Multi-attribute decision-making method and system based on normal swing hesitant fuzzy information and foreground theory

Abstract

The invention discloses a multi-attribute decision-making method and system based on normal swing hesitant fuzzy information and a foreground theory. The method comprises the following steps: constructing an initial decision-making matrix and carrying out normalization processing; generating a multi-dimensional hesitant fuzzy decision matrix by calculating the Hamming distance, the chi-square distance and the trigonometric function distance between each scheme and the positive ideal solution, and converting the multi-dimensional hesitant fuzzy decision matrix into a normal swing hesitant fuzzy decision matrix; the comprehensive hesitant fuzzy entropy method and the logarithm percentage change driven target weighting method are fused to determine the comprehensive weight of the index; mapping the negative ideal solution distance into an income value and mapping the positive ideal solution distance into a loss value in combination with a foreground theory, and generating a foreground value decision matrix and normalizing the foreground value decision matrix; and calculating the correlation degree between the scheme and the dynamic ideal solution through a normal swing hesitant fuzzy weighting correlation coefficient, thereby realizing scheme sorting. According to the method, various kinds of uncertainty information and incomplete psychological characteristics of decision makers can be fully considered, and more accurate index weights and decision results are provided.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-attribute decision making, and in particular to a multi-attribute decision making method based on normal swing hesitant fuzzy information and prospect theory and a cascade reservoir optimization scheduling evaluation system. Background Art

[0002] Multi-attribute decision-making (MADM) is a key approach to evaluating alternative options. While classic MAD methods, such as the Top-of-Sentence Ideal Points Method (TOPSIS), gray relational analysis, gray target models, VIKOR (Variational Kernel Compromise Solution Ranking), fuzzy decision-making methods, and set pair analysis (SPA), have been widely used in evaluating alternative options, these methods only utilize precise value information and ignore the decision maker's psychological behavior. In reality, MAD is a complex and highly uncertain process, as the decision maker's evaluation information often contains cognitive uncertainty. Furthermore, in actual decision-making, decision makers are often not completely rational.

[0003] To express the uncertainty of diverse decision information, some researchers have introduced interval-valued fuzzy sets (IVFSs), intuitionistic fuzzy sets (IFSs), triangular fuzzy sets (TFSs), Pythagorean fuzzy sets (PFSs), and type-2 fuzzy sets, improving the theoretical framework of fuzzy sets. However, these approaches fail to address the problem of decision makers hesitating between several possible values ​​or the difficulty for experts supporting different values ​​to reach consensus in multi-attribute decision-making processes. Therefore, hesitant fuzzy sets (HFSs), another important extension of fuzzy sets, have been proposed. These HFSs allow membership to include multiple evaluation values, effectively capturing the uncertainty of decision information in a significant number of decision scenarios. Normally oscillating hesitant fuzzy sets (NWHFSs) are an extension of hesitant fuzzy sets. While preserving the original hesitant fuzzy information, they exploit the potential uncertainty of the decision, improving the accuracy of decision outcomes through a more complete representation of information. Furthermore, prospect theory can describe the incomplete rationality of people's actual decision-making and evaluation behaviors when they are influenced by uncertain environments. Although numerous decision-making methods related to hesitant fuzzy theory and prospect theory exist, they do not fully consider information uncertainty, and decision-making research combining normal oscillating hesitant fuzzy theory with prospect theory is rare. Therefore, it is very necessary to establish a decision-making method based on normal oscillation hesitant fuzzy theory and prospect theory that takes into account multi-faceted uncertainty information and the psychological behavior of decision makers and can provide more accurate decision results. Summary of the Invention

[0004] In view of the defects of the prior art, the present invention provides a multi-attribute decision-making method and system based on normal swing hesitant fuzzy information and prospect theory.

[0005] In order to achieve the above object of the invention, the technical solution adopted by the present invention is as follows:

[0006] A multi-attribute decision-making method based on normal oscillating hesitant fuzzy information and prospect theory includes the following steps:

[0007] S1, m alternatives A for multi-attribute decision-making problems i (i=1,2,…,m) and n evaluation indicators C j (j=1,2,…,n), forming the initial decision matrix Z=(z ij ) m×n ;

[0008] S2, normalize Z to get the normalized decision matrix R = (r ij ) m×n ;

[0009] S3, positive ideal solution determined by R Calculation Plan A i In indicator C j The decision value t under ij and positive ideal solution r + The jth value of The Hamming distance between Chi-square distance Trigonometric distance Hesitant fuzzy element in and Corresponding respectively and Then we get the hesitant fuzzy decision matrix

[0010] S4, D + Each hesitant fuzzy element in Arrange the values ​​in ascending order to obtain the sorted hesitant fuzzy decision matrix in correspond Then, S + Transformed into normal swing hesitant fuzzy decision matrix It is Type-2 triangular fuzzy information;

[0011] S5, to N + The original hesitant fuzzy information in The comprehensive hesitant fuzzy entropy method is used to determine the weight of each indicator and obtain the weight vector For N + Normal swing information in The weight of each indicator is determined according to the logarithmic percentage change driven target weighting method (LOPCOW), and the weight vector is obtained. Before using LOPCOW, the Type-2 triangular fuzzy information needs to be defuzzified; the final weight is w = 0.5w 1 +(1-0.5)w 2 =(w1,w2,...,w n );

[0012] S6, determine the negative ideal solution by R Use the same method as step 3 to obtain the hesitant fuzzy decision matrix Calculate D separately - The return value of each value and D + The loss value of each value in , thus obtaining the hesitant fuzzy decision matrix of the benefit value and loss value hesitant fuzzy decision matrix Then we get the prospect value hesitant fuzzy decision matrix P = (υ ij ) m×n ,υ ij =(V ij,1 ,V ij,2 ,V ij,3 );

[0013] S7, normalize P to obtain the normalized foreground value hesitant fuzzy decision matrix U = (u ij ) m×n ,u ij =(μ ij,1 ,μ ij,2 ,μ ij,3 ), each hesitant fuzzy element u in U ij The values ​​in are arranged in ascending order to obtain the sorted normalized foreground value hesitant fuzzy decision matrix Y=(y ij ) m×n ,y ij =(ζ ij,1 ,ζ ij,2 ,ζ ij,3 ), then the positive ideal solution is determined by Y

[0014] S8, convert Y into normal swing hesitant fuzzy decision matrix Q = ( <y ij ,ψ(y ij )>) m×n , y + Transformed into normal swing hesitant fuzzy sets

[0015] S9, calculate the solution A corresponding to each row in Q i (i=1,2,...,m) and q + The weighted correlation coefficient ρ between NWw2 (A i,q + );

[0016] S10, sort the solutions and select the best solution, ρ NWw2,i The larger it is, the better the solution.

[0017] Furthermore, the normalization formula described in step S2 is as follows:

[0018] If j∈Benefit-type indicator

[0019] If j∈cost type indicator

[0020] Furthermore, the Hamming distance calculation formula in step S3 is as follows:

[0021]

[0022] Among them, A and B represent hesitant fuzzy sets; h A,φ(k) (x j ) and h B,φ(k) (x j ) represent the hesitant fuzzy element h A (x j ) and h B (x j ) is the kth smallest element in ; #h represents the number of hesitant fuzzy element medians, and n represents the total number of evaluation indicators.

[0023] The chi-square distance calculation formula described in step S3 is as follows:

[0024]

[0025] Where p is a parameter and p≥1.

[0026] The trigonometric function distance calculation formula in step S3 is as follows:

[0027]

[0028] in, Indicates hesitant fuzzy element h A (x j ) in the kth smallest element h A,φ(k) (x j ) to hesitant fuzzy element h B (x j ) is the minimum Euclidean distance.

[0029] Furthermore, the process of converting to a normal swing hesitant fuzzy decision matrix in step S4 is as follows:

[0030] Definition 1 The normal swing hesitant fuzzy set on the domain X is expressed as follows:

[0031] NW={<x,h(x),ψ(h(x))> |x∈X}

[0032] Among them, h(x)=(γ1,γ2,...,γ #h ) is a hesitant fuzzy element in the hesitant fuzzy set H; ψ(h(x)) is the normal swing element corresponding to h(x), expressed as The specific expression is:

[0033]

[0034] in, is the wiggle function, the interval γ k The swing range; is the true preference of h(x). Their expressions are:

[0035]

[0036] in, and σ h are the mean and standard deviation of h(x) respectively, and the expressions are as follows; is the normalized hesitant fuzzy element of h(x), expressed as

[0037]

[0038] ψ(h(x)) is similar to a triangular fuzzy number. When the number of values ​​in the hesitant fuzzy element is 3, ψ(h(x)) can be regarded as a Type-2 triangular fuzzy number.<h(x),ψ(h(x))> is a normal swing hesitant fuzzy element, which is abbreviated as<h,ψ(h)> Therefore, before converting to normal swing hesitant fuzzy elements, the values ​​in the hesitant fuzzy elements need to be arranged in ascending order.

[0039] Furthermore, the comprehensive hesitant fuzzy entropy method described in step S5 is specifically as follows:

[0040] The expression of comprehensive hesitant fuzzy entropy is:

[0041]

[0042] Where h is a hesitant fuzzy element; ξ∈(0,1) is a balance parameter; θ(h) and η(h) are the fuzziness and unsharpness, respectively, and the calculation formula is:

[0043]

[0044] η(h)=|γ max -γ min |

[0045] Among them, #h represents the number of elements in h; γ k is the kth element in h;

[0046] The weight of indicator j is calculated as follows:

[0047]

[0048] Among them, E j is the average entropy of indicator j under all schemes, that is E(h ij ) is the comprehensive hesitant fuzzy entropy of indicator j under scheme i.

[0049] Furthermore, the LOPCOW method described in step S5 is specifically as follows:

[0050] First, based on the normalized matrix R, the percentage value PV of each indicator is calculated according to the following formula:

[0051]

[0052] Among them, σ j is the standard deviation of indicator j under all schemes.

[0053] Then, the weight of each indicator is calculated according to the following formula:

[0054]

[0055] Furthermore, the calculation formula for the gain and loss values ​​in step S6 is:

[0056]

[0057] Among them, Δx is the gap between the decision value and the reference point, Δx ≥ 0 indicates gain, Δx < 0 indicates loss, α and β represent the risk sensitivity coefficients of the decision maker when facing gain and loss, respectively, α, β∈(0,1); λ represents the decision maker's aversion to loss, λ>1, and the larger λ is, the more sensitive the decision maker is to loss.

[0058] Furthermore, the formula for calculating the foreground value in step S6 is:

[0059] V ij =v + (Δx ij )π + (p j )+v - (Δx ij )π - (p j )

[0060] Among them, π(p) is the probability weight function, and the calculation formula is as follows:

[0061]

[0062] Among them, p is the probability, that is, the attribute weight; χ and δ represent the bending parameters of the weight function when facing gains and losses. Studies have shown that χ = ​​0.61 and δ = 0.69 are appropriate.

[0063] Furthermore, the weighted correlation coefficient calculation formula in step S9 is as follows:

[0064]

[0065] Among them, C w (A, B) represents the weighted correlation between the normal oscillating hesitant fuzzy sets A and B; and They represent the hesitant fuzzy element h A (x j ) and h B (x j )’s mean; and They represent the normal swing element ψ(h A (x j )) and ψ(h B (x j The mean of )) is calculated as follows:

[0066]

[0067] The present invention also discloses a cascade reservoir optimization scheduling evaluation system based on the above-mentioned multi-attribute decision-making method, comprising:

[0068] The data acquisition module is used to collect initial evaluation index data for the cascade reservoir optimization scheduling plan, including power generation efficiency index, water abandonment control index, ecological flow satisfaction index and operation stability index, and construct the initial decision matrix;

[0069] Normalization processing module, which normalizes the initial matrix into benefit type or cost type according to the indicator type to generate a standardized decision matrix;

[0070] The positive and negative ideal solution analysis module calculates positive and negative ideal solutions based on the standardized matrix, and generates a hesitant fuzzy decision matrix through multi-dimensional distance measures (Hamming distance, chi-square distance, trigonometric function distance), which is further converted into a normal swing hesitant fuzzy decision matrix containing Type-2 triangular fuzzy swing information;

[0071] The weight fusion module uses the comprehensive hesitant fuzzy entropy method to extract the objective weight from the original hesitant fuzzy information, combines the LOPCOW target weighting method to defuzzify the swing information, and then calculates the objective weight, which is then fused to generate the comprehensive indicator weight;

[0072] The prospect decision module maps the negative ideal solution distance to the benefit value and the positive ideal solution distance to the loss value based on prospect theory. It calculates the prospect value of each solution through the risk sensitivity function and the probability weight function to generate a normalized prospect decision matrix.

[0073] The dynamic sorting module converts the prospect decision matrix into a normal swing hesitant fuzzy decision matrix, and converts the positive ideal solution into a normal swing hesitant fuzzy set. It calculates the correlation between each scheduling scheme and the dynamic positive ideal solution through weighted correlation coefficients, and outputs the real-time sorting results of the cascade reservoir optimization scheduling scheme. The sorting results are used to guide the power generation plan, ecological scheduling and risk control strategy of the reservoir group.

[0074] Compared with the prior art, the advantages of the present invention are:

[0075] 1. By constructing a normalized swing hesitant fuzzy set (NWHFS), this model combines traditional hesitant fuzzy elements (HFEs) with Type-2 triangular fuzzy swing information to simultaneously express both the explicit uncertainty (hesitant fuzziness) and the potential volatility (swing range) of decision values. Compared to a single fuzzy set, this model can more comprehensively capture the ambiguity, hesitation, and dynamic changes in complex decision scenarios, significantly improving the integrity of information representation.

[0076] Multidimensional distance measures such as Hamming distance, chi-square distance, and trigonometric function distance are used to construct a multidimensional hesitant fuzzy decision matrix to avoid the limitations of a single distance measure and enhance the sensitivity and discrimination to scheme differences.

[0077] 2. Combining two objective weights (fuzzy analysis based on hesitant fuzzy entropy and indicator discreteness quantification driven by the LOPCOW method), the inherent laws of data are fused through dynamic weighting to overcome the bias problem of traditional single weighting method and improve the scientific nature of weight distribution.

[0078] 3. Through the calculation of gain-loss values ​​and the probability weight function, the decision maker's risk preferences (such as loss aversion and increasing sensitivity) are embedded in the prospect value decision matrix, effectively simulating irrational decision-making behavior, making the evaluation results more in line with the actual decision-making psychology and avoiding the evaluation distortion caused by traditional rational assumptions.

[0079] 4. A ranking criterion based on the normal swing hesitant fuzzy weighted correlation coefficient is proposed. By calculating the correlation between each solution and the positive ideal solution, and considering the mean distribution (explicit feature) of the hesitant fuzzy information and the fluctuation range (potential uncertainty) of the swing information, the robustness and anti-interference ability of the solution comparison are significantly improved compared with the traditional Euclidean distance or similarity ranking.

[0080] 5. Through multi-stage data processing such as normalization, defuzzification, and dynamic threshold adjustment, it supports the efficient processing of mixed indicators (benefit / cost) and large-scale solution sets. It is suitable for complex decision-making scenarios such as energy scheduling, financial investment, and supply chain management that need to take into account multiple objective conflicts and uncertainties. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 This is a flow chart of the multi-attribute decision-making method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0082] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples.

[0083] like Figure 1 As shown, the present invention provides a multi-attribute decision-making method based on normal swing hesitant fuzzy information and prospect theory, comprising the following steps:

[0084] S1, m scheduling schemes A for the multi-attribute evaluation problem of optimal scheduling of cascade reservoirs i (i=1,2,…,m), n evaluation indicators C j (j=1,2,…,n), forming the initial decision matrix Z=(z ij ) m×n ;

[0085] S2, normalize Z to get the normalized decision matrix R = (r ij ) m×n ;

[0086] S3, positive ideal solution determined by R Calculation Plan A i In indicator C j The decision value r under ij and positive ideal solution r + The jth value of The Hamming distance between Chi-square distance Trigonometric distance Hesitant fuzzy element in and Corresponding respectively and Then we get the hesitant fuzzy decision matrix

[0087] S4, D + Each hesitant fuzzy element in Arrange the values ​​in ascending order to obtain the sorted hesitant fuzzy decision matrix in correspond Then, S + Transformed into normal swing hesitant fuzzy decision matrix

[0088] S5, for N + The original hesitant fuzzy information in The comprehensive hesitant fuzzy entropy method is used to determine the weight of each indicator and obtain the weight vector For N + Normal swing information in That is, Type-2 triangular fuzzy information, after defuzzification, the weight of each indicator is determined according to the logarithmic percentage change driven target weighting method (LOPCOW), and the weight vector is obtained. The final weight is w = 0.5w 1 +(1-0.5)w 2 =(w1,w2,...,w n );

[0089] S6, determine the negative ideal solution by R Use the same method as step 3 to obtain the hesitant fuzzy decision matrix Calculate D separately - The return value of each value and D + The loss value of each value in , thus obtaining the hesitant fuzzy decision matrix of the benefit value and loss value hesitant fuzzy decision matrix Then we get the prospect value hesitant fuzzy decision matrix P = (υ ij ) m×n ,υ ij =(V ij,1 ,V ij,2 ,V ij,3 );

[0090] S7, normalize P to obtain the normalized foreground value hesitant fuzzy decision matrix U = (u ij ) m×n ,u ij =(μ ij,1 ,μ ij,2 ,μ ij,3 ), each hesitant fuzzy element u in Uij The values ​​in are arranged in ascending order to obtain the sorted normalized foreground value hesitant fuzzy decision matrix Y=(y ij ) m×n ,y ij =(ζ ij,1 ,ζ ij,2 ,ζ ij,3 ), then the positive ideal solution is determined by Y

[0091] S8, convert Y into normal swing hesitant fuzzy decision matrix Q = ( <y ij ,ψ(y ij )>) m×n , y + Transformed into normal swing hesitant fuzzy sets

[0092] S9, calculate the solution A corresponding to each row in Q i (i=1,2,...,m) and q + The weighted correlation coefficient ρ between NWw2 (A i ,q + );

[0093] S10, sort the various plans and select the optimal scheduling plan, ρ NWw2,i The larger it is, the better the solution.

[0094] In this embodiment, the normalization formula in step S2 is as follows:

[0095] If j∈Benefit-type indicator

[0096] If j∈cost type indicator

[0097] In this embodiment, the Hamming distance calculation formula in step S3 is as follows:

[0098]

[0099] In this embodiment, the chi-square distance calculation formula in step S3 is as follows:

[0100]

[0101] Where p is a parameter and p≥1.

[0102] In this embodiment, the trigonometric function distance calculation formula in step S3 is as follows:

[0103]

[0104] In this embodiment, the process of converting the matrix into a normal swing hesitant fuzzy decision matrix in step S4 is as follows:

[0105]

[0106] in, is the wiggle function, the interval for The swing range; yes The true preference of . Their expressions are:

[0107]

[0108] in, and σ s They are The mean and standard deviation of are expressed as follows; for The normalized hesitant fuzzy element is expressed as

[0109]

[0110]

[0111] at this time, It can be regarded as a Type-2 triangular fuzzy number. Therefore, when converted to a normal swing hesitant fuzzy element Before, hesitant and vague The values ​​in need to be sorted in ascending order.

[0112] In this embodiment, the comprehensive hesitant fuzzy entropy method described in step S5 is specifically as follows:

[0113] The expression of comprehensive hesitant fuzzy entropy is:

[0114]

[0115] Among them, ξ∈(0,1) is the balance parameter; θ(h) and η(h) are blur and unsharpness respectively, and the calculation formula is:

[0116]

[0117] The weight of indicator j is calculated as follows:

[0118]

[0119] Among them, E j is the average entropy of indicator j under all schemes, that is

[0120] In this embodiment, the defuzzification formula in step S5 is as follows:

[0121]

[0122] In this embodiment, the LOPCOW method described in step S5 is specifically as follows:

[0123] First, for the defuzzified matrix, calculate the percentage value (PV) of each indicator according to the following formula:

[0124]

[0125] Among them, c ij is the defuzzified value corresponding to scheme i under index j; σ j is the standard deviation of indicator j under all schemes.

[0126] Then, the weight of each indicator is calculated according to the following formula:

[0127]

[0128] In this embodiment, the calculation formulas for the gain and loss values ​​in step S6 are:

[0129]

[0130] in, Indicates gain, = represents the risk of loss; α and β represent the decision maker's risk sensitivity to gains and losses, respectively, with α and β ∈ (0, 1); λ represents the decision maker's aversion to loss, with λ > 1, and a larger λ indicates a greater sensitivity to loss. After repeated verification, α = β = 0.88 and λ = 2.25 are the most appropriate values.

[0131] In this embodiment, the formula for calculating the foreground value in step S6 is:

[0132]

[0133] Among them, π(p) is the probability weight function, and the calculation formula is as follows:

[0134]

[0135] Among them, p is the probability, that is, the attribute weight; χ and δ represent the bending parameters of the weight function when facing gains and losses. Studies have shown that χ = ​​0.61 and δ = 0.69 are appropriate.

[0136] In this embodiment, the weighted correlation coefficient calculation formula in step S9 is as follows:

[0137]

[0138] Among them, C w (A i ,q) represents scheme A i The weighted correlation between and q; and Represent the hesitant fuzzy element y ij and The mean of and They represent the normal swing element ψ(y ij )and The mean is calculated as follows:

[0139]

[0140] Among them, y j is any hesitant fuzzy element; #y j is the number of hesitant fuzzy element medians; ψ(y j ) corresponds to y j The normal swing element of

[0141] Experiment: Taking the evaluation of the optimal scheduling scheme for the Three Gorges-Gezhouba cascade system in the middle and lower reaches of the Yangtze River as an example, the present invention was compared and analyzed with four classic multi-attribute decision-making methods and several of their variants to test the effectiveness of the present invention. The optimized scheduling results obtained by DE, PSO, AHA, EO, FDA, MS-ICHOA, and DP in a particularly dry year constitute the alternative solution set A1, A2, A3, A4, A5, A6, and A7. The total power generation, average output, minimum output ratio, total water abandonment, minimum ecological flow satisfaction, maximum ecological flow satisfaction, constraint risk, stability, and maximum water level change ratio constitute the evaluation index set C1, C2, C3, C4, C5, C6, C7, C8, and C9. Among them, C1, C2, C3, C5, and C7 are benefit-oriented indicators, while C4, C6, C8, and C9 are cost-oriented indicators. In addition, the calculation of C3, C5, C6, C7, C8, and C9 all takes the average value of the cascade power stations. The initial decision matrix Z is shown in Table 1. Through sensitivity analysis, the chi-square distance parameter p and the hesitant fuzzy entropy balance parameter ξ included in the present invention are 2.0 and 0.5 respectively. The weights obtained by the present invention are

[0142] w=(0.1258,0.1272,0.1042,0.1244,0.0899,0.0959,0.1127,0.0881,0.1318).

[0143] Table 1 Initial decision matrix Z

[0144]

[0145] Table 2 shows the evaluation results of the present invention and several classic decision-making methods, including the TOPSIS method, the Mahalanobis distance grey target decision based on correlation coefficient (GT-MDCC) method, the VIKOR method, and the grey correlation analysis method (GC). The weights of these comparison methods were determined using the MEREC method, namely w = (0.1886, 0.1886, 0.1886, 0.0144, 0.1886, 0.0142, 0.1886, 0.0143, 0.0142). As can be seen from Table 2, the rankings of the solutions determined by all methods are different. Among them, the TOPSIS method calculates the ranking of solutions based on the relative progress of each solution based on the Euclidean distance between each solution and the ideal solution. In addition to considering the Hamming distance between each solution and the ideal solution, the GC method also introduces the degree of correlation. VIKOR comprehensively ranks the solutions using the group utility value S, the individual regret value G, and the group benefit coefficient Q, increasing the reliability of the results. The GT-MDCC method replaces the Euclidean distance in the traditional grey target decision model with the Mahalanobis distance based on the correlation coefficient, taking into account the correlation between indicators. Therefore, theoretically speaking, the relationship between the comparison methods should be: GT-MDCC>VIKOR>GC>TOPSIS. The rankings of solution A6 obtained by them are 2, 2, 4, and 7, respectively, which are basically consistent with the order of excellence. However, these methods only use precise evaluation values ​​in both weight calculation and solution ranking, and assume that decision makers are completely rational. The present invention fully considers the uncertainty of evaluation information based on multiple distances between indicators, and also reflects the irrational psychological characteristics of decision makers. It is more in line with the actual decision-making process and can obtain more accurate weights and solution rankings. In addition, the ranking of solution A6 obtained by the present invention is 1, which indirectly proves the rationality and superiority of the invention.

[0146] Table 2 Comparison results between the present invention and several classic decision-making methods

[0147]

[0148] Table 3 shows the comparison results of the present invention and several of its variants. Here, Proposed method-1 represents the present invention using the MEREC method to determine the weights, and Proposed method-2 represents the present invention using the hesitant fuzzy decision matrix D - The values ​​in the hesitant fuzzy decision matrix D +The present invention uses the values ​​in the hesitant fuzzy decision matrix Y to replace the foreground values. Proposed method-3 represents the present invention, which uses the hesitant fuzzy weighted geometric operator (HFWG) to aggregate the information of each solution in the sorted normalized foreground value hesitant fuzzy decision matrix Y into hesitant fuzzy elements, and then ranks the solutions according to a scoring function. As shown in Table 3, the optimal solution obtained by Proposed method-1 and the present invention is A6, but the rankings of the other solutions are not exactly the same. Proposed method-2 and Proposed method-3 rank solution A6 3 and 4, respectively, indicating that the performance of the three variants is in a relationship of Proposed method-1 > Proposed method-2 > Proposed method-3. In other words, the weighted correlation coefficient ranking criterion between normal oscillating hesitant fuzzy sets has the greatest impact on the decision results, followed by prospect theory. The least influential method is the weight determination method based on normal oscillating hesitant fuzzy uncertainty information. Although Proposed method-1 also ranks solution A6 first, because its weight calculation process ignores uncertainty, the overall ranking of the solutions obtained is not as reasonable as that of the present invention, let alone the other two variants.

[0149] Table 3 Comparison results of the present invention and its several variants

[0150]

[0151] In summary, compared to several classic multi-attribute decision-making methods, the present invention can provide more accurate indicator weights and decision results for Three Gorges-Gezhouba cascade reservoir optimization operators, demonstrating superior performance. While the weighted correlation coefficient ranking criteria for normal swing hesitant fuzzy sets, prospect theory, and weight determination methods based on normal swing hesitant fuzzy uncertainty information employed in the present invention have different impacts on decision-making outcomes, it must be acknowledged that considering multiple uncertainty information and risk psychology factors in the evaluation method is essential, demonstrating that the present invention is a highly practical method for evaluating reservoir optimization scheduling plans.

[0152] In yet another embodiment of the present invention, a cascade reservoir optimization scheduling evaluation system based on the above-mentioned multi-attribute decision-making method is provided, comprising:

[0153] The data acquisition module is used to collect initial evaluation index data for the cascade reservoir optimization scheduling plan, including power generation efficiency index, water abandonment control index, ecological flow satisfaction index and operation stability index, and construct the initial decision matrix;

[0154] Normalization processing module, which normalizes the initial matrix into benefit type or cost type according to the indicator type to generate a standardized decision matrix;

[0155] The positive and negative ideal solution analysis module calculates positive and negative ideal solutions based on the standardized matrix, and generates a hesitant fuzzy decision matrix through multi-dimensional distance measures (Hamming distance, chi-square distance, trigonometric function distance), which is further converted into a normal swing hesitant fuzzy decision matrix containing Type-2 triangular fuzzy swing information;

[0156] The weight fusion module uses the comprehensive hesitant fuzzy entropy method to extract the objective weight from the original hesitant fuzzy information, combines the LOPCOW target weighting method to defuzzify the swing information, and then calculates the objective weight, which is then fused to generate the comprehensive indicator weight;

[0157] The prospect decision module maps the negative ideal solution distance to the benefit value and the positive ideal solution distance to the loss value based on prospect theory. It calculates the prospect value of each solution through the risk sensitivity function and the probability weight function to generate a normalized prospect decision matrix.

[0158] The dynamic sorting module converts the prospect decision matrix into a normal swing hesitant fuzzy decision matrix, and converts the positive ideal solution into a normal swing hesitant fuzzy set. It calculates the correlation between each scheduling scheme and the dynamic positive ideal solution through weighted correlation coefficients, and outputs the real-time sorting results of the cascade reservoir optimization scheduling scheme. The sorting results are used to guide the power generation plan, ecological scheduling and risk control strategy of the reservoir group.

[0159] In another embodiment of the present invention, a terminal device is provided, which includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of the multi-attribute decision-making method.

[0160] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device for storing programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and, of course, the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space. These instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory.

[0161] One or more instructions stored in a computer-readable storage medium may be loaded and executed by a processor to implement the corresponding steps of the multi-attribute decision-making method in the above embodiment; one or more instructions in the computer-readable storage medium may be loaded and executed by a processor.

[0162] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0163] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0164] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0165] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0166] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the implementation methods of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A multi-attribute decision-making method based on normal swing hesitant fuzzy information and prospect theory, characterized by: The steps include: S1, m alternatives A for multi-attribute decision-making problems i (i=1,2,…,m) and n evaluation indicators C j (j=1,2,…,n), forming the initial decision matrix Z=(z ij ) m×n ; S2, normalize Z to get the normalized decision matrix R = (r ij ) m×n ; S3, positive ideal solution determined by R Calculation Plan A i In indicator C j The decision value r under ij and positive ideal solution r + The jth value of The Hamming distance between Chi-square distance Trigonometric distance Hesitant fuzzy element in and Corresponding respectively and Then we get the hesitant fuzzy decision matrix S4, D + Each hesitant fuzzy element in Arrange the values ​​in ascending order to obtain the sorted hesitant fuzzy decision matrix in correspond Then, S + Transformed into normal swing hesitant fuzzy decision matrix It is Type-2 triangular fuzzy information; S5, to N + The original hesitant fuzzy information in The comprehensive hesitant fuzzy entropy method is used to determine the weight of each indicator and obtain the weight vector For N + Normal swing information in The weight of each indicator is determined according to the logarithmic percentage change driven target weighting method LOPCOW, and the weight vector is obtained Before using LOPCOW, the Type-2 triangular fuzzy information needs to be defuzzified; the final weight is w = 0.5w 1 +(1-0.5)w 2 =(w1,w2,...,w n ); S6, determine the negative ideal solution by R Obtain hesitant fuzzy decision matrix Calculate D separately - The return value of each value and D + The loss value of each value in , thus obtaining the hesitant fuzzy decision matrix of the benefit value and loss value hesitant fuzzy decision matrix Then we get the prospect value hesitant fuzzy decision matrix P = (υ ij ) m×n ,υ ij =(V ij,1 ,V ij,2 ,V ij,3 ); S7, normalize P to obtain the normalized foreground value hesitant fuzzy decision matrix U = (u ij ) m×n , μ ij =(μ ij,1 ,μ ij,2 ,μ ij,3 ), each hesitant fuzzy element u in U ij The values ​​in are arranged in ascending order to obtain the sorted normalized foreground value hesitant fuzzy decision matrix Y=(y ij ) m×n ,y ij =(ζ ij,1 ,ζ ij,2 ,ζ ij,3 ), then the positive ideal solution is determined by Y S8, convert Y into normal swing hesitant fuzzy decision matrix Q = ( <y ij ,ψ(y ij )>) m×n , y + Transformed into normal swing hesitant fuzzy sets S9, calculate the solution A corresponding to each row in Q i (i=1,2,...,m) and q + The weighted correlation coefficient ρ between NWw2 (A i ,q + ); S10, sort the solutions and select the best solution, ρ NWw2,i The larger it is, the better the solution.

2. The multi-attribute decision-making method according to claim 1, characterized in that: The normalization formula described in step S2 is as follows: Among them, z ij It represents the original evaluation value of the i-th alternative on the j-th evaluation index.

3. The multi-attribute decision-making method according to claim 2, wherein: The Hamming distance calculation formula described in step S3 is as follows: Among them, A and B represent hesitant fuzzy sets; h A,φ(k) (x j ) and h B,φ(k) (x j ) represent the hesitant fuzzy element h A (x j ) and h B (x j ) is the kth smallest element in the hesitant fuzzy element; #h represents the number of hesitant fuzzy element medians, and n represents the total number of evaluation indicators; The chi-square distance calculation formula described in step S3 is as follows: Where p is a parameter and p≥1; The trigonometric function distance calculation formula in step S3 is as follows: in, Indicates hesitant fuzzy element h A (x j ) in the kth smallest element h A,φ(k) (x j ) to hesitant fuzzy element h B (x j ) is the minimum Euclidean distance.

4. The multi-attribute decision-making method according to claim 3, characterized in that: The process of converting to a normal swing hesitant fuzzy decision matrix in step S4 is as follows: Definition 1 The normal swing hesitant fuzzy set on the domain X is expressed as follows: NW={<x,h(x),ψ(h(x))> |x∈X} Among them, h(x)=(γ1,γ2,...,γ #h ) is a hesitant fuzzy element in the hesitant fuzzy set H; ψ(h(x)) is the normal swing element corresponding to h(x), expressed as The specific expression is: in, is the wiggle function, the interval γ k The swing range; is the true preference of h(x), and their expressions are: in, and σ h are the mean and standard deviation of h(x) respectively, and the expressions are as follows; is the normalized hesitant fuzzy element of h(x), expressed as 5. The multi-attribute decision-making method according to claim 4, characterized in that: The comprehensive hesitant fuzzy entropy method described in step S5 is specifically as follows: The expression of comprehensive hesitant fuzzy entropy is: Where h is a hesitant fuzzy element; ξ∈(0,1) is a balance parameter; θ(h) and η(h) are the fuzziness and unsharpness, respectively, and the calculation formula is: η(h)=|γ max -c min | The weight of indicator j is calculated as follows: Among them, E j is the average entropy of indicator j under all schemes, that is E(h ij ) is the comprehensive hesitant fuzzy entropy of indicator j under scheme i.

6. The multi-attribute decision-making method according to claim 5, characterized in that: The LOPCOW method described in step S5 is specifically as follows: First, based on the normalized matrix R, the percentage value PV of each indicator is calculated according to the following formula: Among them, σ j is the standard deviation of indicator j under all schemes; Then, the weight of each indicator is calculated according to the following formula:

7. The multi-attribute decision-making method according to claim 6, characterized in that: The calculation formula for the gain and loss values ​​in step S6 is: Among them, Δx is the gap between the decision value and the reference point, Δx ≥ 0 indicates gain, Δx < 0 indicates loss, α and β represent the risk sensitivity coefficients of the decision maker when facing gain and loss, respectively, α, β∈(0,1); λ represents the decision maker's aversion to loss, λ>1, and the larger λ is, the more sensitive the decision maker is to loss.

8. The multi-attribute decision-making method according to claim 7, characterized in that: The formula for calculating the foreground value in step S6 is: In ij =in + (Δx ij )π + (p j )+v - (Δx ij )π - (p j ) Among them, π(p) is the probability weight function, and the calculation formula is as follows: Among them, p is the probability, that is, the attribute weight; χ and δ represent the bending parameters of the weight function when facing gains and losses. Studies have shown that χ = ​​0.61 and δ = 0.69 are appropriate.

9. The multi-attribute decision-making method according to claim 8, characterized in that: The weighted correlation coefficient calculation formula in step S9 is as follows: Among them, C w (A, B) represents the weighted correlation between the normal oscillating hesitant fuzzy sets A and B; and They represent the hesitant fuzzy element h A (x j ) and h B (x j )’s mean; and They represent the normal swing element ψ(h A (x j )) and ψ(h B (x j The mean of )) is calculated as follows:

10. A cascade reservoir optimization operation evaluation system based on the multi-attribute decision-making method according to any one of claims 1 to 9, characterized in that: include: The data acquisition module is used to collect initial evaluation index data for the cascade reservoir optimization scheduling plan, including power generation efficiency index, water abandonment control index, ecological flow satisfaction index and operation stability index, and construct the initial decision matrix; Normalization processing module, which normalizes the initial matrix into benefit type or cost type according to the indicator type to generate a standardized decision matrix; The positive and negative ideal solution analysis module calculates the positive and negative ideal solutions based on the normalized matrix, generates the hesitant fuzzy decision matrix through multi-dimensional distance measurement, and further converts it into a normal swing hesitant fuzzy decision matrix containing Type-2 triangular fuzzy swing information; The weight fusion module uses the comprehensive hesitant fuzzy entropy method to extract the objective weight from the original hesitant fuzzy information, combines the LOPCOW target weighting method to defuzzify the swing information, and then calculates the objective weight, which is then fused to generate the comprehensive indicator weight; The prospect decision module maps the negative ideal solution distance to the benefit value and the positive ideal solution distance to the loss value based on prospect theory. It calculates the prospect value of each solution through the risk sensitivity function and the probability weight function to generate a normalized prospect decision matrix. The dynamic sorting module converts the prospect decision matrix into a normal swing hesitant fuzzy decision matrix, and converts the positive ideal solution into a normal swing hesitant fuzzy set. It calculates the correlation between each scheduling scheme and the dynamic positive ideal solution through weighted correlation coefficients, and outputs the real-time sorting results of the cascade reservoir optimization scheduling scheme. The sorting results are used to guide the power generation plan, ecological scheduling and risk control strategy of the reservoir group.

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