Interactive intuitionistic fuzzy group decision-making method containing time weight

Abstract

An interactive intuitionistic fuzzy group decision-making method containing time weight comprises the following steps: firstly solving the time weight lambda (t), then gathering comprehensive information of a single decision maker in different time periods through a formula # imgabs0 #, and then utilizing a dynamic multi-attribute TOPSIS method of the single decision maker to obtain a dynamic multi-attribute TOPSIS method of the single decision maker. And solving a comprehensive decision matrix # imgabs2 # of a plurality of decision makers through the relative closeness # imgabs1 # of the scheme for a single decision maker, and then using the TOPSIS method for the first time to realize scheme optimization of final group decision. The method is relatively simple in calculation and is a flexible method for interactive intuition fuzzy group decision making; however, in the prior art, the TOPSIS method is only adopted in the last step to calculate the decision information at a time, and the method solves the problems that according to the method, calculation is tedious and not flexible enough, and the actual use scene is poor.

Description

Technical Field

[0001] The invention relates to an intuitive fuzzy group decision-making method, more specifically to an interactive intuitive fuzzy group decision-making method including time weight, belonging to the technical field of group decision-making. Background Art

[0002] The rapid development of the economy and the high-speed dissemination of information have made the support system for group decision-making the mainstream of various industry systems, and the research on group decision-making models has become extremely important. At the same time, the actual economic development and decision-making situation are becoming more and more complex. In order to make the decision-making model more scientific and reasonable, the interactive idea needs to be continuously deepened into the group decision-making model. In addition, the decision-making information has become increasingly complex and more ambiguous. The theory and method of intuitionistic fuzzy sets have begun to develop and improve under this background. All these situations make the interactive intuitionistic fuzzy group decision-making problem an important issue facing today's economic development.

[0003] At present, the computational model of TOPSIS for intuitive fuzzy group decision making is relatively mature, and is used to solve the problem of group decision ranking when the decision maker's information is fuzzy. In addition, the decision maker's decision information will change over time. In order to achieve the dynamic interactivity of the model, the impact of time factors on the decision results needs to be considered.

[0004] In the current model, the calculation method for interactive intuitionistic fuzzy group decision-making first integrates the decision information of all decision makers through the corresponding aggregation operator, and finally uses only one step of the TOPSIS method to achieve the optimal sorting of the schemes for the decision matrix with comprehensive decision information. However, this method only uses the TOPSIS method in the last step to calculate the decision information once, so the calculation is relatively cumbersome; and because of the small number of steps and lack of flexibility, it limits the actual use scenarios. Therefore, there is an urgent need for a method model for interactive intuitionistic fuzzy group decision-making that is relatively simple to calculate and more flexible. Summary of the invention

[0005] The purpose of the present invention is to provide an interactive intuitive fuzzy group decision-making method including time weight in view of the problems existing in the prior art.

[0006] To achieve the above object, the technical solution of the present invention is: comprising the following steps:

[0007] Step 1: Determine the solution set X = {x 1 , x 2 , Λx n}, decision maker P k And the attribute set O = {o 1 , o 2 ,Λo m}, decision maker Pk represents the kth decision maker, where the attribute weights of the decision maker and the weight of the decision maker are known and fixed, and the attribute weight vector of the kth decision maker is ω k =(ω k 1 ,ω k 2 ,Λω k m ) T , the decision maker's weight is ω=(ω 1 ,ω 2 ,Λω k ) T , above k=1,2,…K;

[0008] Step 2: Select P time points, and at each time point, let each decision maker evaluate each attribute of each plan to form an evaluation value matrix F k p , the F k p It represents the evaluation value matrix of each attribute of each scheme by the k-th decision maker at the p-th time;

[0009] Step 3: Using the P time points in step 2 above, use the following time weight determination formula (1) to determine the time weight vector λ(t)=(λ(t 1 ),λ(t 2 ), …λ(tp)) T ,

[0010]

[0011] Step 4: According to the attribute weight vector ω k =(ω k 1 ,ω k 2 ,Λω k m ) T and the time weight vector λ(t)=(λ(t 1 ),λ(t 2 ), …λ(tp)) T , and the evaluation value matrix of each decision maker for each attribute of each plan, and obtain the weighted intuitive fuzzy set decision matrix of the kth decision maker for each attribute of each plan at P time points Then, according to the weighted intuitionistic fuzzy set decision matrix, the decision maker P is determined using the following formulas (2) and (3): k Positive and negative ideal solutions x of weighted intuitionistic fuzzy set decision matrix k+ , x k -,

[0012]

[0013] F k+ and F k- x k+ and x k- The decision maker weighted intuitionistic fuzzy set vector representation is:

[0014]

[0015] In the above, i=1,2,…m;k=1,2,…K;

[0016] Step 5: Use the following formulas (4) and (5) to find the decision maker P k The Euclidean distance between the decision value of each option and the weighted intuitionistic fuzzy positive and negative ideal solutions Then use the following formula (6) to calculate the relative closeness Relative closeness is a quantity that can express the degree of closeness between the decision value of each solution and the positive and negative ideal solutions:

[0017]

[0018] In the above, j=1,2,…n;k=1,2,…K;

[0019] Step 6: Use the relative closeness obtained in step 5 above Forming a relative closeness decision matrix The relative closeness matrix is ​​a matrix about the relationship between all decision makers and all plans. The value of each relative closeness is It can represent the overall evaluation decision value of the kth decision maker for the jth solution. Using the following formula (7), according to the decision maker weight vector ω = (ω 1 ,ω 2 ,Λω k ) T , and obtain the weighted relative closeness decision matrix:

[0020]

[0021] In the above, j=1,2,…n;k=1,2,…K;

[0022] Step 7: Determine the positive and negative ideal solutions x of the decision-making group according to the following formulas (8) and (9): + , x - :

[0023]

[0024] and x k+ and x k- The decision-making group intuitionistic fuzzy set vector representation is:

[0025] In the formula,

[0026] Step 8: Calculate the Euclidean distance between each solution and the positive and negative ideal solutions of the group and And the relative closeness C of each solution to the group positive ideal solution j , above j=1,2,…n;

[0027] Step 9: Use the relative closeness C in step 8 above to calculate the j The values ​​of are sorted in non-increasing order. The larger the value, the closer the solution is to the group's positive ideal solution and the farther it is from the group's negative ideal solution, that is, the better the solution is, so as to find a satisfactory solution and complete the solution optimization.

[0028] In step 8, the Euclidean distance between each solution and the positive and negative ideal solutions of the group is calculated according to the following formulas (10), (11) and (12): and And the relative closeness C of each solution to the group positive ideal solution j , above j=1,2,…n:

[0029]

[0030] Compared with the prior art, the beneficial effects of the present invention are:

[0031] This method uses multiple TOPSIS methods to aggregate the two influencing factors of attributes and time step by step, and then integrates the decisions of multiple experts, and aggregates the various influencing factors step by step to achieve the final group decision-making and final solution optimization; this method is relatively simple to calculate and is a flexible method for interactive intuitive fuzzy group decision-making. The existing technology only uses the TOPSIS method in the last step to calculate the decision information method once. The present invention solves the problems of the method being cumbersome in calculation, inflexible, and in practical usage scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0033] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0034] See also Figure 1, an interactive intuitionistic fuzzy group decision-making method with time weight, uses the group's TOPSIS method and uses relative closeness as the decision variable for the final solution optimization. The TOPSIS method is a ranking method close to the linear weighted average method proposed to solve the multi-attribute problem of a single decision maker. Its basic idea is that the selected satisfactory solution should be as close to the positive ideal solution as possible and as far away from the negative ideal solution as possible. The group's TOPSIS method is basically divided into two parts. First, the decision of a single decision maker on each attribute of each solution is made, and the relative closeness is obtained as the decision maker's comprehensive evaluation value for each solution, and then the group decision matrix is ​​obtained; the relative closeness is obtained again as the decision variable for the final solution optimization. Specifically, it includes the following steps:

[0035] Step 1: Determine the solution set X = {x 1 , x 2 , Λx n}, decision maker P k And the attribute set O = {o 1 , o 2 ,Λo m}, decision maker P k represents the kth decision maker, where the attribute weights of the decision maker and the weight of the decision maker are known and fixed. The attribute weight vector of the kth decision maker is ω k =(ω k 1 ,ω k 2 ,Λω k m ) T , represents the weight vector of all attributes given by the k-th decision maker; the weight of the decision maker is ω=(ω 1 ,ω 2 ,Λω k ) T , satisfying the normalization condition. k The intuitive fuzzy set representing the weight of the k-th decision maker for the i-th attribute. The above k = 1, 2, ... K;

[0036] Step 2: Select P time points, and at each time point, let each decision maker evaluate each attribute of each plan to form an evaluation value matrix F k p , the F k p F represents the evaluation value matrix of each attribute of each scheme by the kth decision maker at the pth time. The evaluation value matrix is ​​actually the decision matrix of the intuitionistic fuzzy set; k p It represents F at the pth time point k, introduce time weight, so there are P F k Every F k The decision matrix (or evaluation value matrix) is made at the Pth time point. k =(F k ij )m×n=(<μ k ij ,V k ij >)m×n, represents the decision matrix of the intuitionistic fuzzy set; F k ij = <μ k ij ,V k ij >, represents the intuitionistic fuzzy set evaluation value of the kth decision maker on the i-th attribute of the j-th solution. k=1,2,…K.

[0037] Step 3: Using the P time points in step 2 above, use the following time weight determination formula (1) to determine the time weight vector λ(t)=(λ(t 1 ),λ(t 2 ),…λ(t p )) T ,

[0038]

[0039] Step 4: According to the attribute weight vector ω k =(ω k 1 ,ω k 2 ,Λω k m ) T and the time weight vector λ(t)=(λ(t 1 ),λ(t 2 ),…λ(t p )) T , and the evaluation value matrix of each decision maker for each attribute of each plan, and obtain the weighted intuitive fuzzy set decision matrix of the kth decision maker for each attribute of each plan at P time points Then, according to the weighted intuitionistic fuzzy set decision matrix, the decision maker P is determined using the following formulas (2) and (3): k Positive and negative ideal solutions x of weighted intuitionistic fuzzy set decision matrix k+ , x k- ,

[0040]

[0041] F k+and F k- x k+ and x k- The decision maker weighted intuitionistic fuzzy set vector representation is:

[0042]

[0043] In the above, i=1, 2, ...m; k=1, 2, ...K.

[0044] Step 5: Use the following formulas (4) and (5) to find the decision maker P k The Euclidean distance between the decision value of each option and the weighted intuitionistic fuzzy positive and negative ideal solutions Then use the following formula (6) to calculate the relative closeness Relative closeness is a quantity that can express the degree of closeness between the decision value of each solution and the positive and negative ideal solutions:

[0045]

[0046] In the above, j=1, 2, ...n; k=1, 2, ...K.

[0047] Step 6: Use the relative closeness obtained in step 5 above Forming a relative closeness decision matrix The relative closeness matrix is ​​a matrix about the relationship between all decision makers and all plans. The value of each relative closeness is It can represent the overall evaluation decision value of the kth decision maker for the jth solution. Using the following formula (7), according to the decision maker weight vector ω = (ω 1 ,ω 2 ,Λω k ) T , and obtain the weighted relative closeness decision matrix:

[0048]

[0049] In the above, j=1, 2, ...n; k=1, 2, ...K.

[0050] Step 7: Determine the positive and negative ideal solutions x of the decision-making group according to the following formulas (8) and (9): + , x - :

[0051]

[0052] and x k+ and x k- The decision-making group intuitionistic fuzzy set vector representation is:

[0053] In the formula,

[0054] Step 8: Calculate the Euclidean distance between each solution and the positive and negative ideal solutions of the group and And the relative closeness C of each solution to the group positive ideal solution j , j = 1, 2, ... n. Specifically, according to the following formulas (10), (11) and (12), the Euclidean distance between each solution and the positive and negative ideal solutions of the group is calculated: and And the relative closeness C of each solution to the group positive ideal solution j , above j=1,2,…n:

[0055]

[0056] Step 9: Use the relative closeness C in step 8 above to calculate the j The values ​​of are sorted in non-increasing order. The larger the value, the closer the solution is to the group's positive ideal solution and the farther it is from the group's negative ideal solution, that is, the better the solution is, so as to find a satisfactory solution and complete the solution optimization. Specific embodiment one:

[0058] Step 1: Two experts make decisions on three sets of protection solutions. The expert set is represented as (z 1 ,z 2 ), the solution set is represented as (A 1 ,A 2 ,A 3 ), the expert weight vector is known to be δ=(0.6,0.4). The attribute weight vector is in the form of an intuitive fuzzy number, expressed as ω=(<0.25,0.25>,<0.20,0.20>,<0.15,0.15>,<0.18,0.18>,<0.22,0.22>).

[0059] Step 2: The evaluation and testing process of the protection plan is divided into three stages, with the initial stage taking one month, the mid-term taking two months, and the final stage taking one month. The evaluation value matrices at the three time points are shown in Tables 1, 2, and 3 below.

[0060] Table 1 Attribute evaluation values ​​of various schemes in the early stage

[0061]

[0062] Table 2 Attribute evaluation values ​​of each mid-term plan

[0063]

[0064] Table 3 Attribute evaluation values ​​of each scheme in the later stage

[0065]

[0066] In step 3, the time weight function is used According to the actual situation, the interval between the first and middle stages is 1 month, and the interval between the middle and late stages is 2 months. Thus, we can get:

[0067]

[0068] Then:

[0069]

[0070] The time weight vector is obtained as:

[0071] λ(t)=(0.61,0.37,0.02) T

[0072] In this embodiment, the known attribute weight vector ω = (0.25, 0.20, 0.15, 0.18, 0.22) and the time weight vector λ(t) = (0.61, 0.37, 0.02) are used. T , weight the decision information of decision maker z1 in the early, middle and late stages by attributes and time, and obtain the decision maker z 1 The weighted decision matrices at three times are:

[0073] Table 4 Weighted decision matrix of early decision maker z1

[0074] A1 A2 A3 x1 <0.076，0.364> <0.114,0.322> <0.092，0.407> x2 <0.098，0.254> <0.049,0.385> <0.061,0.298> x3 <0.064,0.273> <0.073,0.182> <0.064,0.182> x4 <0.077,0.243> <0.066,0.243> <0.077,0.243> x5 <0.114，0.221> <0.101,0.221> <0.087,0.221>

[0075] Table 5 Weighted decision matrix of mid-term decision maker z1

[0076] Al A2 A3 x1 <0.051，0.274> <0.074，0.229> <0.056,0.274> x2 <0.063,0.167> <0.033,0.352> <0.037,0.352> x3 <0.028,0.339> <0.039,0.051> <0.044,0.150> x4 <0.053,0.160> <0.047,0.207> <0.053,0.207> x5 <0.053,0.265> <0.053，0.265> <0.069，0.173>

[0077] Table 6 Weighted decision matrix of late decision maker z1

[0078] Al A2 A3 xl <0.003,0.204> <0.004,0.105> <0.003,0.204> x2 <0.004,0.104> <0.002，0.203> <0.002,0.303> x3 <0.002，0.202> <0.002,0.103> <0.002，0.103> x4 <0.003,0.153> <0.003,0.153> <0.002,0.153> x5 <0.003，0.104> <0.003，0.104> <0.003，0.154>

[0079] Combining the weighted decision matrices of the three time periods, adding the above three matrices together, the weighted decision matrix of decision maker z1 is obtained as follows:

[0080] Table 7 Weighted decision matrix of decision maker z1

[0081] A1 A2 A3 x1 <0.219,0.842> <0.192,0.656> <0.151,0.885> x2 <0.165,0.525> <0.084,0.940> <0.100,0.953> x3 <0.094，0.814> <0.114，0.336> <0.110,0.435> x4 <0.133,0.556> <0.116,0.603> <0.132,0.603> x5 <0.170,0.590> <0.157,0.590> <0.072,0.548>

[0082] The decision information of decision maker z2 in the early, middle and late stages is weighted by attributes and time to obtain the decision maker z 2 The weighted decision matrices at three times are:

[0083] Table 8 Weighted decision matrix of early decision maker z2

[0084] Al A2 A3 x1 <0.069,0.322> <0.122,0.322> <0.092，0.322> x2 <0.098，0.254> <0.061,0.298> <0.061,0.254> x3 <0.055，0.228> <0.069,0.228> <0.055,0.228> x4 <0.082,0.243> <0.071，0.243> <0.082，0.243> x5 <0.107,0.264> <0.094,0.264> <0.081,0.264>

[0085] Table 9 Weighted decision matrix of mid-term decision maker z2

[0086] Al A2 A3 x1 <0.046,0.229> <0.074,0.229> <0.060,0.274> x2 <0.059,0.167> <0.044,0.213> <0.044，0.213> x3 <0.039，0.197> <0.039,0.197> <0.039,0.197> x4 <0.050，0.160> <0.050,0.207> <0.050，0.253> x5 <0.057，0.219> <0.049,0.311> <0.065,0.219>

[0087] Table 10 Weighted decision matrix of late decision maker z2

[0088] A1 A2 A3 x1 <0.003,0.105> <0.005,0.154> <0.003,0.105> x2 <0.003,0.104> <0.002,0.303> <0.002，0.203> x3 <0.002,0.202> <0.002，0.103> <0.002，0.103> x4 <0.003,0.203> <0.002，0.203> <0.003,0.153> x5 <0.003,0.154> <0.003,0.154> <0.003,0.154>

[0089] Combining the weighted decision matrices of the three time periods, adding the above three matrices together, the weighted decision matrix of decision maker z2 is obtained as follows:

[0090] Table 11 Weighted decision matrix of decision maker z2

[0091] A1 A2 A3 x1 <0.117,0.665> <0.201,0.705> <0.155,0.701> x2 <0.160,0.524> <0.108,0.813> <0.107,0.670> x3 <0.096，0.627> <0.110,0.528> <0.096,0.528> x4 <0.135,0.606> <0.124,0.653> <0.135,0.650> x5 <0.167,0.637> <0.146,0.729> <0.149,0.637>

[0092] Step 4: From Table 4, we can get the positive and negative ideal solutions of the weighted decision matrix of decision maker z1:

[0093] x 1 + =(<0.193,0.665>,<0.164,0.524>,<0.114,0.435>,<0.133,0.556>,<0.170,0.548>) T ,

[0094] x 1 -=(<0.130,0.885>,<0.084,0.952>,<0.094,0.814>,<0.115,0.603>,<0.157,0.590>) T .

[0095] From Table 8, we can get the positive and negative ideal solutions of the weighted decision matrix of decision maker z2:

[0096] x 2 + =(<0.201,0.665>,<0.160,0.524>,<0.110,0.528>,<0.135,0.606>,<0.167,0.637>) T ,

[0097] x 2 -=(<0.117,0.705>,<0.107,0.813>,<0.096,0.627>,<0.124,0.653>,<0.1146,0.729>)T .

[0098] Step 5: Calculate the Euclidean distances between each plan of decision maker z1 and the positive and negative ideal solutions:

[0099] D A1 1+ =0.4068D A1 1 - = 0.3989,

[0100] D A2 1+ =0.3867D A2 1 - = 0.4230,

[0101] D A3 1+ =0.4552D A2 1 -=0.3748.

[0102] The relative closeness of each plan decided by decision maker z1 to the positive ideal solution is obtained as follows:

[0103] C A1 1 =0.3989 / (0.3989+0.4068)=0.495,

[0104] C A2 1 =0.4230 / (0.4230+0.3867)=0.522,

[0105] C A3 1 =0.3748 / (0.3748+0.4552)=0.453.

[0106] The Euclidean distances between each plan of decision maker z2 and the positive and negative ideal solutions are calculated as follows:

[0107] D A1 2+ =0.1251D A1 2 - = 0.2871,

[0108] D A2 2+ =0.2872D A2 2 - = 0.1251,

[0109] D A3 2+ =0.1445D A2 2-=0.2002.

[0110] The relative closeness of each plan decided by decision maker z1 to the positive ideal solution is obtained as follows:

[0111] C A1 2 =0.2871 / (0.2871+0.1251)=0.697,

[0112] C A2 2 =0.1251 / (0.1251+0.2872)=0.303,

[0113] C A3 2 =0.2002 / (0.2002+0.1445)=0.581.

[0114] According to the relative closeness of each plan obtained by each decision maker's evaluation of the attribute value of each plan, the relative closeness matrix is ​​obtained as follows:

[0115] Table 12 Relative closeness matrix

[0116] A1 A2 A3 Z1 0.495 0.522 0.453 Z2 0.697 0.303 0.581

[0117] Step 6: According to the decision maker weight vector δ = (0.6, 0.4), the weighted relative closeness matrix is ​​obtained as follows:

[0118] Table 13 Weighted relative closeness matrix

[0119] A1 A2 A3 Z1 0.297 0.3132 0.2718 Z2 0.2788 0.1212 0.2324

[0120] Step 7: Obtain the positive and negative ideal solutions of the weighted relative closeness matrix for each solution:

[0121] x + =(0.3132,0.2788) T ,

[0122] x - =(0.2718,0.1212) T .

[0123] Step 8: Calculate the Euclidean distances between each solution and the positive and negative ideal solutions:

[0124] D1 + =0.011D1-=0.113,

[0125] D2 + =0.111D2-=0.029,

[0126] D3+ =0.044D3-=0.079.

[0127] Thus, for group decision making, the relative closeness of each solution to the positive ideal solution is obtained as follows:

[0128] C1=0.113 / (0.113+0.011)=0.911,

[0129] C2=0.029 / (0.029+0.111)=0.207,

[0130] C3=0.079 / (0.079+0.044)=0.642.

[0131] Step nine, sort in non-increasing order according to the final relative closeness value. Since C1>C3>C2, the first solution is the best, that is, solution A1 has the best protection effect and is the optimal solution.

[0132] See also Figure 1 , this decision method first obtains the time weight λ(t), and then uses the formula Gather the comprehensive information of a single decision maker in different time periods, and then use the single decision maker dynamic multi-attribute TOPSIS method to compare the relative closeness of the single decision maker's plan Obtain the comprehensive decision matrix of multiple decision makers The TOPSIS method is used again to achieve the optimal solution for the final group decision.

[0133] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, and the above structures should be regarded as belonging to the protection scope of the present invention.

Claims

1. An interactive intuitionistic fuzzy group decision-making method including time weight, characterized in that: The following steps are included: Step 1: Determine the solution set X = {x1, x2, Λx n }, decision maker P k And the attribute set O = {o1, o2, Λo m }, decision maker P k represents the kth decision maker, where the attribute weights of the decision maker and the weight of the decision maker are known and fixed, and the attribute weight vector of the kth decision maker is ω k =(ω k 1, ω k 2, Λω k m ) T , the decision maker's weight is ω=(ω1,ω2,Λω k ) T , k=1, 2, ...K; Step 2: Select P time points, and at each time point, let each decision maker evaluate each attribute of each plan to form an evaluation value matrix F k p , the F k p It represents the evaluation value matrix of each attribute of each scheme by the k-th decision maker at the p-th time; Step 3: Using the P time points in step 2 above, use the following time weight determination formula (1) to determine the time weight vector λ(t) = (λ(t1), λ(t2), ...λ(t p )) T , Step 4: According to the attribute weight vector ω k =(ω k 1, ω k 2, Λω k m ) T and the time weight vector λ(t)=(λ(t1),λ(t2),…λ(t p )) T , and the evaluation value matrix of each decision maker for each attribute of each plan, and obtain the weighted intuitive fuzzy set decision matrix of the kth decision maker for each attribute of each plan at P time points Then, according to the weighted intuitionistic fuzzy set decision matrix, the decision maker P is determined using the following formulas (2) and (3): k Positive and negative ideal solutions x of weighted intuitionistic fuzzy set decision matrix k+ , x k- , F k+ and F k- x k+ and x k- The decision maker weighted intuitionistic fuzzy set vector representation is: In the above, i=1, 2, ...m; k=1, 2, ...K; Step 5: Use the following formulas (4) and (5) to find the decision maker P k The Euclidean distance between the decision value of each option and the weighted intuitionistic fuzzy positive and negative ideal solutions Then use the following formula (6) to calculate the relative closeness Relative closeness is a quantity that can express the degree of closeness between the decision value of each solution and the positive and negative ideal solutions: In the above, j=1, 2, ..., n; k=1, 2, ..., K; Step 6: Use the relative closeness obtained in step 5 above Forming a relative closeness decision matrix The relative closeness matrix is ​​a matrix about the relationship between all decision makers and all plans. The value of each relative closeness is It can represent the overall evaluation decision value of the kth decision maker for the jth solution. Using the following formula (7), according to the decision maker weight vector ω = (ω1, ω2, Λω k ) T , and obtain the weighted relative closeness decision matrix: In the above, j=1, 2, ..., n; k=1, 2, ..., K; Step 7: Determine the positive and negative ideal solutions x of the decision-making group according to the following formulas (8) and (9): + , x - : and x k+ and x k- The decision-making group intuitionistic fuzzy set vector representation is: In the formula, Step 8: Calculate the Euclidean distance between each solution and the positive and negative ideal solutions of the group and And the relative closeness C of each solution to the group positive ideal solution j , above j = 1, 2, ... n; Step 9: Use the relative closeness C in step 8 above to calculate the j The values ​​of are sorted in non-increasing order. The larger the value, the closer the solution is to the group's positive ideal solution and the farther it is from the group's negative ideal solution, that is, the better the solution is, so as to find a satisfactory solution and complete the solution optimization.

2. The interactive intuitionistic fuzzy group decision-making method including time weight according to claim 1, characterized in that: In step 8, the Euclidean distance between each solution and the positive and negative ideal solutions of the group is calculated according to the following formulas (10), (11) and (12): and And the relative closeness C of each solution to the group positive ideal solution j , above j = 1, 2, ... n:

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