CN110581783A - Communication scheme decision method based on AHP and TOPSIS - Google Patents
Communication scheme decision method based on AHP and TOPSIS Download PDFInfo
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Abstract
A communication scheme decision method based on AHP and TOPSIS is characterized by that it makes comprehensive evaluation on several indexes which can affect communication quality based on AHP algorithm, and constructs a pair comparison judgment matrix, calculates the maximum characteristic value and correspondent characteristic vector of said matrix, and makes them undergo the process of normalization treatment to obtain weight distribution vector of every decision index which can affect communication quality, and utilizes the decision index value which can affect communication quality to construct decision matrix based on TOPSIS algorithm and make it implement normalization treatment, then combines it with the weight distribution vector of the above-mentioned optimum communication scheme decision index to jointly construct normalized weight matrix of optimum communication scheme decision index, and determines maximum value and minimum value in every decision index which can affect communication quality, respectively form positive ideal solution and negative ideal solution, and calculates the Euclidean distance of positive ideal solution and negative ideal solution, then utilizes said distance to calculate the relative closeness of every communication scheme and ideal solution and make comparison, the communication scheme corresponding to the maximum value in relative proximity is taken as the final decision result.
Description
Technical Field
The invention relates to the field of decision algorithm and communication scheme, in particular to a communication scheme decision method based on AHP and TOPSIS.
background
in the communication process, the communication quality is not ideal due to some objective factors, and the effectiveness and reliability of communication are difficult to ensure. In order to ensure high-quality communication, various factors such as transmission speed, communication distance, time delay and the like need to be considered, but the effectiveness and reliability of communication are often contradictory. Therefore, it is important to select a communication scheme that can maximally meet the requirements by comprehensively considering various factors, and different communication schemes are comprehensively evaluated by combining a reliable decision algorithm with various decision indexes, so that an important method for improving the communication quality is to help us to select a proper communication scheme.
Disclosure of Invention
The invention provides a communication scheme decision method based on AHP and TOPSIS, which comprises the steps of obtaining a weight distribution vector of a decision index influencing communication quality by using an AHP algorithm, constructing a decision matrix of the decision index influencing communication quality in the TOPSIS algorithm, and constructing a weighted normalized matrix of the decision index influencing communication quality by combining the weight distribution vector. Determining a positive ideal solution and a negative ideal solution in the decision index, calculating the relative closeness of each communication scheme and the ideal solution, and taking the communication scheme with the highest relative closeness as a selection target.
A communication scheme decision method based on AHP and TOPSIS is characterized by comprising the following steps:
Step 1: selecting indexes influencing communication quality, such as signal-to-noise ratio, time delay, distance and the like, as decision bases of an optimal communication scheme, and establishing a hierarchical structure model of the communication scheme and the decision indexes thereof;
Step 2: constructing a judgment matrix of decision indexes influencing communication quality, calculating a maximum eigenvalue of the matrix and a corresponding normalized eigenvector thereof, and performing consistency check to obtain a decision index weight distribution vector of an optimal communication scheme;
And step 3: acquiring decision index values influencing communication quality in each communication scheme, constructing a decision matrix, carrying out normalized processing, and combining the decision matrix with the weight distribution vector of the decision index influencing communication quality determined by the AHP algorithm in the step 2 to jointly construct a normalized weighting matrix about the decision index of the optimal communication scheme;
And 4, step 4: determining a positive ideal solution and a negative ideal solution in the optimal communication scheme decision index according to the normalized weighting matrix of the optimal communication scheme decision index obtained in the step 3, and simultaneously calculating the distance between each communication scheme and the positive ideal solution and the negative ideal solution;
And 5: and 4, calculating the relative closeness of the ideal solutions in the decision indexes of various communication schemes and the optimal communication scheme by using the distance results in the step 4, and sequencing the superiority and inferiority to obtain a final decision result.
further, in the step 1, a decision system of an optimal communication scheme is constructed by analyzing a plurality of indexes affecting communication quality;
Dividing a decision system of an optimal communication scheme into a target layer, a criterion layer and a scheme layer by establishing a hierarchical structure model of each communication scheme and a decision index thereof;
Wherein, the target layer is a decided optimal communication scheme; the criterion layer comprises a plurality of specific indexes which influence the communication quality, such as decision indexes of signal-to-noise ratio, time delay, distance and the like; the scheme layer comprises a plurality of communication schemes participating in decision making;
Wherein, the scheme set formed by the plurality of communication schemes participating in the decision is T ═ { T ═ T1,t2,…,ti,…,tmM denotes the number of communication schemes participating in the decision, tiIndicating the selected ith communication scheme; n decision indexes influencing the communication quality are selected to form a set X ═ X according to a plurality of indexes with different influence degrees on the communication quality, such as signal-to-noise ratio, time delay, distance and the like1,x2,…,xj,…,xn}; wherein x isjAnd n represents the number of the selected decision indexes influencing the communication quality.
Further, in the step 2, the importance of a plurality of indexes affecting the communication quality included in the alignment layer is compared pairwise, and pairwise judgment matrixes are constructed;
With aijRepresenting selected shadowsI-th index x of response communication qualityiand the jth index xjThe importance ratio of ajiIndicating a selected j-th indicator x affecting the quality of the communicationjAnd the ith index xiAnd should satisfy aij=1/ajiall comparison results are represented by the matrix A ═ aij)n×nRepresents; the normalized eigenvector S corresponding to the maximum eigenvalue λ max of a is ═ S1,s2,…,sj,…sn]TA weight assignment vector as a plurality of decision indicators affecting the communication quality, wherein sjThe j index which influences the communication quality accounts for the weight value in the optimal communication scheme decision system, and n represents the number of the selected decision indexes which influence the communication quality;
According to a formula, calculating a consistency index CI to measure the degree of deviation of the judgment matrix from complete consistency;
Calculating a consistency ratio CR which is CI/RI, wherein the value range of RI is between 0 and 2, and RI values corresponding to n are manually selected in the range to calculate CR;
When CR <0.10, the consistency of the judgment matrix A is considered to be acceptable, otherwise, the judgment matrix is corrected and adjusted appropriately, and the weight distribution vector of the decision index is recalculated, namely, the step 2 is repeated.
Further, in step 3, each communication scheme is used to perform communication under the same environment, specific values of the selected multiple indexes affecting the communication quality in each communication scheme are sequentially measured, and a decision matrix W is constructed as a decision index value in an optimal communication scheme decision system (W ═ Wij)m×n(ii) a Wherein, wijA decision index value which represents the j (th) decision index value of the ith communication scheme and influences the communication quality;
The decision matrix is normalized and sorted, part of cost type indexes are converted into benefit type indexes, the higher the influence trend of all indexes influencing the communication quality on each communication scheme is, the more favorable the communication is, the conversion formula isReuse of normalization formulaAfter normalization, a new matrix P ═ P (P) is obtainedij)m×nwherein p isijRepresenting the j decision index value influencing the communication quality of the ith communication scheme after normalized sorting, wherein m represents the number of the communication schemes participating in decision, and n represents the number of the selected decision index values influencing the communication quality;
Then, the optimal communication scheme decision index weight distribution vector S ═ S determined with AHP1,s2,…sj,…Sn]TIn combination, each decision index influencing communication quality in the optimal communication scheme decision system is given different weight, and a weighted normalized matrix R (R) related to the optimal communication scheme decision index is constructedij)m×nWherein r isij=pijsj,rijand the j decision index value which expresses the weighted ith communication scheme and influences the communication quality.
further, in the step 4, the positive ideal solution and the negative ideal solution, i.e. the maximum value and the minimum value in each decision index, use Z+Represents the positive ideal solution, Z-represents a negative ideal solution, as follows:
Z+=[maxr1,maxr2,…,maxrj,…,maxrn]
Z-=[minr1,minr2,…,minrj,…,minrn]
Wherein n represents the number of selected decision indicators affecting the communication quality, maxrjIndicating the maximum value, minr, of the j-th decision index affecting the communication qualityjRepresenting the smallest value in the jth decision index influencing the communication quality; then, the ith communication scheme and the positive ideal solution Z are calculated by the following formula+Negative ideal solution Z-Distance D of+iAnd D-i:
Where j is 1,2, …, n, rijRepresenting a j decision index value which influences the communication quality after the ith communication scheme which is currently involved in the calculation is weighted; sequentially calculating m communication schemes in the scheme set T and the ideal solution Z according to the method+Negative ideal solution Z-The distance of (c).
further, in the step 5, relative closeness of the m communication schemes to the ideal solution is calculated according to the distance between each communication scheme and the positive ideal solution and the negative ideal solution, respectively, and the relative closeness is calculated by using the following formula:
(i=1,2,…,m)0≤Ci≤1
In the calculation result, CiThe closer to 1, the more Cithe corresponding communication scheme is closest to the positive ideal solution and is farthest from the negative ideal solution, namely, the more the requirement of a decision target is met, the corresponding communication scheme corresponds to CiThe communication scheme with the largest value is used as the final decision result.
the invention combines two decision methods of AHP and TOPSIS communication schemes, not only overcomes the defect that the AHP algorithm is too simple to sort various decision indexes, but also solves the problem that the weight of the indexes needs to be determined in the decision process of the TOPSIS algorithm, and leads the result to be more objective and reliable. A plurality of indexes influencing communication quality are selected as decision indexes, and different weights are given to the decision indexes based on an AHP algorithm. And combining the weights in a TOPSIS algorithm to construct a weighted decision matrix, determining an ideal solution, evaluating the advantages and disadvantages of various communication schemes by measuring the relative closeness of the ideal solution, and selecting a reasonable communication scheme so as to improve the communication quality. The method is technically feasible and has practical value.
Drawings
Fig. 1 is a flow chart of a communication scheme decision method based on AHP and TOPSIS according to the present application.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings in the specification.
the communication scheme decision method based on AHP and TOPSIS comprises the following steps:
step 1: and selecting indexes influencing the communication quality, such as signal-to-noise ratio, time delay, distance and the like, as decision bases of the optimal communication scheme, and establishing a hierarchical structure model of the communication scheme and the decision indexes thereof.
And (3) constructing a decision system of an optimal communication scheme by analyzing a plurality of indexes influencing the communication quality. By establishing a hierarchical structure model of each communication scheme and decision indexes thereof, a decision system of the optimal communication scheme is divided into a target layer, a criterion layer and a scheme layer. Wherein, the target layer decides an optimal communication scheme. The criterion layer comprises a plurality of specific indexes which influence the communication quality, such as signal-to-noise ratio, time delay, distance and other decision indexes. The scheme layer includes a plurality of communication schemes that participate in the decision-making. Wherein, the scheme set formed by the plurality of communication schemes participating in the decision is T ═ { T ═ T1,t2,…,ti,…,tmM denotes the number of communication schemes participating in the decision, tiIndicating the selected ith communication scheme. N decision indexes influencing the communication quality are selected to form a set X ═ X according to a plurality of indexes with different influence degrees on the communication quality, such as signal-to-noise ratio, time delay, distance and the like1,x2,…,xj,…,xn}. Wherein x isjAnd n represents the number of the selected decision indexes influencing the communication quality.
Step 2: and constructing a judgment matrix of the decision index influencing the communication quality, calculating the maximum eigenvalue of the matrix and the corresponding normalized eigenvector thereof, and performing consistency check to obtain the decision index weight distribution vector of the optimal communication scheme.
the importance of multiple indexes affecting communication quality included in alignment layer is determinedAnd comparing every two to construct a judgment matrix. With aijIndicating a selected i-th indicator x affecting the quality of the communicationiand the jth index xjThe importance ratio of ajiindicating a selected j-th indicator x affecting the quality of the communicationjAnd the ith index xiAnd should satisfy aij=1/ajiall comparison results are represented by the matrix A ═ aij)n×nAnd (4) showing. The normalized eigenvector S corresponding to the maximum eigenvalue λ max of a is ═ S1,s2,…sj,…sn]TA weight assignment vector as a plurality of decision indicators affecting the communication quality. Wherein s isiand n is the number of the selected decision indexes influencing the communication quality. And calculating a consistency index CI according to a formula to measure the degree of the deviation of the judgment matrix from the complete consistency. And calculating the consistency ratio CR, wherein the value range of RI is between 0 and 2, and RI corresponding to n is manually selected in the range to calculate CR. When CR is reached<At 0.10, the consistency of the judgment matrix a is considered to be acceptable, otherwise, the judgment matrix should be modified and adjusted appropriately, and the weight distribution vector of the decision index is recalculated, i.e. step 2 is repeated.
and step 3: and (3) obtaining decision index values influencing the communication quality in each communication scheme, constructing a decision matrix, carrying out normalization processing, and combining the decision matrix with the weight distribution vector of the decision index influencing the communication quality determined by the AHP algorithm in the step (2) to jointly construct a normalized weighting matrix related to the decision index of the optimal communication scheme.
using each communication scheme to carry out communication under the same environment, sequentially measuring specific values of a plurality of selected indexes influencing the communication quality in each communication scheme, and constructing a decision matrix W (W is a decision index value in an optimal communication scheme decision system)ij)m×n。wijAnd (3) a decision index value which represents the j (th) decision index value of the ith communication scheme and influences the communication quality. The decision matrix is normalized and sorted, and part of cost type indexes are converted into benefit type indexes, so that all influences on communicationThe higher the influence trend of the quality index on each communication scheme is, the more favorable the communication is, the conversion formula isReuse of normalization formulaafter normalization, a new matrix P ═ P (P) is obtainedij)m×n. Wherein p isijAnd (3) representing the j-th decision index value influencing the communication quality of the ith communication scheme after the normalization arrangement, wherein m represents the number of the communication schemes participating in the decision, and n represents the number of the selected decision indexes influencing the communication quality. Then, the optimal communication scheme decision index weight distribution vector S ═ S determined with AHP1,s2,…,sj,…sn]TIn combination, each decision index influencing communication quality in the optimal communication scheme decision system is given different weight, and a weighted normalized matrix R (R) related to the optimal communication scheme decision index is constructedij)m×nWherein r isij=pijsj,rijand the j decision index value which expresses the weighted ith communication scheme and influences the communication quality.
And 4, step 4: and 3, determining a positive ideal solution and a negative ideal solution in the optimal communication scheme decision index according to the normalized weighting matrix of the optimal communication scheme decision index obtained in the step 3. Distances of the communication schemes from the positive ideal solution and the negative ideal solution are calculated simultaneously.
Weighted normalization matrix R ═ (R) according to optimal communication scheme decision metricsij)m×nDetermining positive and negative ideal solutions, i.e. maximum and minimum values in each decision indicator, of selected decision indicators affecting communication quality, using Z+Represents the positive ideal solution, Z-Represents a negative ideal solution, as follows:
Z+=[maxr1,maxr2,…,maxrj,…,maxrn]
Z-=[minr1,minr2,…,minrj,…,minrn]
wherein n represents the number of selected decision indicators affecting the communication quality, maxrjIndicating the maximum value, minr, of the j-th decision index affecting the communication qualityjAnd the minimum value of the j decision index influencing the communication quality is shown. Then, the ith communication scheme and the positive ideal solution Z are calculated by the following formula+Negative ideal solution Z-Distance D of+iAnd D-i:
Where j is 1,2, …, n, rijAnd representing the j decision index value which influences the communication quality after the ith communication scheme which is currently involved in the calculation is weighted. Sequentially calculating m communication schemes in the scheme set T and the ideal solution Z according to the method+Negative ideal solution Z-The distance of (c).
And 5: and 4, calculating the relative closeness of the ideal solutions in the decision indexes of various communication schemes and the optimal communication scheme by using the distance results in the step 4, and sequencing the superiority and inferiority to obtain a final decision result.
And calculating the relative closeness of the m communication schemes to the ideal solution according to the distance between each communication scheme and the positive ideal solution and the negative ideal solution. Relative proximity is calculated using the following formula
(i=1,2,…,m)0≤Ci≤1
In the calculation result, CiThe closer to 1, the more CiThe corresponding communication scheme is closest to the positive ideal solution and is farthest from the negative ideal solution, namely, the more the requirement of a decision target is met, the corresponding communication scheme corresponds to Cithe communication scheme with the largest value is used as the final decision result.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited to the above embodiment, but equivalent modifications or changes made by those skilled in the art according to the present disclosure should be included in the scope of the present invention as set forth in the appended claims.
Claims (6)
1. A communication scheme decision method based on AHP and TOPSIS is characterized by comprising the following steps:
Step 1: selecting indexes influencing communication quality, such as signal-to-noise ratio, time delay, distance and the like, as decision bases of an optimal communication scheme, and establishing a hierarchical structure model of the communication scheme and the decision indexes thereof;
Step 2: constructing a judgment matrix of decision indexes influencing communication quality, calculating a maximum eigenvalue of the matrix and a corresponding normalized eigenvector thereof, and performing consistency check to obtain a decision index weight distribution vector of an optimal communication scheme;
And step 3: acquiring decision index values influencing communication quality in each communication scheme, constructing a decision matrix, carrying out normalized processing, and combining the decision matrix with the weight distribution vector of the decision index influencing communication quality determined by the AHP algorithm in the step 2 to jointly construct a normalized weighting matrix about the decision index of the optimal communication scheme;
And 4, step 4: determining a positive ideal solution and a negative ideal solution in the optimal communication scheme decision index according to the normalized weighting matrix of the optimal communication scheme decision index obtained in the step 3, and simultaneously calculating the distance between each communication scheme and the positive ideal solution and the negative ideal solution;
And 5: and 4, calculating the relative closeness of the ideal solutions in the decision indexes of various communication schemes and the optimal communication scheme by using the distance results in the step 4, and sequencing the superiority and inferiority to obtain a final decision result.
2. The AHP and TOPSIS based communication scheme decision method of claim 1, wherein: in the step 1, a decision system of an optimal communication scheme is constructed by analyzing a plurality of indexes influencing the communication quality;
Dividing a decision system of an optimal communication scheme into a target layer, a criterion layer and a scheme layer by establishing a hierarchical structure model of each communication scheme and a decision index thereof;
wherein, the target layer is a decided optimal communication scheme; the criterion layer comprises a plurality of specific indexes which influence the communication quality, such as decision indexes of signal-to-noise ratio, time delay, distance and the like; the scheme layer comprises a plurality of communication schemes participating in decision making;
Wherein, the scheme set formed by the plurality of communication schemes participating in the decision is T ═ { T ═ T1,t2,…,ti,…,tmM denotes the number of communication schemes participating in the decision, tiIndicating the selected ith communication scheme; n decision indexes influencing the communication quality are selected to form a set X ═ X according to a plurality of indexes with different influence degrees on the communication quality, such as signal-to-noise ratio, time delay, distance and the like1,x2,…,xj,…,xn}; wherein x isjAnd n represents the number of the selected decision indexes influencing the communication quality.
3. The AHP and TOPSIS based communication scheme decision method of claim 1, wherein: in the step 2, the importance of a plurality of indexes affecting the communication quality included in the alignment rule layer is compared pairwise, and pairwise judgment matrixes are constructed;
With aijIndicating a selected i-th indicator x affecting the quality of the communicationiAnd the jth index xjThe importance ratio of ajiIndicating a selected j-th indicator x affecting the quality of the communicationjAnd the ith index xiAnd should satisfy aij=1/ajiAll comparison results are represented by the matrix A ═ aij)n×nRepresents; the normalized eigenvector S corresponding to the maximum eigenvalue λ max of a is ═ S1,s2,…,sj,…sn]TA weight assignment vector as a plurality of decision indicators affecting the communication quality, wherein sjIndicating j-th index affecting communication qualityThe weight value occupied in the optimal communication scheme decision system, n represents the number of selected decision indexes influencing the communication quality;
According to a formula, calculating a consistency index CI to measure the degree of deviation of the judgment matrix from complete consistency;
calculating a consistency ratio CR which is CI/RI, wherein the value range of RI is between 0 and 2, and RI values corresponding to n are manually selected in the range to calculate CR;
When CR <0.10, the consistency of the judgment matrix A is considered to be acceptable, otherwise, the judgment matrix is corrected and adjusted appropriately, and the weight distribution vector of the decision index is recalculated, namely, the step 2 is repeated.
4. The AHP and TOPSIS based communication scheme decision method of claim 1, wherein: in step 3, each communication scheme is used to communicate in the same environment, the specific values of the selected multiple indexes affecting the communication quality in each communication scheme are measured in sequence, and the measured values are used as decision index values in an optimal communication scheme decision system to construct a decision matrix W (W is the value of W in the decision system of the optimal communication scheme)ij)m×n(ii) a Wherein, wijA decision index value which represents the j (th) decision index value of the ith communication scheme and influences the communication quality;
The decision matrix is normalized and sorted, part of cost type indexes are converted into benefit type indexes, the higher the influence trend of all indexes influencing the communication quality on each communication scheme is, the more favorable the communication is, the conversion formula isReuse of normalization formulaAfter normalization, a new matrix P ═ P (P) is obtainedij)m×nwherein p isijrepresenting the j decision index value influencing the communication quality of the ith communication scheme after the normalization arrangement, m representing the number of the communication schemes participating in the decision, and n representing the number of the selected decision indexes influencing the communication quality;
Then, the optimal communication scheme decision index weight distribution vector S ═ S determined with AHP1,s2,…sj,…sn]TIn combination, each decision index influencing communication quality in the optimal communication scheme decision system is given different weight, and a weighted normalized matrix R (R) related to the optimal communication scheme decision index is constructedij)m×nWherein r isij=pijsj,rijAnd the j decision index value which expresses the weighted ith communication scheme and influences the communication quality.
5. The AHP and TOPSIS based communication scheme decision method of claim 1, wherein: in the step 4, the positive ideal solution and the negative ideal solution, i.e. the maximum value and the minimum value in each decision index, use Z+Represents the positive ideal solution, Z-Represents a negative ideal solution, as follows:
Z+=[maxr1,maxr2,…,maxrj,…,maxrn]
Z-=[minr1,minr2,…,minrj,…,minrn]
Wherein n represents the number of selected decision indicators affecting the communication quality, maxrjIndicating the maximum value, minr, of the j-th decision index affecting the communication qualityjRepresenting the smallest value in the jth decision index influencing the communication quality; then, the ith communication scheme and the positive ideal solution Z are calculated by the following formula+Negative ideal solution Z-Distance D of+iAnd D-i:
where j is 1,2, …, n, rijIndicating current participation in the calculationThe jth decision index value which influences the communication quality after the ith communication scheme is weighted; sequentially calculating m communication schemes in the scheme set T and the ideal solution Z according to the method+Negative ideal solution Z-The distance of (c).
6. The AHP and TOPSIS based communication scheme decision method of claim 1, wherein: in the step 5, relative closeness of the m communication schemes and the ideal solution is respectively calculated according to the distance between each communication scheme and the positive ideal solution and the negative ideal solution, and the relative closeness is calculated by using the following formula:
In the calculation result, CiThe closer to 1, the more CiThe corresponding communication scheme is closest to the positive ideal solution and is farthest from the negative ideal solution, namely, the more the requirement of a decision target is met, the corresponding communication scheme corresponds to Cithe communication scheme with the largest value is used as the final decision result.
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