CN111311110A - Cluster decision method based on dual hesitation fuzzy MULTIMORA and multi-granularity probability rough cluster - Google Patents
Cluster decision method based on dual hesitation fuzzy MULTIMORA and multi-granularity probability rough cluster Download PDFInfo
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Abstract
The invention discloses a cluster decision method based on dual hesitation fuzzy multiorifice and multi-granularity probability rough set, which can depict decision information containing multiple uncertainties, carry out information fusion for eliminating the individual subjectivity of a decision maker on the multi-source decision information, consider decision risk and fault-tolerant rate, provide decision conclusion with strong stability, and input dual hesitation fuzzy information systems (U, V, R)iD); outputting the optimal alternative x*(ii) a The specific steps comprise that each decision maker is calculated to give each alternative scheme xjCorresponding dual hesitation ambiguity conditional probability P (D | x)ij) (ii) a Determining the weight value omega corresponding to each decision makeri(ii) a For each alternative xjCalculating the comprehensive utility value ξ according to the corresponding dual hesitation fuzzy condition probabilityjAnd the comprehensive deviation psijAnd a combined utility value ζjAnd sorting them separately; determining a final sorting result through a sorting ranking function under the theory of advantage to obtain an optimal alternative scheme x*. The invention providesA multi-attribute group decision solution based on decision conclusion stability and interpretability.
Description
Technical Field
The invention relates to the technical field of multi-attribute group decision in decision science, in particular to a group decision method based on dual hesitation fuzzy multiorifice and a multi-granularity probability rough set.
Technical Field
Decision making generally refers to the thought process and behavior that people make choices among many alternatives. Since a single decision maker is limited in knowledge, experience, cognitive abilities, etc., it is difficult to take into account all aspects of a complex decision problem. In order to embody scientization and democratization, a plurality of important decision-making processes usually require a group to participate, and the decision-making conclusion is also completed by the group through negotiation, coordination or negotiation, and the decision-making form participated by a plurality of decision-makers is group decision-making. Furthermore, given that many complex decision problems are solved by interrelated, constraining, or even mutually exclusive attributes, a decision maker is required to analyze a limited number of solutions from the perspective of the attributes and select an optimal solution, thereby forming a multi-attribute decision. In the past 90 s or so, research on multi-attribute group decision has gradually emerged as a cross research direction of group decision and multi-attribute decision. The multi-attribute group decision-making refers to how to integrate preference information given by each decision-making person into group preference information on the premise that a plurality of decision-making persons all give scheme preference information, and a method for sequencing, preferring or grading each decision-making scheme by using a constructed theoretical model.
In recent years, with the development of scientific technology and the advent of the big data era, people can easily obtain a large amount of data for decision making. Meanwhile, due to the limitation of a data acquisition mode, decision data naturally have many uncertainties, decision makers have personal subjectivity, decision data analysis lacks stability and the like, so that the acquisition of a high-quality decision conclusion is influenced. In general, the solution of the multi-attribute group decision problem can be roughly divided into three stages of information representation, information fusion and information analysis. The information representation stage usually needs to process the decision data and has the limitation of multiple uncertainties naturally; the information fusion stage generally needs to deal with the limitation that decision makers have personal subjectivity; the information analysis stage usually needs to deal with the limitation that the decision data analysis lacks stability. However, since the classical decision data modeling technology has great challenges in solving the limitations in the three stages, a decision maker needs to establish a decision data modeling theory and method which are integrated with the actual decision characteristics. Specifically, the challenges of the above three aspects are represented by:
⑴ in the information presentation stage, the data collected by the decision maker often presents a plurality of uncertainties such as ambiguity, inaccuracy and hesitation, and the complexity of problem solution is increased to a certain extent. U.S. scholars Zadeh proposed the concept of fuzzy sets in 1965, and the value range of classical centralized membership is popularized from 0 or 1 to [0,1], so that the decision maker can further characterize the ambiguity concept, and meanwhile, the development of fuzzy multi-attribute group decision is promoted.
⑵ it is a core technical difficulty to integrate the preference information given by each decision maker into group preference information in the information fusion stage.
⑶ in the stage of information analysis, it is a core technical difficulty to use the established theoretical model to order, prioritize or grade each decision-making scheme.
In order to solve the challenges of the three aspects, the invention establishes a decision data modeling theory and a method which are integrated with actual decision characteristics. Specifically, the following common solutions are utilized to incorporate the actual decision feature, respectively:
⑴ dual hesitation fuzzy set, the degree of the dual hesitation fuzzy set element belonging to and not belonging to the set is expressed as membership degree and non-membership degree, each part contains several possible values, for example, the degree of some element x belonging to a set D may be 0.6 or 0.7, and the degree of x not belonging to a set D may be 0.1 or 0.2, then one dual hesitation fuzzy element in the dual hesitation fuzzy set can be marked as ({0.6,0.7}, {0.1,0.2}), so it can be seen that the dual hesitation fuzzy set can describe the ambiguity, hesitation and inexactness of the decision information at the same time.
⑵ Multi-granularity probability rough set, which possesses the advantages of both rough set and probability rough set in solving the decision problem, on one hand, the rough set adopts parallel computing idea to process operation by multiple binary relations, thus greatly improving the efficiency of information fusion, and in addition, the rough set contains optimistic version based on the information fusion strategy of finding out the same existence and pessimistic version based on the information fusion strategy of finding out the same row, and can process the risk type decision problem to some extent.
⑶ MULTIMOORA, namely Multi-Objective Optimization by rational analysis plus the full Multi-Objective Optimization, the method is proposed by Brauers in 2011 for enhancing the stability of Multi-attribute decision, the core idea is that a Multi-attribute decision method combining two different decision modes is superior to a single decision mode Multi-attribute decision method, a Multi-attribute decision method combining three different decision modes is superior to a Multi-attribute decision method combining two different decision modes, and the like.
In view of that the dual hesitation fuzzy set, the multi-granularity probability rough set and the multi-attribute group decision can solve the challenges of the three aspects in the aspects of information representation, information fusion and information analysis in the multi-attribute group decision, and meanwhile, a comprehensive method for simultaneously combining the three models is also lacked in the field of multi-attribute group decision. Therefore, it is necessary to provide a multi-granularity probability rough set model fused into multihesive fuzzy environment and establish a corresponding multi-attribute group decision method. The multi-attribute group decision method can depict decision information containing various uncertainties, carries out information fusion for eliminating the individual subjectivity of decision makers on the multi-source decision information, considers decision risk and fault tolerance rate and provides decision conclusions with strong stability, and the motivation block diagram provided by the invention is shown in fig. 1.
In summary, in order to establish a data modeling theory and a method for integrating actual decision characteristics facing complex multi-attribute group decision, the invention constructs a group decision method based on dual hesitation fuzzy multigrainy probability rough set and multi-grainy probability rough set according to the concepts of dual hesitation fuzzy set, multi-grainy probability rough set and multigrainy probability rough set.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the three challenges in information representation, information fusion and information analysis in the multi-attribute group decision, and provides a group decision method based on dual hesitation fuzzy multi-granularity probability rough set and multi-granularity probability rough set by utilizing the clear characteristics of the dual hesitation fuzzy multi-granularity rough set and multi-granularity probability rough set.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
the cluster decision method based on dual hesitation fuzzy multioora and the multi-granularity probability rough set can depict decision information containing various uncertainties, carry out information fusion for eliminating the individual subjectivity of a decision maker on the multi-source decision information, consider decision risk and fault-tolerant rate and provide a decision conclusion with strong stability, and comprises the following steps:
step 1, model establishment for dual hesitation fuzzy multi-attribute group decision
Step 1.1 creation and representation of multi-attribute group decision: aiming at a scheme matching problem in multi-attribute group decision, establishing a plurality of decision matrixes, wherein each decision matrix consists of three parts, namely a candidate set, an attribute set and a decision weight set, and the candidate set is assumed to be U and is expressed as U ═ x1,x2,…,xpP represents the number of alternatives; the attribute set is V, denoted V ═ y1,y2,…,yqQ represents the number of attributes for evaluating each alternative scheme; the decision weight set is ω, denoted ω ═ ω1,ω2,…,ωm}TM represents the number of decision-makers in the group decision, where ωi∈[0,1]And is
(i ═ 1,2, …, m) holds, all decision makers evaluate each alternative with each attribute in the set of attributes and give an evaluation value;
step 1.2, establishing and representing the even hesitation fuzzy information system: firstly, each decision maker establishes a respective decision matrix, the numerical value in the matrix is the evaluation value of a certain alternative scheme under a certain attribute, the evaluation value is a dual-hesitation fuzzy element, and thus each decision matrix given by the decision maker can be regarded as a dual-discourse domain dual-hesitation fuzzy relation RiE DHFR (U × V) (i ═ 1,2, …, m); then, the decision maker further establishes a standard evaluation set D belonging to DHF (V) by utilizing each attribute in the attribute set, wherein the expression form of D is a dual hesitation fuzzy set; finally, according to the U, V, R established in step 1.1 and step 1.2iAnd D, the establishment of a fuzzy information system for dual hesitations can be completed and is expressed as (U, V, R)iD), i.e. (U, V, R)iD) can be considered as the problem input part in the cluster decision method based on dual hesitation fuzzy multivora and multi-granularity probability rough clusters;
step 1.3, solving the problem of even hesitation fuzzy multi-attribute group decision:
calculating each decision matrix R given by the decision makeri(i ═ 1,2, …, m) of the alternatives xj(j ═ 1,2, …, p) similarity to the criteria evaluation set D, and information fusion is performed on each obtained similarity by using MULTIMIOORA, and then similarity with stronger stability after information fusion is obtained, and finally similarity after information fusion is used for candidate x1,x2,…,xpSorting is carried out, and the alternative scheme corresponding to the maximum similarity degree is the optimal alternative scheme x*；
Step 2, model calculation of cluster decision method based on dual hesitation fuzzy multivora and multi-granularity probability rough set
Inputting a model: dual hesitation fuzzy information system (U, V, R)i,D)；
And (3) outputting a model: best alternative x*；
According to the requirements of model input and model output, obtaining the optimal alternative scheme x by the following steps*：
Step 2.1, calculating the dual hesitation fuzzy conditional probability P (D | x) corresponding to each alternative xj given by each decision makerij)；
Step 2.2 determining the weight value omega corresponding to each decision makeri；
Step 2.3 for each alternative xj(j is 1,2, …, p) corresponding m dual hesitation fuzzy conditional probabilities, and the comprehensive utility value ξ is obtained by calculating the dual hesitation fuzzy weighted arithmetic mean operator in the ratio system methodjAnd pair ξjSorting is carried out;
step 2.4 for each alternative xjThe comprehensive deviation psi is obtained by calculating m dual hesitation fuzzy conditional probabilities corresponding to (j ═ 1,2, …, p) by using the dual hesitation fuzzy positive and negative ideal reference points in the reference point methodjAnd is aligned with psijSorting is carried out;
step 2.5 for each alternative xj(j ═ 1,2, …, p) corresponding m dual hesitation fuzzy conditional probabilities, and the integrated utility value ζ is calculated by using the dual hesitation fuzzy weighted geometric mean operator in the complete phase multiplicationjAnd is paired with ζjSorting is carried out;
step 2.6, comparing the sequencing results obtained in the step 2.3 to the step 2.5 pairwise by using an advantage theory, and calculating a sequencing ranking rank function value;
step 2.7, determining the final sequencing result to obtain the optimal alternative scheme x*。
Further, in the step 1.2 of establishing and representing the dual hesitation fuzzy information system, the dual-discourse domain dual hesitation fuzzy relation RiE DHFR (U × V) (i ═ 1,2, …, m), the standard evaluation set D e dhf (V) and the construction of the dual hesitation fuzzy elements are according to the following method:
the method a comprises the following steps: assuming that U is a discourse domain, a dual hesitation fuzzy set D on U can be expressed as two functions hD(x) And gD(x) Their application to the discourse domain U will return to [0,1 respectively]Subset in the interval, called D ═ tone<x,hD(x),gD(x)>| x ∈ U } is a dual hesitation fuzzy set on U, and hD(x) And gD(x) Is at [0,1]]The set of the above several possible values reflects the possible membership and possible non-membership of the element x in the domain U to the set D, which is called D (x) ═ (h)D(x),gD(x) Is a dual hesitation fuzzy element; in a dual hesitation fuzzy set, let γ ∈ h for all elements x in the discourse domain UD(x)，η∈gD(x)，γ+＝max{γ|γ∈hD(x)}，η+＝max{η|η∈gD(x) Where max represents an operation of taking the maximum value), 0. ltoreq. gamma, η. ltoreq.1 and 0. ltoreq. gamma+,η+No more than 1 is true; in addition, all the dual hesitation fuzzy sets in the discourse domain U are called DHF (U), and then the standard evaluation set D belongs to the DHF (V) to represent that any one dual hesitation fuzzy set D is taken from all the dual hesitation fuzzy sets DHF (V) in the discourse domain V;
the method b: let U and V be two domains of discourse, a dual-domain dual-discourse fuzzy relation R on UxV can be expressedAs a function of two hR(x, y) and gR(x, y) which, when applied to UxV, will return to [0,1, respectively]Subset in the interval, called R ═ tone<(x,y),hR(x,y),gR(x,y)>L (x, y) belongs to U multiplied by V, is a dual-discourse domain dual hesitation fuzzy relation on U multiplied by V, and hR(x, y) and gR(x, y) is in [0,1]]The set of the last several possible values reflects possible membership and possible non-membership of the relationship between the element x in the domain of discourse U and the element y in the domain of discourse V; in a dual-discourse domain dual hesitation fuzzy relation, for all sequence pairs (x, y) on UxV, let gamma be hR(x,y)，η∈gR(x,y)，γ+＝max{γ|γ∈hR(x,y)}，η+＝max{η|η∈gR(x, y) }, then 0 is less than or equal to gamma, η is less than or equal to 1, and 0 is less than or equal to gamma+,η+No more than 1 is true; in addition, all dual-discourse domain dual hesitation ambiguity on U × V is called DHFR (U × V), so that the dual-discourse domain dual hesitation ambiguity RiThe epsilon DHFR (U multiplied by V) represents any dual hesitation fuzzy relation Ri(i ═ 1,2, …, m) was taken from all dual hesitation ambiguity relations DHFR (U × V) on U × V.
Further, said step 2.1 is intended to calculate that each decision maker gives each alternative xjCorresponding dual hesitation ambiguity conditional probability P (D | x)ij) The dual hesitation ambiguity conditional probability P (D | x)ij) The establishment of (A) is based on the following method:
the method c comprises the following steps: let U and V be two domains of discourse, RiBelongs to DHFR (U multiplied by V) (i is 1,2, …, m) is a dual-discourse domain dual-hesitation fuzzy relation on the U multiplied by V, any dual-hesitation fuzzy set D belongs to DHF (V), xj∈U(j＝1,2,…,p),ykE.v (k 1,2, …, q), and refers to an arbitrary object xjConditional probability of e.u
Wherein (D (y)k))cRepresents D (y)k) The complement of (a) is to be added,
represents
Complement of, D (y)k) According to yke.V (k is 1,2, …, q) marks elements in D e DHF (V);
the operation in the above mathematical expression relates to the basic operation rule of the dual hesitation fuzzy set, and specifically relates to the addition, subtraction, multiplication and division operation in the four arithmetic rules and the complement, intersection and union operation in the set operation rule, and the basic operation rule of the dual hesitation fuzzy set is as follows:
suppose that: for any one dual hesitation fuzzy element d (x) ═ (h)D(x) gD (x)), first order hD(x) And gD(x) The numerical values contained in (1) are arranged in ascending order, and are called hD(x) The element in the middle row at the sigma position is gammaτ(σ)(x)，gD(x) The element at position σ in the middle is ητ(σ)(x) (ii) a Then, for any two dual hesitation fuzzy elements, if the numbers of numerical values contained in the possible membership degrees or the possible non-membership degrees are different, supplementing the maximum numerical values of the possible membership degrees or the possible non-membership degrees of the contained fewer numerical values until the numbers of the numerical values contained in the possible membership degrees or the possible non-membership degrees of the two dual hesitation fuzzy elements are the same;
the method d comprises the following steps: hesitation fuzzy set D for any two pairs1And D2，D1And D2The corresponding dual hesitation fuzzy element is d1(x) And d2(x) For any x ∈ U, the following operation rule exists between them:
⑺D1the complement of (D)1 cE, E e
⑻D1And D2The intersection of (A) is denoted as D1∩D2Is provided with
⑼D1And D2The union of (D)1∪D2Is provided with
Wherein the operation signc∩ is defined on the dual hesitation blur set, and the operation sign ~, # v-V is defined on the dual hesitation blur element.
Further, the step 2.3 uses the dual hesitation fuzzy weighted arithmetic mean operator in the ratio system method to calculate the comprehensive utility value ξjAnd sorting the average values based on the combined utility value ξ of the dual hesitation fuzzy weighted arithmetic mean operatorjThe establishment of (A) is based on the following method:
the method e comprises the following steps: di(xj) (i-1, 2, …, m) are m dual hesitation fuzzy elements, ω - ω { ω ═ ω1,ω2,…,ωm}TIs di(xj) The weight vector of (1), then
The composite utility value ξ may then be evaluated according to the concept of the dual hesitation fuzzy element scoring function as followsjSorting is carried out, and the larger the score function value is, the better the comprehensive utility value is;
the method f: let d (x) ═ hD(x),gD(x) Is any one of the dual hesitation fuzzy elements, the score function of d (x) is
Wherein # hD(x) And # gD(x) Each represents hD(x) And gD(x) The number of numerical values in (1) is, for any two pairs of even hesitation fuzzy elements d (x) and d ' (x), if s (d) (x) is less than s (d ' (x)), d (x) is less than d ' (x).
Further, the step 2.4 obtains the comprehensive deviation psi by calculating the dual hesitation fuzzy positive and negative ideal reference points in the reference point methodjAnd sorting, wherein the comprehensive deviation psi of the positive and negative ideal reference points is based on dual hesitation fuzzyjThe establishment of (A) is based on the following method:
method g: let the ideal points be ({1}, {0}), di(xj) (i-1, 2, …, m) are m dual hesitation fuzzy elements, ω - ω { ω ═ ω1,ω2,…,ωm}TIs di(xj) A weight vector of (1), then
Then, according to the concept of the dual hesitation fuzzy element score function given by the method f, the comprehensive deviation psi can be obtainedjAnd (4) sequencing, wherein the smaller the deviation value is, the better the comprehensive deviation is.
Further, the step 2.5 of calculating the integrated utility value ζ by using the dual hesitation fuzzy weighting geometric mean operator in the complete phase multiplicationjAnd sequencing, wherein the comprehensive utility value zeta of the geometric mean operator is weighted based on the dual hesitation fuzzyjBuilding ofThe method is based on the following steps:
the method h comprises the following steps: di(xj) (i-1, 2, …, m) are m dual hesitation fuzzy elements, ω - ω { ω ═ ω1,ω2,…,ωm}TIs di(xj) The weight vector of (1), then
Then, according to the concept of the dual hesitation fuzzy element score function given by the method f, the comprehensive utility value zeta can be obtainedjAnd (4) sorting, wherein the larger the score function value is, the better the comprehensive utility value is.
Furthermore, in step 2.6, the ranking results obtained in steps 2.3 to 2.5 are compared pairwise by using the dominance theory to determine the final ranking result, and the establishment of a specific comparison scheme in the dominance theory is based on the following method:
the method i comprises the following steps: for alternative x1,x2,…,xpUsing the value of the combined utility ξjComprehensive deviation psijAnd a combined utility value ζjObtaining respective descending sorting results, weighing ξj，ψjAnd ζjThe function of the rank is Ind (ξ)j)，Ind(ψj) And Ind (ζ)j) And is and
then
Is an optimal scheme.
Compared with the prior art, the invention has the following advantages:
1. the invention provides a multi-attribute group decision method under a dual hesitation fuzzy background by combining a dual hesitation fuzzy set theory and aiming at three challenges of information representation, information fusion and information analysis stages in complex multi-attribute group decision, and the ambiguity, the hesitation and the inaccuracy of decision information can be simultaneously described.
2. The method utilizes the thought of the multi-granularity probability rough set in the stages of information fusion and information analysis, can improve the operation efficiency of the traditional method, can consider the influence of decision risk and model fault tolerance on a final decision conclusion, and can adapt to the requirement of complex multi-attribute group decision.
3. The invention emphasizes that the concept of multi-attribute group decision-making is integrated into the construction of the multi-attribute group decision-making method, the stability of decision-making conclusion can be improved, the influence of the factor that the results are different due to different decision-making methods is effectively reduced, and the quality of multi-attribute group decision-making is obviously improved.
Drawings
FIG. 1 is a block diagram of the present invention;
FIG. 2 is a decision model of the cluster decision method of the present invention based on dual hesitation fuzzy MULTIMOORA and multi-granularity probability rough clustering;
FIG. 3 is a block diagram of model computation for a cluster decision method based on dual hesitation fuzzy multivora and multi-granularity probability rough clustering in accordance with the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific embodiments.
Talents are the most important and scarce strategic resource in a country. At present, the characteristics and the functions of talent resources as the first resources for the development of the economic society are more obvious, and talent competition becomes the core of comprehensive national competition. Who can cultivate and attract more excellent talents can take advantage and initiative in the future period of comprehensive national competition. Practice fully proves that the realization of "best effort and best use" is the core of talent strategy.
In the field of human resources, a human-post matching theory aims to scientifically and reasonably match various abilities of people with specific requirements of a working post so as to achieve the purposes of making the best of people and making the best of people, and further realize efficient operation of organizations. With the increase of the cognition degree of the importance of the human-guard matching, the human-guard matching problem is widely concerned by many managers, and the research on human-guard matching models and methods is gradually increased. However, the existing post matching model and method have the limitations that uncertain decision information is difficult to be described properly, the subjectivity of the decision method is strong, the stability of a decision conclusion is not strong, and the like. Therefore, a scientific and reasonable personnel matching method is necessary to be established from the perspective of quantitative analysis to provide constructive opinions for enterprise managers. The embodiment is used for carrying out the personnel matching problem in a certain software development enterprise by utilizing the group decision method based on dual hesitation fuzzy multivora and the multi-granularity probability rough set.
As shown in fig. 2 and fig. 3, the cluster decision method based on dual hesitation fuzzy multivora and multi-granularity probability rough cluster includes the following steps:
step 1, model establishment for dual hesitation fuzzy multi-attribute group decision
Step 1.1 creation and representation of multi-attribute group decision: in the personnel matching process in a certain software development enterprise, the personnel matching process is quantitatively modeled into one scheme matching problem in multi-attribute group decision, a plurality of personnel matching decision matrixes are established by a plurality of personnel resource experts in the enterprise, each personnel matching decision matrix consists of an alternative position set, an employee capability evaluation attribute set and a personnel resource expert weight set, wherein the alternative position set is assumed to be U, and is expressed as U ═ x { (x)1,x2,…,xpP represents the number of the alternative posts; the employee capability assessment attribute set is V, denoted V ═ y1,y2,…,yqQ represents the number of attributes for evaluating each alternative post; the human resource expert weight set is ω, denoted ω ═ ω1,ω2,…,ωm}T(i-1, 2, …, m), where m represents the number of human resource experts in the multiple attribute group decision, where ω isi∈[0,1]And is
If so, all human resource experts evaluate each attribute in the employee capability evaluation attribute set of each alternative post and give an evaluation value;
step 1.2, establishing and representing the even hesitation fuzzy information system: first, according toAccording to the dual hesitation fuzzy set theory, each human resource expert establishes a respective human sentry matching decision matrix, the numerical value in the matrix is a specific evaluation value of a certain alternative sentry under the employee capability evaluation attribute, and the evaluation value is a dual hesitation fuzzy element in the method, so that each human sentry matching decision matrix given by the human resource expert can be regarded as a dual-domain dual hesitation fuzzy relation RiE DHFR (U × V) (i ═ 1,2, …, m); then, the human resource expert establishes an employee ability evaluation set D belonging to DHF (DHF) (V) by utilizing each attribute in the employee ability evaluation attribute set, wherein the expression form of D is a dual hesitation fuzzy set; finally, according to the U, V, R established in step 1.1 and step 1.2iAnd D, the establishment of a corresponding dual hesitation fuzzy information system under the condition of the human-sentry matching can be completed, and the system is expressed as (U, V, R)iD), i.e. (U, V, R)iD) can be regarded as a human-job matching input part in the cluster decision method based on dual hesitation fuzzy MULTIMOORA and the multi-granularity probability rough set;
step 1.3, solving the problem of even hesitation fuzzy multi-attribute group decision:
calculating the matching decision matrix R of each post given by the human resource expertsi(i-1, 2, …, m) optionallyj(j ═ 1,2, …, p) and employee ability evaluation set D, and using MULTIMIOORA to make information fusion of obtained similarity, and further obtaining similarity with stronger stability after information fusion, finally using similarity after information fusion to make use of candidate position x1,x2,…,xpSorting is carried out, and the candidate post corresponding to the maximum similarity degree is the optimal candidate post x*；
In step 1.2, the dual-discourse domain dual-hesitation fuzzy relation R is established and expressed in the dual-hesitation fuzzy information systemiE DHFR (U × V) (i ═ 1,2, …, m), the employee competency evaluation set D e dhf (V), and the construction of the dual hesitation fuzzy elements were according to methods a and b described above.
In this embodiment, the domain of discourse U ═ x1,x2,x3,x4,x5Represents a set of alternative posts for performing post matching by a certain software development enterprise, wherein elements in U are divided into pointsRespectively representing algorithm engineers, administrative assistants, marketing specialists, sales representatives and financial specialists; another domain of discourse V ═ y1,y2,y3,y4,y5The evaluation attribute set is the staff capability evaluation attribute set matched with the human posts, wherein the elements in V respectively represent mathematical capability, computer application capability, foreign language capability, writing capability and organization management capability; the enterprise has organized an exploration team consisting of three human resource experts, each providing a human-job matching decision matrix denoted R1、R2And R3As shown in tables 1,2 and 3 below. Further, the employee competency evaluation set D is represented as:
TABLE 1 human resource expert's set-up human-job matching decision matrix
TABLE 2 the second human resources expert's set-up of the human-job matching decision matrix
TABLE 3 Risk match decision matrix created by the third human resources expert
Step 2, model calculation of cluster decision method based on dual hesitation fuzzy multivora and multi-granularity probability rough set
The model of the cluster decision method based on dual hesitation fuzzy multivora and the multi-granularity probability rough cluster is shown in fig. 2:
inputting a model: dual hesitation fuzzy information system (U, V, R)i,D)；
And (3) outputting a model: best alternative x*；
According to the requirements of model input and model output, obtaining the optimal alternative scheme x by the following steps*The model calculation flow diagram is shown in fig. 3:
step 2.1 calculate each alternative x given by each decision makerjCorresponding dual hesitation ambiguity conditional probability P (D | x)ij) Where the dual hesitation ambiguity conditional probability P (D | x)ij) According to the above-mentioned methods c and d;
step 2.2 determining the weight value omega corresponding to each decision makeri；
Step 2.3 for each alternative xj(j is 1,2, …, p) corresponding m dual hesitation fuzzy conditional probabilities, and the comprehensive utility value ξ is obtained by calculating the dual hesitation fuzzy weighted arithmetic mean operator in the ratio system methodjAnd pair ξjSorting is performed, wherein the integrated utility value ξjAccording to the above-mentioned method e and method f;
step 2.4 for each alternative xjThe comprehensive deviation psi is obtained by calculating m dual hesitation fuzzy conditional probabilities corresponding to (j ═ 1,2, …, p) by using the dual hesitation fuzzy positive and negative ideal reference points in the reference point methodjAnd is aligned with psijSorting is carried out, wherein the comprehensive deviation psijAccording to the above method g;
step 2.5 for each alternative xj(j ═ 1,2, …, p) corresponding m dual hesitation fuzzy conditional probabilities, and the integrated utility value ζ is calculated by using the dual hesitation fuzzy weighted geometric mean operator in the complete phase multiplicationjAnd is paired with ζjSorting is performed, wherein the integrated utility value ζjAccording to the above method h;
step 2.6, comparing the sequencing results obtained in the step 2.3-step 2.5 pairwise by using an advantage theory, and calculating a sequencing ranking rank function value, wherein the establishment of a specific comparison scheme in the advantage theory is based on the method i;
step 2.7, determining the final sequencing result to obtain the optimal alternative scheme x*。
The embodiment specifically calculates as follows:
step 2.1 measurementGiving each alternative post x by calculating each human resource expertjCorresponding dual hesitation ambiguity conditional probability P (D | x)ij)；
P(D|x12)＝({0.1059,0.1576},{0.5621,0.664})；
P(D|x13)＝({0.1057,0.1558},{0.6265,0.6972})；
P(D|x14)＝({0.1798,0.2531},{0.4951,0.5913})；
P(D|x15)＝({0.0736,0.12},{0.678,0.767})；
P(D|x21)＝({0.0838,0.1458},{0.6508,0.77})；
P(D|x22)＝({0.1034,0.1828},{0.5749,0.6639})；
P(D|x23)＝({0.0898,0.1692},{0.5948,0.6972})；
P(D|x24)＝({0.1485,0.2309},{0.5039,0.5991})；
P(D|x25)＝({0.0647,0.1042},{0.6251,0.752})；
P(D|x31)＝({0.082,0.1414},{0.6593,0.7525})；
P(D|x32)＝({0.0803,0.1367},{0.6123,0.7092})；
P(D|x33)＝({0.1155,0.182},{0.6285,0.7202})；
P(D|x34)＝({0.1645,0.2531},{0.387,0.5593})；
P(D|x35)＝({0.0736,0.1216},{0.6229,0.7416})。
step 2.2, determining the weight value omega corresponding to each human resource experti；
In order to conveniently perform contrast analysis with other similar multi-attribute group decision methods, three human resource experts are set with equal weight, namely
Step 2.3 for each alternative position xj(j is 1,2, …,5) corresponding three dual hesitation fuzzy conditional probabilities, and the comprehensive utility value ξ is obtained by calculating the dual hesitation fuzzy weighted arithmetic mean operator in the ratio system methodjAnd pair ξjSorting is carried out;
ξ1＝DHFWA(P(D|x11),P(D|x21),P(D|x31) {0.0826,0.1379}, {0.6631,0.7641 }); in the same way, it is not difficult to obtain:
ξ2＝({0.0966,0.1592},{0.5827,0.6787})；
ξ3＝({0.1037,0.1691},{0.6164,0.7048})；
ξ4＝({0.1644,0.2458},{0.4588,0.583})；
ξ5＝({0.0706,0.1153},{0.6415,0.7535})；
Step 2.4 for each alternative position xj(j ═ 1,2, …,5) corresponding three dual hesitation fuzzy conditional probabilities, and the comprehensive deviation psi is calculated by using the dual hesitation fuzzy positive and negative ideal reference points in the reference point methodjAnd is aligned with psijSorting is carried out;
Step 2.5 for each alternative position xj(j ═ 1,2, …,5) corresponding three dual hesitation fuzzy conditional probabilities, and the integrated utility value ζ is obtained by calculation using the dual hesitation fuzzy weighted geometric mean operator in the complete phase multiplicationjAnd is paired with ζjSorting is carried out;
ζ1＝DHFWG(P(D|x11),P(D|x21),P(D|x31) {0.0826,0.1376}, {0.6633,0.7643 }); in the same way, it is not difficult to obtain:
ζ2＝({0.0958,0.1579},{0.5837,0.6798})；
ζ3＝({0.1031,0.1687},{0.6169,0.7051})；
ζ4＝({0.1638,0.2455},{0.4645,0.5836})；
ζ5＝({0.0705,0.115},{0.6429,0.7538})；
Step 2.6, comparing the sequencing results obtained in the step 2.3 to the step 2.5 pairwise by using an advantage theory, and calculating a sequencing ranking rank function value;
Ind(ξ4)＝Ind(ψ4)＝Ind(ζ4)＝1；
Ind(ξ2)＝Ind(ψ2)＝Ind(ζ2)＝2；
Ind(ξ3)＝Ind(ψ3)＝Ind(ζ3)＝3；
Ind(ξ1)＝Ind(ψ1)＝Ind(ζ1)＝4；
Ind(ξ5)＝Ind(ψ5)＝Ind(ζ5)＝5。
step 2.7 determining the final ranking resultTo obtain the optimal alternative position x*。
The final ordering result of the alternative posts is x4＞x2＞x3＞x1＞x5I.e. post x4(sales representatives) are the best job matching results.
Compared with the decision method in the prior art, the invention carries out comparative analysis
In the embodiment, the method for making the group decision based on the dual hesitation fuzzy multi-attribute group and the multi-granularity probability rough set is used for solving the problem of the human-sentry matching group decision, and in the method for making the group decision based on the dual hesitation fuzzy multi-granularity probability rough set, the work of researching the multi-attribute group decision method by using the multi-granularity modeling thought is still less, wherein the representative method is the method for making the group decision based on the dual hesitation fuzzy multi-granularity rough set in the dual discourse domain. Next, with the same human-sentry matching problem as the background in the embodiment of the present invention, a cluster decision method based on dual-domain dual-hesitation fuzzy multi-granularity rough clusters is used to perform a comparative analysis as follows:
⑴ where U and V are two domains of discourse, RiE DHFR (U × V) (i ═ 1,2, …, m) is a dual-discourse domain dual hesitation fuzzy relation on U × V, there is any one dual hesitation fuzzy set D e dhf (V), and the optimistic dual hesitation fuzzy multi-granularity about D is roughly approximated by the following:
wherein
Similarly, the pessimistic dual hesitation blur multi-granularity rough lower approximation and upper approximation for D is:
wherein
⑵ against the same post matching problem as in the present example, it is not difficult to obtain:
⑶ three synthetic sets are computed, namely an optimistic synthetic set, a pessimistic synthetic set, and a compromise synthetic set, as follows:
⑷ calculating the score function values of each post in the optimistic synthesis set, the pessimistic synthesis set and the compromise synthesis set, without obtaining x in the optimistic synthesis set1,x2,…,x5The corresponding score function values are 0.66, 0.605, 0.63, 0.845 and 0.635 respectively, and the final ordering result of the alternative posts is x4＞x1＞x5＞x3＞x2(ii) a Pessimistic synthetic set x1,x2,…,x5The corresponding score function values are 0.7, 0.605, 0.65, 0.815 and 0.665 respectively, and the final ordering result of the alternative positions is x4＞x1＞x5＞x3＞x2(ii) a X in the compromise synthesis set1,x2,…,x5The corresponding score function values are 0.9415, 0.8912, 0.9276, 0.9806 and 0.9262 respectively, and the final ordering result of the alternative posts is x4＞x1＞x3＞x5＞x2. In summary, the optimal human-sentry matching result obtained by using the optimistic synthesis set, the pessimistic synthesis set and the compromise synthesis set is position x4(sales representatives).
As can be seen from the sentry matching result based on the dual-domain dual hesitation fuzzy multi-granularity rough set, the obtained optimal sentry matching result is consistent with the sentry matching result based on the dual hesitation fuzzy MULTIMORA and the multi-granularity probability rough set constructed by the invention, and the optimal sentry matching result is displayedThe result of the people's post matching is post x4(sales representatives). However, the two population decision methods described above result for x1,x2,…,x5Is not consistent except for x4The reason why the difference phenomenon is the greatest is that the ordering orders of the rest positions are different from each other, and the emphasis is different for each group decision method, some emphasis is on fusion efficiency, some emphasis is on processing decision risk, and some emphasis is on reducing decision error, that is, the stability of the final decision conclusion is not strong, and the interpretability is not outstanding.
The cluster decision method based on dual hesitation fuzzy MULTIMOORA and the multi-granularity probability rough set constructed by the invention is used for reasonably depicting decision information containing multiple uncertainties, carrying out information fusion for eliminating the personal subjectivity of a decision maker on the multi-source decision information, considering decision risk and fault tolerance rate, providing a decision conclusion with strong stability by simultaneously using the advantages of the dual hesitation fuzzy set, the multi-granularity probability rough set and the MULTIMOORA in the aspects of information representation, information fusion and information analysis in multi-attribute cluster decision, and powerfully filling the blank that the comprehensive method combining the three models is lacked in the field of multi-attribute cluster decision. In conclusion, the group decision method constructed by the invention provides a complex multi-attribute group decision method under the background of the big data era from the theory and practice, and can reasonably establish a decision conclusion with strong interpretability, thereby better providing a solution for the multi-attribute group decision problem widely existing in various fields such as project investment, medical diagnosis, personnel management and the like in the social and economic development.
Claims (7)
1. The cluster decision method based on dual hesitation fuzzy multionara and the multi-granularity probability rough cluster is characterized by comprising the following steps of: the method comprises the following steps:
step 1, model establishment for dual hesitation fuzzy multi-attribute group decision
Step 1.1 creation and representation of multi-attribute group decision: aiming at a scheme matching problem in multi-attribute group decision, a plurality of decision matrixes are established, wherein each decision matrix consists of a set of alternatives and a genusThe character set and the decision maker weight set are composed of three parts, wherein, the alternative set is assumed to be U, and is expressed as U ═ x1,x2,…,xpP represents the number of alternatives; the attribute set is V, denoted V ═ y1,y2,…,yqQ represents the number of attributes for evaluating each alternative scheme; the decision weight set is ω, denoted ω ═ ω1,ω2,…,ωm}TM represents the number of decision-makers in the group decision, where ωi∈[0,1]And is
If yes, all decision makers evaluate each alternative scheme by using each attribute in the attribute set and give an evaluation value;
step 1.2, establishing and representing the even hesitation fuzzy information system: firstly, each decision maker establishes a respective decision matrix, the numerical value in the matrix is the evaluation value of a certain alternative scheme under a certain attribute, the evaluation value is a dual-hesitation fuzzy element, and thus each decision matrix given by the decision maker can be regarded as a dual-discourse domain dual-hesitation fuzzy relation RiE DHFR (U × V) (i ═ 1,2, …, m); then, the decision maker further establishes a standard evaluation set D belonging to DHF (V) by utilizing each attribute in the attribute set, wherein the expression form of D is a dual hesitation fuzzy set; finally, according to the U, V, R established in step 1.1 and step 1.2iAnd D, the establishment of a fuzzy information system for dual hesitations can be completed and is expressed as (U, V, R)iD), i.e. (U, V, R)iD) can be considered as the problem input part in the cluster decision method based on dual hesitation fuzzy multivora and multi-granularity probability rough clusters;
step 1.3, solving the problem of even hesitation fuzzy multi-attribute group decision:
calculating each decision matrix R given by the decision makeri(i ═ 1,2, …, m) of the alternatives xj(j ═ 1,2, …, p) degrees of similarity to the criteria evaluation set D, and the degrees of similarity obtained were measured by MULTIMORAInformation fusion is carried out, the similarity degree with strong stability after the information fusion is further obtained, and finally the similarity degree after the information fusion is utilized to the alternative scheme x1,x2,…,xpSorting is carried out, and the alternative scheme corresponding to the maximum similarity degree is the optimal alternative scheme x*；
Step 2, model calculation of cluster decision method based on dual hesitation fuzzy multivora and multi-granularity probability rough set
Inputting a model: dual hesitation fuzzy information system (U, V, R)i,D)；
And (3) outputting a model: best alternative x*；
According to the requirements of model input and model output, obtaining the optimal alternative scheme x by the following steps*：
Step 2.1 calculate each alternative x given by each decision makerjCorresponding dual hesitation ambiguity conditional probability P (D | x)ij)；
Step 2.2 determining the weight value omega corresponding to each decision makeri；
Step 2.3 for each alternative xj(j is 1,2, …, p) corresponding m dual hesitation fuzzy conditional probabilities, and the comprehensive utility value ξ is obtained by calculating the dual hesitation fuzzy weighted arithmetic mean operator in the ratio system methodjAnd pair ξjSorting is carried out;
step 2.4 for each alternative xjThe comprehensive deviation psi is obtained by calculating m dual hesitation fuzzy conditional probabilities corresponding to (j ═ 1,2, …, p) by using the dual hesitation fuzzy positive and negative ideal reference points in the reference point methodjAnd is aligned with psijSorting is carried out;
step 2.5 for each alternative xj(j ═ 1,2, …, p) corresponding m dual hesitation fuzzy conditional probabilities, and the integrated utility value ζ is calculated by using the dual hesitation fuzzy weighted geometric mean operator in the complete phase multiplicationjAnd is paired with ζjSorting is carried out;
step 2.6, comparing the sequencing results obtained in the step 2.3 to the step 2.5 pairwise by using an advantage theory, and calculating a sequencing ranking rank function value;
step 2.7 determines the final ranking result, resulting in the optimal alternative x.
2. The method of claim 1, wherein the dual hesitation fuzzy multivora and multi-granularity probability rough cluster are based on a cluster decision method comprising: step 1.2, in the establishment and representation of the dual hesitation fuzzy information system, the dual-discourse domain dual hesitation fuzzy relation RiThe method for constructing the dual hesitation fuzzy element belongs to the group of the standard evaluation set D belonging to DHFR (U multiplied by V) (i is 1,2, …, m), and comprises the following steps:
the method a comprises the following steps: assuming that U is a discourse domain, a dual hesitation fuzzy set D on U can be expressed as two functions hD(x) And gD(x) Their application to the discourse domain U will return to [0,1 respectively]Subset in the interval, called D ═ tone<x,hD(x),gD(x)>| x ∈ U } is a dual hesitation fuzzy set on U, and hD(x) And gD(x) Is at [0,1]]The set of the above several possible values reflects the possible membership and possible non-membership of the element x in the domain U to the set D, which is called D (x) ═ (h)D(x),gD(x) Is a dual hesitation fuzzy element; in a dual hesitation fuzzy set, let γ ∈ h for all elements x in the discourse domain UD(x)，η∈gD(x)，γ+＝max{γ|γ∈hD(x)}，η+＝max{η|η∈gD(x) Is 0 to gamma, η to 1 and 0 to gamma+,η+No more than 1 is true; in addition, all the dual hesitation fuzzy sets in the discourse domain U are called DHF (U), and then the standard evaluation set D belongs to the DHF (V) to represent that any one dual hesitation fuzzy set D is taken from all the dual hesitation fuzzy sets DHF (V) in the discourse domain V;
the method b: let U and V be two domains of discourse, a dual-domain dual hesitation ambiguity relation R on UxV can be expressed as two functions hR(x, y) and gR(x, y) which, when applied to UxV, will return to [0,1, respectively]Subset in the interval, called R ═ tone<(x,y),hR(x,y),gR(x,y)>L (x, y) belongs to U multiplied by V, is a dual-discourse domain dual hesitation fuzzy relation on U multiplied by V, and hR(x, y) and gR(x, y) is in [0,1]]The set of the above several possible values reflects the element x andpossible membership and possible non-membership of the relationship between elements y in the domain of discourse V; in a dual-discourse domain dual hesitation fuzzy relation, for all sequence pairs (x, y) on UxV, let gamma be hR(x,y)，η∈gR(x,y)，γ+＝max{γ|γ∈hR(x,y)}，η+＝max{η|η∈gR(x, y) }, then 0 is less than or equal to gamma, η is less than or equal to 1, and 0 is less than or equal to gamma+,η+No more than 1 is true; in addition, all dual-discourse domain dual hesitation ambiguity on U × V is called DHFR (U × V), so that the dual-discourse domain dual hesitation ambiguity RiThe epsilon DHFR (U multiplied by V) represents any dual hesitation fuzzy relation Ri(i ═ 1,2, …, m) was taken from all dual hesitation ambiguity relations DHFR (U × V) on U × V.
3. The method of claim 1, wherein the dual hesitation fuzzy multivora and multi-granularity probability rough cluster are based on a cluster decision method comprising: the calculation in said step 2.1 gives each alternative x for each decision makerjCorresponding dual hesitation ambiguity conditional probability P (D | x)ij) The dual hesitation ambiguity conditional probability P (D | x)ij) The establishing method comprises the following steps:
the method c comprises the following steps: let U and V be two domains of discourse, RiBelongs to DHFR (U multiplied by V) (i is 1,2, …, m) is a dual-discourse domain dual-hesitation fuzzy relation on the U multiplied by V, any dual-hesitation fuzzy set D belongs to DHF (V), xj∈U(j＝1,2,…,p),ykE.v (k 1,2, …, q), and refers to an arbitrary object xjConditional probability of e.u
Wherein (D (y)k))cRepresents D (y)k) The complement of (a) is to be added,
represents
Complement of, D (y)k) According to yke.V (k is 1,2, …, q) marks elements in D e DHF (V);
the operation in the above mathematical expression relates to the basic operation rule of the dual hesitation fuzzy set, and specifically relates to the addition, subtraction, multiplication and division operation in the four arithmetic rules and the complement, intersection and union operation in the set operation rule, and the basic operation rule of the dual hesitation fuzzy set is as follows:
suppose that: for any one dual hesitation fuzzy element d (x) ═ (h)D(x),gD(x) First order h)D(x) And gD(x) The numerical values contained in (1) are arranged in ascending order, and are called hD(x) The element in the middle row at the sigma position is gammaτ(σ)(x)，gD(x) The element at position σ in the middle is ητ(σ)(x) (ii) a Then, for any two dual hesitation fuzzy elements, if the numbers of numerical values contained in the possible membership degrees or the possible non-membership degrees are different, supplementing the maximum numerical values of the possible membership degrees or the possible non-membership degrees of the contained fewer numerical values until the numbers of the numerical values contained in the possible membership degrees or the possible non-membership degrees of the two dual hesitation fuzzy elements are the same;
the method d comprises the following steps: hesitation fuzzy set D for any two pairs1And D2，D1And D2The corresponding dual hesitation fuzzy element is d1(x) And d2(x) For any x ∈ U, the following operation rule exists between them:
⑴
⑵
⑶
⑷
⑸
⑹
⑺D1the complement of (D)1 cE, E e
⑻D1And D2The intersection of (A) is denoted as D1∩D2Is provided with
⑼D1And D2The union of (D)1∪D2Is provided with
Wherein the operation signc∩ is defined on the dual hesitation blur set, and the operation sign ~, # v-V is defined on the dual hesitation blur element.
4. The cluster decision method based on dual hesitation fuzzy multivora and multi-granularity probability rough cluster as claimed in claim 1, wherein the synthetic utility value ξ is obtained by calculation of dual hesitation fuzzy weighted arithmetic mean operator in the ratio system method in the step 2.3jAnd sorting the average values based on the combined utility value ξ of the dual hesitation fuzzy weighted arithmetic mean operatorjThe establishing method comprises the following steps:
the method e comprises the following steps: di(xj) (i-1, 2, …, m) are m dual hesitation fuzzy elements, ω - ω { ω ═ ω1,ω2,…,ωm}TIs di(xj) The weight vector of (1), then
The composite utility value ξ may then be evaluated according to the concept of the dual hesitation fuzzy element scoring function as followsjSorting is carried out, and the larger the score function value is, the better the comprehensive utility value is;
the method f: let d (x) ═ hD(x),gD(x) Is any one of the dual hesitation fuzzy elements, the score function of d (x) is
Wherein # hD(x) And # gD(x) Each represents hD(x) And gD(x) The number of numerical values in (1) is, for any two pairs of even hesitation fuzzy elements d (x) and d ' (x), if s (d) (x) is less than s (d ' (x)), d (x) is less than d ' (x).
5. The method of claim 4, wherein the dual hesitation fuzzy multivora and multi-granularity probability rough cluster are based on a cluster decision method comprising: in the step 2.4, the comprehensive deviation psi is calculated by using the dual hesitation fuzzy positive and negative ideal reference points in the reference point methodjAnd sorting, wherein the comprehensive deviation psi of the positive and negative ideal reference points is based on dual hesitation fuzzyjThe establishing method comprises the following steps:
method g: let the ideal points be ({1}, {0}), di(xj) (i-1, 2, …, m) are m dual hesitation fuzzy elements, ω - ω { ω ═ ω1,ω2,…,ωm}TIs di(xj) A weight vector of (1), then
Then, according to the concept of the dual hesitation fuzzy element score function given by the method f, the comprehensive deviation psi can be obtainedjAnd (4) sequencing, wherein the smaller the deviation value is, the better the comprehensive deviation is.
6. The method of claim 4, wherein the dual hesitation fuzzy multivora and multi-granularity probability rough cluster are based on a cluster decision method comprising: the step 2.5 of calculating by utilizing dual hesitation fuzzy weighting geometric mean operator in complete phase multiplication to obtain a comprehensive utility value zetajAnd sequencing, wherein the comprehensive utility value zeta of the geometric mean operator is weighted based on the dual hesitation fuzzyjThe establishing method comprises the following steps:
the method h comprises the following steps: di(xj) (i-1, 2, …, m) are m dual hesitation fuzzy elements, ω - ω { ω ═ ω1,ω2,…,ωm}TIs di(xj) The weight vector of (1), then
Then, according to the concept of the dual hesitation fuzzy element score function given by the method f, the comprehensive utility value zeta can be obtainedjAnd (4) sorting, wherein the larger the score function value is, the better the comprehensive utility value is.
7. The method of claim 1, wherein the dual hesitation fuzzy multivora and multi-granularity probability rough cluster are based on a cluster decision method comprising: comparing the sorting results obtained in the steps 2.3-2.5 pairwise in the step 2.6 by using an advantage theory to determine a final sorting result, wherein the establishment method of a specific comparison scheme in the advantage theory comprises the following steps:
the method i comprises the following steps: for alternative x1,x2,…,xpUsing the value of the combined utility ξjComprehensive deviation psijAnd a combined utility value ζjObtaining respective descending sorting results, weighing ξj，ψjAnd ζjThe function of the rank is Ind (ξ)j)，Ind(ψj) And Ind (ζ)j) And is and
then
Is an optimal scheme.
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| CN112149949A (en) * | 2020-07-31 | 2020-12-29 | 北京邮电大学 | Satellite communication system efficiency evaluation method based on hesitation fuzzy and analytic hierarchy process |
| 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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| CN112506977B (en) * | 2020-12-14 | 2024-02-09 | 大连大学 | Interval intuitionistic fuzzy multi-attribute group decision provider selection method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112149949A (en) * | 2020-07-31 | 2020-12-29 | 北京邮电大学 | Satellite communication system efficiency evaluation method based on hesitation fuzzy and analytic hierarchy process |
| CN112149949B (en) * | 2020-07-31 | 2023-11-24 | 北京邮电大学 | Satellite communication system efficiency evaluation method based on hesitation blurring and analytic hierarchy process |
| CN112506977B (en) * | 2020-12-14 | 2024-02-09 | 大连大学 | Interval intuitionistic fuzzy multi-attribute group decision provider selection method |
| 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 |
| CN113469565A (en) * | 2021-07-21 | 2021-10-01 | 中国人民解放军国防科技大学 | Multifunctional equipment scheme selection method under capacity uncompensable mechanism and related equipment |
| CN113469565B (en) * | 2021-07-21 | 2023-08-22 | 中国人民解放军国防科技大学 | Multifunctional equipment scheme selection method under capability uncompensated mechanism and related equipment |
| CN113761659A (en) * | 2021-09-09 | 2021-12-07 | 北京航空航天大学 | Nested multi-attribute evaluation decision method and device for similar solid-liquid power space carrier |
| CN113761659B (en) * | 2021-09-09 | 2024-04-30 | 北京航空航天大学 | Nested multi-attribute evaluation decision-making method and device for solid-liquid power-like space vehicles |
| CN116596372A (en) * | 2023-04-27 | 2023-08-15 | 广东科技学院 | Logistics node selection method, device, equipment and storage medium |
| CN116596372B (en) * | 2023-04-27 | 2024-02-02 | 广东科技学院 | Logistics node selection method, device, equipment and storage medium |
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