1> a2> ... > an, then attribute weight ωjIt can be used to normalization area
Between the fuzzy eccentricity that hesitates obtain, i.e.,Wherein as j ≠ 0,As j=0, Sj=[1,1].
Step 2.3 calculates alternative decision making scheme pkThe bulk properties value of (k=1,2 ..., m)
Step 2.4 calculates alternative decision making scheme pkThe score value of corresponding bulk properties value
Step 2.5 determines optimal alternative decision making scheme
According to above step, the present embodiment is specifically calculated and is analyzed as follows:
The attribute a with relevance of step 2.1 calculating alternative decision making schemeiAnd ajBetween section hesitation fuzzy message
Energy coefficient ψij；Calculate the section hesitation fuzzy message energy between the attribute of the overseas outstanding personnel's introduction decision problem of the colleges and universities
Coefficient, calculated result are as follows:
Similarly, ψ is obtained13=[0.025,0.1], ψ14=
[0.045,0.08], ψ23=[0.05,0.1], ψ24=[0.02,0.045], ψ34=[0.125,0.205]；
Step 2.2 utilizes the linear precedence relationship computation attribute weights omega between attributej；
In the present embodiment, the linear precedence relationship a between talent evaluation attribute is utilized1> a2> a3> a4Computation attribute weight；
It is e (a that the section on vertex, which hesitates and obscures eccentricity,1)={ [2.5,5], [5,10] }, e (a2)={ [2.5,3.3],
[5,10] }, e (a3)={ [2.5,5], [5,10] }, e (a4)={ [3.3,5] }；
Then hesitating after fuzzy eccentricity is normalized to the above section has
S can further be obtained0=[1,1], S1={ [0.25,0.5], [0.5,1] }, S2=[0.25,0.5], [0.76,
1]},S3={ [0.25,0.5], [0.5,1] }, S4={ [0.5,0.76] }；
Talent evaluation attribute weight is ω1=[1,1], ω2={ [0.25,0.5], [0.5,1] }, ω3=[0.06,
0.25], [0.38,1] }, ω4={ [0.02,0.13], [0.19,1] }；
Step 2.3 calculates alternative decision making scheme pkThe bulk properties value of (k=1,2 ..., m)
Applicant p is calculated in the present embodimentkThe bulk properties value of (k=1,2 ..., 5) is as follows；
Similarly, it obtains
Step 2.4 calculates alternative decision making scheme pkThe score value of corresponding bulk properties value
The score value that each applicant corresponds to bulk properties value is finally calculated in the present embodiment, can be obtained
Step 2.5 determines optimal alternative decision making scheme
FoundationSequence from big to small obtains applicant's sequence p5> p4> p3> p1> p2, therefore the colleges and universities are overseas
Optiman is applicant p in outstanding personnel's introduction5。
In the present embodiment, the step 2 considers the section hesitation fuzzy graph multiple attribute decision making (MADM) side of relevance and dominance relation
It is followed in the model construction of method, in the calculating of step 2.1 to 2.3 as given a definition and operation principle:
It defines 1. and sets a=[aL,aU] and b=[bL,bU] it is interval number, there is following operation rule:
If I) aL=bLAnd aU=bU, then a=b；
II) a+b=[aL+bL,aU+bU], a-b=[min (aL-bL,aU-bU),max(aL-bL,aU-bU)]；
III) work as aLAnd bLWhen being all larger than 0,
It defines 2. and sets a=[aL,aU] and b=[bL,bU] it is interval number, the possibility degree of a >=b and a≤b are defined as shape
Formula:
In order to improve the operation efficiency of section hesitation fuzzy set, in conjunction with it is assumed hereinafter that giving the letter of section hesitation fuzzy set
Change operation rule:
1. for 1 section hesitation fuzzy setIt enables whereinIn interval number by ascending order arrange, claimForIn the big number of t, the lower bound of the interval number and the upper bound are denoted asWith
2. for 2 section hesitation fuzzy setsWithIf whereinWithIn interval number number it is different,
It then hesitates to the section containing less interval number and obscures member supplement wherein maximum interval number, finally makeWithIn
Interval number number it is identical；
It defines 3. and sets V as a nonempty finite domain, there are section hesitation fuzzy setsDefinition is such as
Lower operation rule:
①
②
③
④
⑤
⑥
The step 2 considers the model construction of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation
In, step 2.4 and 2.5 calculating in follow as given a definition and operation principle:
4. are defined to setIt hesitates for 1 section fuzzy first,It representsThe number of middle interval number claims
ForScoring function for 2 section hesitation fuzzy setsWithIf
Then
The present invention and decision-making technique comparative analysis in the prior art
The present embodiment is the section hesitation Fuzzy Multiple Attribute Decision Making problem with relevance and dominance relation, in numerous classics
In multiple attributive decision making method, Integrated Operator method merges decision information using different Integrated Operators, later according to scheme
Score value is ranked up scheme, is a kind of common multiple attributive decision making method.By relevance the considerations of the present embodiment and preferentially
The section hesitation fuzzy graph decision-making technique of relationship obscures the preferential weighted operator of Einstein with based on section hesitation, and is based on area
Between the comparing property of multiple attributive decision making method of hesitation Fuzzy priority weighted operator be analyzed as follows:
1) it and is hesitated based on section and obscures the comparative analysis of multiple attributive decision making method of the preferential weighted operator of Einstein
The multiple attributive decision making method of the preferential weighted operator of Einstein is obscured according to hesitating based on section, if section hesitation mould
Paste decision matrix is D=(dkj)m×n(k=1,2 ..., m, j=1,2 ..., n), then the section fuzzy Einstein that hesitates is preferential
It is weighted and averaged operator and section hesitates and obscures the preferential following of weighted geometric operator representation of Einstein
1. section hesitates, fuzzy Einstein is preferentially weighted and averaged operator:
The fuzzy preferential weighted geometric operator of Einstein 2. section hesitates:
WhereinTk1=1 (k=1,2 ..., m), E (s
(dki)) it is dkiScoring function s (dki) desired value.
It, can be by section hesitation mould of each applicant under corresponding talent's evaluation attributes according to the above preferential Integrated Operator of 2 class
Hesitation obscures first score value between paste number is integrated and acquires integrated back zone, and applicant corresponding to larger score value is sea
The optiman that outer outstanding personnel introduces, final decision the result shows that: preferentially weight and puts down using the section fuzzy Einstein that hesitates
It is p that equal operator and section, which hesitate and obscure applicant's sequence obtained by the preferential weighted geometric operator of Einstein,5> p4> p3> p1>
p2, section hesitation fuzzy graph multiple attributive decision making method acquired results one with relevance the considerations of the present embodiment and dominance relation
It causes, i.e., optiman is applicant p5。
2) with the comparative analysis of the multiple attributive decision making method based on section hesitation Fuzzy priority weighted operator
According to the multiple attributive decision making method based on section hesitation Fuzzy priority weighted operator, if section hesitation fuzzy decision square
Battle array is D=(dkj)m×n(k=1,2 ..., m, j=1,2 ..., n), then section hesitation Fuzzy priority weighted average operator and area
Between the following of hesitation Fuzzy priority weighted geometric operator representation
1. hesitation Fuzzy priority in section is weighted and averaged operator:
2. section hesitation Fuzzy priority weighted geometric operator:
WhereinTk1=1 (k=1,2 ..., m), s (dki)
For dkiScoring function value.
It is similar with the comparative analysis that front is carried out, section of each applicant under corresponding talent's evaluation attributes is hesitated
Hesitation obscures first score value between fuzzy number is integrated and acquires integrated back zone, and applicant corresponding to larger score value is
The optiman that overseas outstanding personnel introduces, final decision the result shows that: be weighted and averaged operator using section hesitation Fuzzy priority
Gained applicant is ordered as p5> p4> p3> p1> p2, and using set forth herein method acquired results are consistent, and utilize section still
Applicant obtained by the Fuzzy priority weighted geometric operator of Henan is ordered as p5> p4> p1> p3> p2, set forth herein obtained by method with utilization
As a result not quite identical, it is readily seen that p1With p3Between sequence have differences, but the above ranking results do not influence most preferably to apply for
The selection of person, i.e. optiman are still applicant p5。
According to the above comparative analysis as a result, the multiple attributive decision making method based on the above-mentioned preferential Integrated Operator of 4 class can be reasonable
The hesitation Fuzzy Multiple Attribute Decision Making problem in section with dominance relation is solved, but is come from specific theoretical model and decision analysis process
See not yet have the case where relevance between consideration attribute, i.e., it, can not in the recruitment of the universities talents described in the present embodiment background
Influence of the existing relevance to multiple attribute decision making (MADM) result between talent evaluation attribute is embodied, in extreme circumstances, when closing between attribute
When the numerical value of connection property differs greatly, the gained result of decision is easy to appear the situation inconsistent with the method for the present invention.Such as according to base
Occur in the section hesitation Fuzzy priority weighted geometric operator gained result of decision, applicant's sequence inconsistent with result before
The case where, i.e., existing relevance affects obtaining for final decision result between attribute.
Different from the common multiple attributive decision making method based on Integrated Operator, hesitation fuzzy graph in section proposed by the present invention is more
The characteristics of attribute decision-making technique takes full advantage of fuzzy graph and advantage can not only effectively indicate what multiple attribute decision making (MADM) information had
Incompleteness and hesitation, and existing relevance can be handled in section hesitation fuzzy enviroment between attribute simultaneously and preferential closed
It is the characteristics of utilizes section hesitation fuzzy graph and advantage, has relevance and preferential pass while being generally existing in reality
The complicated uncertain multi-attribute decision-making problem of system provides a kind of effective solution scheme, meanwhile, section proposed by the present invention is still
Henan fuzzy graph multiple attributive decision making method has further highlighted the important section that hesitation fuzzy graph is modeled in complicated multiple attribute decision making (MADM)
Learn meaning and potential using value.
Claims (9)
1. considering the section hesitation fuzzy graph decision-making technique of relevance and dominance relation, characterized by the following steps:
Step 1. considers the model foundation of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation
The foundation and expression of 1.1 decision informations: being directed to a Multiple Attribute Decision Problems, firstly, determining the Multiple Attribute Decision Problems
Attribute between there is relevance and dominance relation simultaneously；Then, alternative collection, property set and attribute weight are established；Enable this more
The alternative decision making scheme of attribute decision problem integrates as P, P={ p1,p2,...,pm, property set V, V={ a1,a2,...,an,
Attribute weight is ω, ω=(ω1,ω2,...,ωn)T, policymaker is to alternative pk(k=1,2 ..., m) utilize attribute aj
(j=1,2 ..., n) it is evaluated；
The building of 1.2 section hesitation fuzzy decision matrixes and section hesitation fuzzy graph: 1.1 decision informations in step 1 are completed
Foundation and expression after, policymaker is to alternative pk(k=1,2 ..., m) utilize attribute aj(j=1,2 ..., n) it is commented
Valence；Using the theory of section hesitation fuzzy set, evaluation result d is provided with the form of section hesitation fuzzy numberkj, to constitute section
Hesitation fuzzy decision matrix D, D=(dkj)m×n；Fuzzy network theory is recycled to construct section hesitation fuzzy graph；
The selection of the integrated analysis and optimal case of 1.3 section hesitation fuzzy messages: multiple attributes of integrated alternative decision making scheme
Under section hesitation fuzzy message after, to alternative decision making scheme p1,p2,...,pmCorresponding bulk properties value is analyzed and is selected
Select optimal case；
Step 2. considers that the model of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation calculates
Input: section hesitation fuzzy decision matrix D=(dkj)m×n, linear precedence relationship between attribute describes relevance between attribute
Section hesitation fuzzy graph；
Output: optimal alternative；
It is required according to the input information of model and output, by the attribute a with relevance for calculating alternative decision making schemeiAnd aj
Between section hesitation fuzzy message energy coefficient, attribute weight ωj, alternative decision making scheme pkThe totality of (k=1,2 ..., m)
Attribute value, and to alternative decision making scheme pk(k=1,2 ..., bulk properties value comparative analysis m), finally determine it is excellent it is alternative certainly
Plan scheme.
2. the section hesitation fuzzy graph decision-making technique according to claim 1 for considering relevance and dominance relation, feature
Be: the step 1 consider the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation model foundation it
The foundation and expression of 1.1 decision informations, establish alternative collection, property set and attribute weight；Enable the Multiple Attribute Decision Problems
Alternative decision making scheme integrates as P, P={ p1,p2,...,pm, property set V, V={ a1,a2,...,an, attribute weight ω, ω
=(ω1,ω2,...,ωn)T；And between attribute there is linear precedence relationship be a1> a2> ... > an, wherein a1> a2It indicates to belong to
Property a1Compared to a2It is more important, higher priority is possessed in multiple attribute decision making (MADM)；Policymaker is to alternative pk(k=1,2 ...,
M) attribute a is utilizedj(j=1,2 ..., n) it is evaluated.
3. the section hesitation fuzzy graph decision-making technique according to claim 2 for considering relevance and dominance relation, feature
Be: the step 1 consider the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation model foundation it
The building of 1.2 section hesitation fuzzy decision matrixes and section hesitation fuzzy graph: building for 1.1 decision informations in step 1 is completed
After vertical and expression, policymaker is to alternative pk(k=1,2 ..., m) utilize attribute aj(j=1,2 ..., n) it is evaluated；Benefit
With the theory of section hesitation fuzzy set, evaluation result d is provided with the form of section hesitation fuzzy numberkj, to constitute section hesitation
Fuzzy decision matrix D, D=(dkj)m×n；Fuzzy network theory is recycled to construct section hesitation fuzzy graph；Especially by following steps
Complete the building of section hesitation fuzzy decision matrix and section hesitation fuzzy graph；
Firstly, interval of definition hesitation fuzzy set is as follows:
If V be a nonempty finite domain, int [0,1] represent [0,1] on it is all close subinterval composition set, 1 on V
A section hesitation fuzzy set is represented by function h, which, which is applied on V, can return to 1 subset on int [0,1], claims
For 1 section hesitation fuzzy set on V,It is the set of several possibility interval numbers in int [0,1], indicates in V
Element x belongs toDegree of membership, claimIt hesitates fuzzy first, is expressed as sectionWherein γ
=[γL,γU] it is 1 interval number, the lower bound of the interval number and the upper bound are denoted as γL=inf γ and γU=sup γ, in addition, V
Upper all section hesitation fuzzy sets are denoted as IVHF (V)；
After the foundation and expression for completing 1.1 decision informations in step 1, policymaker is to alternative pk(k=1,2 ..., m)
Utilize attribute aj(j=1,2 ..., n) it is evaluated；Using the definition of section hesitation fuzzy set, with section hesitation fuzzy number
Form provides evaluation result dkj, to constitute section hesitation fuzzy decision matrix D, D=(dkj)m×n；
Secondly, ambiguity in definition figure is as follows:
If V is 1 nonempty finite set, the equivalence relation being defined on V × V~{ (x, x): x ∈ V } is following form:Or (x1,y1)=(x2,y2) or x1=y2, y1=x2；ClaimFor the quotient set obtained by this equivalence relation,
And xy, yx or [(x, y)] are referred to as the equivalence class comprising (x, y)；If it existsThen claiming ordered pair (V, E) is 1 undirected simple
Figure,
If V is 1 nonempty finite set, ambiguity in definition figure G is following form:
G=(μ, ρ),
Wherein μ: V → [0,1], ρ: V × V → [0,1], and for all x, y ∈ V, there is ρ (xy)≤μ (x) ∧ μ (y) to set up, this
When G=(μ, ρ) be figure G*The fuzzy graph μ of=(V, E) is referred to as the fuzzy vertex set about fuzzy graph G, and ρ is about fuzzy graph G's
Fuzzy side collection；
Again, interval of definition hesitation fuzzy graph:
If V is 1 nonempty finite set, interval of definition hesitation fuzzy graph G is following form:
WhereinIt is 1 section hesitation fuzzy set on V, meetsV → int [0,1],It is 1 section hesitation on V × V
Fuzzy set meetsV × V → int [0,1], and have for all x, y ∈ VIt sets up,
At this timeIt is figure G*The section hesitation fuzzy graph of=(V, E) claimsStill for the section about section hesitation fuzzy graph G
Henan obscures vertex set,Side collection is obscured to hesitate about the section of section hesitation fuzzy graph G；
Finally, building section hesitation fuzzy graph:
It enablesIt is 1 section hesitation fuzzy set on property set V, meetsV → int [0,1],It is 1 section on V × V
Hesitation fuzzy set meetsV × V → int [0,1], for any aiAnd aj, haveAt
It is vertical, thus give figure G*The section hesitation fuzzy graph of=(V, E)ClaimFor about section hesitation fuzzy graph G's
Section, which hesitates, obscures vertex set,Side collection is obscured to hesitate about the section of section hesitation fuzzy graph G, whereinIt represents
Section, which hesitates, obscures side collectionCorresponding section, which hesitates, obscures member,WithRepresent the fuzzy vertex set of section hesitation
Corresponding section hesitates fuzzy first.
4. the section hesitation fuzzy graph decision-making technique according to claim 3 for considering relevance and dominance relation, feature
It is: during the step 2 considers that the model of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation calculates,
Input: section hesitation fuzzy decision matrix D=(dkj)m×n, linear precedence relationship between attribute describes relevance between attribute
Section hesitation fuzzy graph；
Output: optimal alternative；
It is required according to the input information of model and output, by the attribute a with relevance for calculating alternative decision making schemeiAnd aj
Between section hesitation fuzzy message energy coefficient, attribute weight ωj, alternative decision making scheme pkThe totality of (k=1,2 ..., m)
Attribute value, and to alternative decision making scheme pk(k=1,2 ..., bulk properties value comparative analysis m), finally determine it is excellent it is alternative certainly
Plan scheme；Specific step is as follows:
The attribute a with relevance of step 2.1 calculating alternative decision making schemeiAnd ajBetween section hesitation fuzzy message energy
Coefficient ψij；
Step 2.2 utilizes the linear precedence relationship computation attribute weights omega between attributej；
Step 2.3 calculates alternative decision making scheme pkThe bulk properties value of (k=1,2 ..., m)
Step 2.4 calculates alternative decision making scheme pkThe score value of corresponding bulk properties value
Step 2.5 determines optimal alternative decision making scheme
5. the section hesitation fuzzy graph decision-making technique according to claim 4 for considering relevance and dominance relation, feature
It is: during the step 2 considers that the model of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation calculates,
Step 2.1 is followed into 2.3 calculating as given a definition and operation principle:
It defines 1. and sets a=[aL,aU] and b=[bL,bU] it is interval number, there is following operation rule:
1. if aL=bLAnd aU=bU, then a=b；
2. a+b=[aL+bL,aU+bU], a-b=[min (aL-bL,aU-bU),max(aL-bL,aU-bU)]；
3. working as aLAnd bLWhen being all larger than 0, ab=[aLbL,aUbU],
It defines 2. and sets a=[aL,aU] and b=[bL,bU] it is interval number, the possibility degree of a >=b and a≤b are defined as form:
In order to improve the operation efficiency of section hesitation fuzzy set, transported in conjunction with it is assumed hereinafter that giving simplifying for section hesitation fuzzy set
Calculate rule:
1. for 1 section hesitation fuzzy setIt enables whereinIn interval number by ascending order arrange, claimForIn the big number of t, the lower bound of the interval number and the upper bound are denoted asWith
2. for 2 section hesitation fuzzy setsWithIf whereinWithIn interval number number it is different, then it is right
Section containing less interval number, which hesitates, obscures member supplement wherein maximum interval number, finally makesWithIn area
Between several numbers it is identical；
It defines 3. and sets V as a nonempty finite domain, there are section hesitation fuzzy setsIt is defined as follows operation
Rule:
①
②
③
④
⑤
⑥
During the step 2 considers that the model of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation calculates,
Step 2.4 and 2.5 calculating in follow as given a definition and operation principle:
4. are defined to setIt hesitates for 1 section fuzzy first,It representsThe number of middle interval number claims
ForScoring function for 2 section hesitation fuzzy setsWith
IfThen
6. the section hesitation fuzzy graph decision-making technique according to claim 5 for considering relevance and dominance relation, feature
It is: during the step 2 considers that the model of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation calculates,
The attribute a with relevance of step 2.1 calculating alternative decision making schemeiAnd ajBetween section hesitation fuzzy message energy
Coefficient ψij；Circular are as follows:
For 2 attribute a with relevanceiAnd aj(i, j=1,2 ..., n), section hesitation fuzzy message energy coefficient indicate
ForHesitation fuzzy message energy coefficient in section represents aiFor ajInfluence each other degree,
InIt representsThe number of middle interval number.
7. the section hesitation fuzzy graph decision-making technique according to claim 6 for considering relevance and dominance relation, feature
It is: during the step 2 considers that the model of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation calculates,
The attribute a with relevance of step 2.1 calculating alternative decision making schemeiAnd ajBetween section hesitation fuzzy message energy
Coefficient ψij；Wherein, calculated section hesitation fuzzy message energy coefficient is between [0,0] and [1,1], when section hesitation mould
When the maximum value of paste information energy coefficient reaches [1,1], relevance is maximum between indicating attribute, when section hesitation fuzzy message energy
Coefficient reaches minimum value for [0,0], between expression attribute independently of each other.
8. the section hesitation fuzzy graph decision-making technique according to claim 7 for considering relevance and dominance relation, feature
It is: during the step 2 considers that the model of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation calculates,
The attribute a with relevance of step 2.1 calculating alternative decision making schemeiAnd ajBetween section hesitation fuzzy message energy
Coefficient ψij；Including calculating the section hesitation fuzzy message energy coefficient in alternative decision making scheme between all any two attributes
ψij。
9. the section hesitation fuzzy graph decision-making party according to claim 1 to 8 for considering relevance and dominance relation
Method, it is characterised in that: the step 2 considers the mould of the section hesitation fuzzy graph multiple attributive decision making method of relevance and dominance relation
During type calculates,
Step 2.2 utilizes the linear precedence relationship computation attribute weights omega between attributej；Specifically:
The eccentricity of vertex correspondence is obscured firstly, calculating each section and hesitating, ifIt is figure G*The section of=(V, E)
Hesitation fuzzy graph hesitates there are n+1 section and obscures vertex u=a0,a1,...,an-1,an=v, then section, which hesitates, obscures centrifugation
Rate is
Secondly, seeking eccentricity e (a to each attribute of property set V in the Multiple Attribute Decision Problems described in step 1j) (j=1,
2 ..., n), and be normalizedUtilize the linear precedence relationship between attribute, computation attribute
Weights omegaj；
When there is linear precedence relationship a between attribute1> a2> ... > an, then attribute weight ωjIt can be used to normalize section still
Henan obscures eccentricity and obtains, i.e.,Wherein as j ≠ 0,As j=0, Sj=[1,1].
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111080053A (en) * | 2019-11-01 | 2020-04-28 | 国网江苏省电力有限公司经济技术研究院 | EHF-WAS-based power grid development strategy efficiency and benefit evaluation method |
| CN111311110A (en) * | 2020-03-06 | 2020-06-19 | 山西大学 | Cluster decision method based on dual hesitation fuzzy MULTIMORA and multi-granularity probability rough cluster |
| CN113034033A (en) * | 2021-04-15 | 2021-06-25 | 中国人民解放军战略支援部队航天工程大学 | Method for determining variety of newly-researched equipment spare parts |
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