Product form design multi-attribute decision-making method driven by crowd intelligence in cloud environment

Abstract

The invention relates to a crowd-driven product form design multi-attribute decision-making method in a cloud environment, which comprises the following steps of: performing quantitative calculation on qualitative product attributes by using a graduatory hesitant fuzzy set, and establishing a multi-attribute evaluation system of a product form design scheme; establishing a grey correlation coefficient decision matrix based on expert knowledge in the aspect of expert decision, and calculating the overall score of the basic alternative scheme by using a multi-criterion compromise solution sorting method and an improved osculation value method; in the aspect of user decision making, user weights are obtained by calculating the similarity between user evaluation matrixes, and product form scheme scores based on user preferences are calculated by adopting an approximate ideal solution sorting method; optimizing a product form design scheme by aggregating the expert evaluation value and the user preference value; the effectiveness and feasibility of the method are explained by application cases; according to the method, mass and multivariate crowd-sourcing individual advantages in the cloud platform are brought into play, and the public of different field backgrounds and roles are concentrated to participate in the decision of the product form design scheme, so that the comprehensiveness and accuracy of the decision are improved.

Description

Technical Field

[0001] This invention belongs to the field of multi-attribute decision-making technology for product form design, specifically relating to a multi-attribute decision-making method for product form design driven by collective intelligence in a cloud environment. Background Technology

[0002] The literature "Multi-attribute decision-making evaluation of product innovation design schemes considering customer needs and preferences" (Computer Integrated Manufacturing Systems, 2015, Vol. 21(02), pp. 417-426) discloses a multi-attribute decision-making evaluation method for product innovation design schemes considering customer needs and preferences. Based on the analysis of customer needs and preferences, this method proposes a method for determining the weights of evaluation indicators that integrates the Kano model and rough set theory, improving the rationality of indicator weight determination and effectively reflecting customer needs and preferences in the evaluation process. Considering the fuzziness and uncertainty of decision information in scheme evaluation, a grey relational analysis model for multi-attribute decision-making of product innovation design schemes based on rough number decision information processing is constructed. The optimal product innovation design scheme is achieved by incorporating the aforementioned indicator weights and calculating the rough number interval difference coefficients of each scheme. While the method described in the literature comprehensively considers user preferences and the fuzziness of user decision information, it does not consider the weights of users with different backgrounds or the hesitation of user decision information. Furthermore, this method only considers the user role when selecting decision-making members, resulting in a deficiency in global decision-making and an inability to make a relatively balanced choice. Summary of the Invention

[0003] To overcome the problems of a single decision-making body and low user participation in product form design decision-making in a cloud environment, this invention aims to provide a multi-attribute decision-making method for product form design driven by collective intelligence in a cloud environment. Based on the analysis of the collective intelligence service model for product form design in a cloud environment and the product form decision-making problem in a cloud environment, this method employs a multi-attribute decision-making approach that integrates expert knowledge and user preferences to optimize the product form design scheme that best balances expert and user satisfaction. First, it uses Pythagorean hesitant fuzzy sets to quantify qualitative product attributes and establish a multi-attribute evaluation system for product form design schemes. Second, in terms of expert decision-making, it establishes a gray relational coefficient decision matrix based on expert knowledge and calculates the overall score of the basic alternative schemes using a multi-criteria compromise solution ranking method and an improved closeness value method. In terms of user decision-making, it obtains user weights by calculating the similarity between user evaluation matrices and uses an approximation ideal solution ranking method to calculate the product form scheme score based on user preferences. Finally, it optimizes the product form design scheme by aggregating the expert evaluation values ​​and user preference values. Ultimately, this method broadens the scale of decision-making members and the sources of decision-making information, improving the objectivity and accuracy of the decision results, which is of great significance for the direction of product form design and the feasibility of improvement schemes.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A multi-attribute decision-making method for product form design driven by crowd intelligence in a cloud environment includes the following steps:

[0006] Step 1: Establish a multi-attribute evaluation system for product form design schemes based on Pythagorean hesitant fuzzy sets;

[0007] Step 2: Based on the multi-attribute evaluation system for product form design schemes established in Step 1, a calculation method for multi-attribute indicators of product form design decision is given, and qualitative product attributes are quantitatively calculated.

[0008] Step 3: Construct a product form solution decision model based on expert knowledge, establish a multi-attribute decision-making technology framework for product form design based on expert knowledge, and calculate the solution evaluation value based on expert knowledge according to expert evaluation.

[0009] Step 4: Construct a product form solution decision model based on user preferences, establish a multi-attribute decision-making technology framework for product form design based on user preferences, and calculate the solution evaluation value based on user preferences according to user evaluation.

[0010] Step 5, the collective intelligence solution selection method, makes a final decision by integrating solution evaluation values ​​based on expert knowledge and solution evaluation values ​​based on user preferences, and obtains the final solution evaluation value.

[0011] The specific steps for establishing a multi-attribute evaluation system for product form design based on Pythagorean hesitant fuzzy sets, as described in step 1, are as follows:

[0012] Based on the characteristics of product form design decisions, and considering the hesitancy and fuzziness of evaluators, a Pythagorean hesitant fuzzy set is used for evaluation to objectively describe the uncertainty and fuzziness of attributes and the relationships between attributes in product form design schemes. Its mathematical description is as follows:

[0013] Let X be a universe of discourse, and M be a Pythagorean hesitant module set on X:

[0014] M = { <x,Γ M (x),ψ M (x)>|x∈X} (1)

[0015] In equation (1), X is the set of all alternative product form designs, M is a Pythagorean hesitant fuzzy set on X, used to represent the fuzziness and uncertainty of a certain product form design x in the multi-attribute decision-making process, and Γ M (x) and Ψ M (x) are all non-empty finite sets on [0,1], Γ M(x) represents the membership degree of x to M, reflecting the degree to which the decision-maker believes that the product form design scheme x meets or exceeds the evaluation criteria in a certain attribute; ψ M (x) represents the non-membership degree of x belonging to M, reflecting the degree to which the decision-maker believes that the product form design scheme x does not meet or is inferior to the evaluation criteria in a certain attribute. Furthermore... μ M ∈Γ M (x), v M ∈ψ M (x), with μ M v M ∈[0,1],

[0016] The aforementioned method for calculating multi-attribute indicators for product form design decisions is developed collaboratively by domain experts and users in a cloud environment using the Pythagorean hesitant fuzzy number α=<Γ. α ,Ψ α The algorithm provides evaluations of each attribute of each alternative, and uses the Pythagorean hesitant fuzzy weighted geometric mean operator to aggregate the evaluation information from each attribute, calculating the final comprehensive score. The mathematical description is as follows:

[0017] Suppose there are m alternative solutions set P = {P1, P2, P3, ..., P...} m}, where n attributes are represented as F = {F1, F2, F3, ..., F}. n}, u sets of experts D = [D1, D2, D3, ..., D u ], q sets of user groups U = [U1, U2, U3, ..., U q Expert D u and user U q Scheme P is evaluated in the form of Pythagorean hesitant fuzzy numbers. i Corresponding attribute F j The satisfaction and dissatisfaction levels are evaluated and assigned values, denoted as α. ij =<Γ ij , ψ ij > and construct a Pythagorean hesitant fuzzy number decision expert individual evaluation matrix. and user individual evaluation matrix in and These represent the opinions of the u-th expert and the q-th user on solution P, respectively. i The value of the j-th attribute in the evaluation matrix is ​​used to obtain the normalized individual decision matrix after standardization of the evaluation matrix based on Pythagorean hesitant fuzzy sets. and By combining the Pythagorean hesitant fuzzy integration operator, the attributes of each scheme are integrated, and the score value of each attribute of the scheme is calculated by Equation (2).

[0018]

[0019]

[0020] The overall score for each attribute in the alternative options is:

[0021]

[0022] In equation (2): S α Let Γ be the score function of α, representing the comprehensive score of a certain attribute among the alternatives; α | and |ψ α | respectively represent Γ α , ψ α The number of elements in the attribute is derived from the ratings given by designers and users.

[0023] In a cloud environment, α1 and α2 represent the evaluation information of two different decision-makers. The Euclidean distance between α1 and α2 is:

[0024]

[0025] In equation (3), l(Γ) and l(Ψ) represent the number of elements in the membership set and the non-membership set, This represents the number of membership degrees in α1. This represents the number of membership degrees in α2. This represents the number of non-membership degrees in α1. Let l(∏) represent the number of non-membership degrees in α2, and l(∏) represent the number of elements in the hesitancy set. and Let α1 and α2 represent the degree of hesitation, respectively, and their calculation formulas are as follows:

[0026]

[0027] In equation (4), π α This indicates the degree of hesitation among decision-makers during the product form design process.

[0028] The product form solution decision model based on expert knowledge described in step 3 is implemented as follows:

[0029] By combining grey relational analysis, multi-criteria compromise solution ranking, and improved closeness value method, the decision-making process fully considers the correlation between the evaluation indicators of the alternatives and can intuitively express the closeness of the alternatives to the ideal solution, thus achieving multi-angle evaluation. The process provides an expert evaluation language based on Pythagorean hesitant fuzzy sets and converts it into specific numerical values ​​to construct a preliminary decision matrix. Then, grey relational analysis is introduced to construct a grey relational coefficient decision matrix, calculate the correlation weights of attributes, and quantify the differences and correlations between different alternatives. Finally, the multi-criteria compromise solution ranking and improved closeness value method are combined to calculate the solution evaluation value based on expert knowledge. The specific solution is as follows:

[0030] 1) Constructing an evaluation matrix for solutions based on expert knowledge

[0031] First, determine the set of alternative solutions P and the set of evaluation attributes F. Experts then evaluate each solution based on its actual performance across all attributes and using Pythagorean hesitation fuzzy numbers, constructing an m×n preliminary decision matrix C = (c ij ) m×n Secondly, the matrix is ​​standardized as follows:

[0032]

[0033]

[0034] In equations (5)-(6), C is the individual expert evaluation matrix; mn This represents the score given by an individual expert to the performance of solution m on attribute n; This is the standardized expert individual evaluation matrix; This refers to standardized individual expert evaluation information;

[0035] 2) Calculate the overall score of each attribute of the scheme.

[0036] By integrating the expert evaluation matrix C' using the Pythagorean hesitant fuzzy weighted geometric mean operator, the comprehensive score S of each attribute of the scheme is obtained by calculating it using equation (2). α ;

[0037] 3) Establish the grey relational coefficient decision matrix and determine the attribute weights.

[0038] For each attribute in the decision matrix, the grey relational coefficient between it and the ideal sequence C0 is calculated using grey relational analysis. All the calculated grey relational coefficients are used to form a new decision matrix, namely the grey relational coefficient decision matrix ξ. The correlation between each attribute is then calculated to obtain the importance of each attribute to the overall scheme and the degree of influence between attributes.

[0039]

[0040] In equation (7), and Let represent the positive and negative ideal solutions for the j-th attribute of the i-th scheme, respectively;

[0041]

[0042] In equation (8): ξ ij Let represent the grey relational coefficient between the j-th attribute of the i-th solution and the ideal solution; C0(j) is the j-th attribute value in the ideal solution; x(i,j) is the value of the i-th solution in the matrix with respect to the j-th attribute; ρ is the resolution coefficient, which is 0.5; min and maxmax represent the minimum and maximum operations that take all i and j values ​​respectively.

[0043]

[0044] In equation (9): ξ is the grey relational coefficient decision matrix, ξ mn It represents the grey relational coefficient between the nth attribute of the mth solution and the ideal solution.

[0045] The grey relational degree r of the attribute is:

[0046]

[0047] In equation (10), n is the number of attributes. After normalization, the weight w of the j-th attribute is... j for:

[0048]

[0049] 4) Obtain the evaluation value of the solution based on expert knowledge.

[0050] First, the group utility value S of each solution is determined using the multi-criteria compromise solution ranking method. i Individual Regret Value R i And the profit ratio value Q i Furthermore, the improved closeness value method is used to amplify the differences between the alternatives, allowing for a more accurate assessment of their merits. By combining the multi-criteria compromise solution ranking method and the improved closeness value method, a more comprehensive and balanced decision can be made.

[0051] ① Calculate the group utility value S i Individual Regret Value R i And the profit ratio value Q i

[0052]

[0053] In equation (12), v is the decision coefficient, taken as 0.5, and the benefit ratio value Q is used. iThe optimal solution is determined by measuring its closeness to the ideal solution, with the benefit ratio value Q. i The smaller the solution, the better;

[0054] ② Calculate the closeness value (OV) i

[0055]

[0056] In equations (13)-(15): This is the worst-case ideal solution in the virtual system. They are respectively and The weighted Euclidean distance; OV i The approximation value (OV) represents the approximation value of the product form factor. i Smaller solutions perform better;

[0057] ③ Aggregate evaluation value

[0058]

[0059] In equation (16), and The profit ratio value Q is respectively i And closeness value OV i The normalized value; λ is the distribution coefficient, taken as λ = 0.5.

[0060] Step 4, which describes the construction of a product form solution decision model based on user preferences, is specifically implemented as follows:

[0061] In the product form solution decision model based on user preferences, a user evaluation language based on Pythagorean hesitant fuzzy sets is given and converted into specific numerical values. The evaluation matrix based on user preferences is constructed using Pythagorean hesitant fuzzy sets. Then, the similarity between user evaluation decision matrices is calculated by Hamming distance to obtain the weights of different users, making the weight determination more scientific. Finally, the approximation ideal solution ranking method is introduced to calculate the closeness between the alternative solutions and the ideal solution to obtain the preference information value.

[0062] 1) Construct a solution evaluation matrix based on user preferences

[0063] User U q Based on the degree of preference for each attribute of the scheme, the scheme P is analyzed in the form of a Pythagorean hesitant fuzzy number. i Corresponding attribute F j Assign the value r ij Based on the given evaluation information, construct a user individual evaluation matrix R = (r ij ) m×n The standardized matrix is

[0064]

[0065]

[0066] In equations (17)-(18), R is the individual user evaluation matrix; r mn This represents the rating given by an individual user to the performance of solution m on attribute n; This is a standardized user individual evaluation matrix; This refers to standardized individual user evaluation information.

[0067] 2) Determine user weight

[0068] Because different users have different needs and priorities, conflicting evaluation information may arise, failing to accurately reflect user satisfaction. Therefore, the similarity of hesitant fuzzy Pythagorean matrices is used to calculate user weights. The Hamming distance is used to calculate the similarity (SIM) between user evaluation matrices to obtain the support (Sup) of a user's preference regarding other users. A higher similarity indicates greater support for the user, and greater support indicates more persuasive evaluation information from the corresponding user, i.e., user weight (γ). Therefore, a larger weight can be assigned to that user. The calculation formula is as follows:

[0069]

[0070] In equations (19)-(23), SIM(q,l) represents user U q and U l Evaluate the similarity between matrices. For fuzzy numbers and The similarity, also known as Hamming distance; w j Attribute weights; SIM is the similarity matrix of all users; Sup q User U q Support, Υ q User U q The weights;

[0071] 3) Calculate user preference values ​​for alternative options.

[0072] To comprehensively consider multiple attributes, an approximation-to-ideal-solution ranking method is introduced to take into account the scheme preference information value. Decisions are made based on the degree of closeness between the alternative scheme and the ideal scheme, which can well take into account the attribute values ​​of the scheme indicators.

[0073] ① The standardized decision matrix and user weights are aggregated to obtain the Pythagorean hesitation fuzzy weighted score of each attribute of the alternative solutions;

[0074] ②Based on the Pythagorean hesitant fuzzy distance mapping, the distances between each scheme and the positive and negative ideal schemes are calculated;

[0075]

[0076] In the formula: d + (P i ) and d - (P i These are schemes P and P respectively. i The distance to the positive and negative ideal solutions; and These represent the satisfaction and non-satisfaction of attribute j in the positive ideal solution, respectively. and w represents the satisfaction and non-satisfaction of attribute j in the negative ideal solution, respectively; j It is the weight of the attribute;

[0077] ③ The merits of each scheme are calculated by the ratio of the distances between each scheme and the positive and negative ideal schemes:

[0078]

[0079] In the formula: τ i The final score is based on user preferences; a higher value indicates that the solution is optimal.

[0080] The method for optimizing the collective intelligence solution described in step 5 is as follows:

[0081] To ensure that the decision-making results reflect both the objectivity of the expert group and the preferences of different user groups, a deviation minimization approach is used to integrate expert and user evaluation information for the final decision. The alternative solutions are then ranked based on their comprehensive scores to obtain the final optimal solution.

[0082]

[0083] In the formula, the candidate solutions are ranked according to the comprehensive score minη to obtain the final decision result. The larger the value of η, the more balanced the satisfaction of experts and users with the candidate solutions, which is the optimal solution.

[0084] The beneficial effects of this invention are:

[0085] This invention addresses the shortcomings of existing multi-attribute decision-making methods for product form design, which often fail to consider user subjective preferences and designers' objective evaluations. Furthermore, existing cloud-based multi-attribute decision-making methods for product form design lack research on hesitant and fuzzy evaluation information from different groups. This invention proposes a crowdsourcing decision-making method in a cloud environment that integrates user preferences and designers' professional knowledge. It introduces Pythagorean hesitant fuzzy sets to describe the evaluation information of both users and designers, resolving the uncertainty and fuzziness of evaluation information in the cloud environment and improving the objectivity of the decision results. Moreover, during the user decision-making process, user weights are obtained by considering the support level of user preferences, and similarity is directly obtained by calculating the distance between individual user evaluation matrices, avoiding information loss and making the decision results more accurate. Attached Figure Description

[0086] Figure 1 This is a flowchart of the method of the present invention.

[0087] Figure 2 This is a diagram of the intelligent service model for product form design in a cloud environment in the method of this invention.

[0088] Figure 3 This is a diagram illustrating alternative design schemes for a coffee machine, an application example of the method of this invention. Detailed Implementation

[0089] The present invention will now be described in detail with reference to specific embodiments.

[0090] See Figure 1 A multi-attribute decision-making method for product form design driven by collective intelligence in a cloud environment, which can also be seen as a multi-attribute decision-making method for product form that integrates expert knowledge and user preferences, includes the following steps:

[0091] Analyzing product form design and crowdsourced service models in a cloud environment

[0092] Cloud-based product form collaborative design refers to a collaborative innovation activity conducted under the new economic model, leveraging the open environment of the internet to attract and gather experts and the public from multiple disciplines through competition and cooperation. This involves building a cloud platform and attracting external resources through diverse incentive mechanisms, integrating and optimizing distributed public knowledge to obtain diverse problem-solving approaches and a large number of innovative product form design solutions. The participants in cloud-based product form design activities are no longer limited to professional designers; users, industry practitioners, experts from various fields, enterprises, and governments are all involved, reflecting the diverse and heterogeneous nature of the cloud environment. This asynchronous collaborative model also contributes to the innovation of design solutions, based on its service process.

[0093] This cloud-based product form design platform primarily provides product form design services. The platform virtually gathers design entities offering various design services within the cloud environment, centrally managing and controlling each entity. Simultaneously, based on the task requirements issued by the platform, each design entity leverages their individual experience to generate creative ideas, integrating attributes such as form, color, and materials to create diverse and differentiated product form solutions. Furthermore, by incorporating knowledge from multiple disciplines and roles, accurate and rational design decisions are made to arrive at the optimal solution. Throughout the entire design process, there is no need for communication between design entities, nor do they need to know the specific information of other members. The entire design process is handled by the cloud platform, which performs task decomposition, allocation, and scheduling, and provides feedback to the user on the final solution. (See [link to relevant documentation]). Figure 2 .

[0094] A multi-attribute evaluation system for product form design based on Pythagorean hesitant fuzzy sets;

[0095] In the actual product form design decision-making process, decision-makers are multidisciplinary and multi-role, and their psychological and personalized preferences are characterized by uncertainty and ambiguity. Although the evaluation process can remain objective and reasonable, the original evaluation data originates from the decision-makers' subjective experience, making it difficult to provide relatively accurate evaluation information for different scheme attributes. Therefore, based on the characteristics of product form collective design services in a cloud environment, and combined with the characteristics of decision-makers, the cloud service platform needs to establish a multi-attribute evaluation system for product form design.

[0096] This invention uses Pythagorean hesitant fuzzy sets for evaluation, which can more objectively describe the uncertainty and fuzziness of attributes and the relationships between attributes in product form design schemes. Its mathematical description is as follows:

[0097] Let X be a universe of discourse, and M be a Pythagorean hesitant module set on X:

[0098] M = { <x,Γ M (x),ψ M (x)>|x∈X} (1)

[0099] In equation (1), X is the set of all alternative product form designs, M is a Pythagorean hesitant fuzzy set on X, used to represent the fuzziness and uncertainty of a certain product form design x in the multi-attribute decision-making process, and Γ M (x) and Ψ M (x) are all non-empty finite sets on [0,1], Γ M (x) represents the membership degree of x to M, reflecting the degree to which the decision-maker believes that the product form design scheme x meets or exceeds the evaluation criteria in a certain attribute; ψ M(x) represents the non-membership degree of x belonging to M, reflecting the degree to which the decision-maker believes that the product form design scheme x does not meet or is inferior to the evaluation criteria in a certain attribute. Furthermore... μ M ∈Γ M (x), v M ∈ψ M (x), with μ M v M ∈[0,1],

[0100] The aforementioned method for calculating multi-attribute indicators for product form design decisions is developed collaboratively by domain experts and users in a cloud environment using the Pythagorean hesitant fuzzy number α=<Γ. α ,Ψ α The algorithm provides evaluations of each attribute of the alternative solutions and, based on the Pythagorean hesitant fuzzy weighted geometric mean operator, aggregates the evaluation information obtained from each attribute to calculate the final comprehensive score. Its mathematical description is as follows:

[0101] Suppose there are m alternative solutions set P = {P1, P2, P3, ..., P...} m}, where n attributes are represented as F = {F1, F2, F3, ..., F}. n}, u sets of experts D = [D1, D2, D3, ..., D u ], q sets of user groups U = [U1, U2, U3, ..., U q Expert D u and user U q Scheme P is evaluated in the form of Pythagorean hesitant fuzzy numbers. i Corresponding attribute F j The satisfaction and dissatisfaction levels are evaluated and assigned values, denoted as α. ij =<Γ ij , ψ ij > and construct a Pythagorean hesitant fuzzy number decision expert individual evaluation matrix. and user individual evaluation matrix in and These represent the opinions of the u-th expert and the q-th user on solution P, respectively. i The value of the j-th attribute in the evaluation matrix is ​​used to obtain the normalized individual decision matrix after standardization of the evaluation matrix based on Pythagorean hesitant fuzzy sets. and By combining the Pythagorean hesitant fuzzy integration operator, the attributes of each scheme are integrated, and the score value of each attribute of the scheme is calculated by Equation (2).

[0102]

[0103] The overall score for each attribute in the alternative options is:

[0104]

[0105] In equation (2): S α Let Γ be the score function of α, representing the comprehensive score of a certain attribute among the alternatives; α | and |ψ α | respectively represent Γ α , ψ α The number of elements in the attribute is derived from the ratings given by designers and users.

[0106] In a cloud environment, α1 and α2 represent the evaluation information of two different decision-makers. The Euclidean distance between α1 and α2 is:

[0107]

[0108] In equation (3), l(Γ) and l(Ψ) represent the number of elements in the membership set and the non-membership set, This represents the number of membership degrees in α1. This represents the number of membership degrees in α2. This represents the number of non-membership degrees in α1. Let l(∏) represent the number of non-membership degrees in α2, and l(∏) represent the number of elements in the hesitancy set. and Let α1 and α2 represent the degree of hesitation, respectively, and their calculation formulas are as follows:

[0109]

[0110] In equation (4), π α This indicates the degree of hesitation among decision-makers during the product form design process.

[0111] Step 3: Product form solution decision model based on expert knowledge;

[0112] In product form solution decision-making based on expert knowledge, combining grey relational analysis, multi-criteria compromise solution ranking, and improved closeness value method can fully consider the correlation between various evaluation indicators of alternative solutions and intuitively express the closeness of alternative solutions to the ideal solution, achieving multi-angle evaluation. Therefore, by converting expert evaluation language into specific numerical values ​​based on Pythagorean hesitant fuzzy logic to construct a preliminary decision matrix; then, grey relational analysis is introduced to construct a grey relational coefficient decision matrix to calculate the attribute weights considering the correlation, thereby quantifying the differences and correlations between different alternative solutions; finally, the multi-criteria compromise solution ranking and improved closeness value method are combined to calculate the solution evaluation value based on expert knowledge; the specific steps are as follows:

[0113] 1) Constructing an evaluation matrix for solutions based on expert knowledge

[0114] First, determine the set of alternative solutions P and the set of evaluation attributes F. Experts then evaluate each solution based on its actual performance across all attributes and using Pythagorean hesitation fuzzy numbers, constructing an m×n preliminary decision matrix C = (c ij ) m×n Secondly, the matrix is ​​standardized as follows:

[0115]

[0116] In equations (5)-(6), C is the individual expert evaluation matrix; mn This represents the score given by an individual expert to the performance of solution m on attribute n; This is the standardized expert individual evaluation matrix; This refers to standardized individual expert evaluation information;

[0117] 2) Calculate the overall score of each attribute of the scheme.

[0118] By integrating the expert evaluation matrix C' using the Pythagorean hesitant fuzzy weighted geometric mean operator, the comprehensive score S of each attribute of the scheme is obtained by calculating it using equation (2). α ;

[0119] 3) Establish the grey relational coefficient decision matrix and determine the attribute weights.

[0120] For each attribute in the decision matrix, the grey relational coefficient between it and the ideal sequence C0 is calculated using grey relational analysis. All the calculated grey relational coefficients are used to form a new decision matrix, namely the grey relational coefficient decision matrix ξ. The correlation between each attribute is then calculated to obtain the importance of each attribute to the overall scheme and the degree of influence between attributes.

[0121]

[0122] In equation (7), and Let represent the positive and negative ideal solutions for the j-th attribute of the i-th scheme, respectively;

[0123]

[0124] In equation (8): ξ ij Let represent the grey relational coefficient between the j-th attribute of the i-th solution and the ideal solution; C0(j) is the j-th attribute value in the ideal solution; x(i,j) is the value of the i-th solution in the matrix with respect to the j-th attribute; ρ is the resolution coefficient, which is 0.5; min and max represent the minimum and maximum operations that take all i and j values ​​respectively.

[0125]

[0126] In equation (9): ξ is the grey relational coefficient decision matrix, ξ mn It represents the grey relational coefficient between the nth attribute of the mth solution and the ideal solution.

[0127] The grey relational degree r of the attribute is:

[0128]

[0129] In equation (10), n is the number of attributes. After normalization, the weight w of the j-th attribute is... j for:

[0130]

[0131] 4) Obtain the evaluation value of the solution based on expert knowledge.

[0132] First, the group utility value S of each solution is determined using the multi-criteria compromise solution ranking method. i Individual Regret Value R i And the profit ratio value Q i Furthermore, the improved closeness value method is used to amplify the differences between the alternatives, allowing for a more accurate assessment of their merits. By combining the multi-criteria compromise solution ranking method and the improved closeness value method, a more comprehensive and balanced decision can be made.

[0133] ① Calculate the group utility value S i Individual Regret Value R i And the profit ratio value Q i

[0134]

[0135] In equation (12), v is the decision coefficient, taken as 0.5, and the benefit ratio value Q is used. i The optimal solution is determined by measuring its closeness to the ideal solution, with the benefit ratio value Q. i The smaller the scheme, the better [Wang Chengxiang, Han Feng & Liu Zelong. (2024). Research on the optimal scheme of high-speed railway to introduce railway hub based on cloud model. Journal of Railway Science and Engineering (06), 2131-2141];

[0136] ② Calculate the closeness value (OV) i

[0137]

[0138] In equations (13)-(15): This is the worst-case ideal solution in the virtual system. They are respectively and The weighted Euclidean distance; OV i The approximation value (OV) represents the approximation value of the product form factor. i The smaller the value, the better the performance [Yang Wenhai, Wang Lifang, Wang Kun, Zhao Lijuan. Application of improved close value method in water environment quality assessment [J]. Journal of Water Resources and Water Engineering, 2005, (02): 69-71+74];

[0139] ③ Aggregate evaluation value

[0140]

[0141] In equation (16), and The profit ratio value Q is respectively i And closeness value OV i The normalized value; λ is the distribution coefficient, taken as λ = 0.5.

[0142] Step 4, which describes the construction of a product form solution decision model based on user preferences, is specifically implemented as follows:

[0143] In the product form solution decision model based on user preferences, a user evaluation language based on Pythagorean hesitant fuzzy sets is given and converted into specific numerical values. The evaluation matrix based on user preferences is constructed using Pythagorean hesitant fuzzy sets. Then, the similarity between user evaluation decision matrices is calculated by Hamming distance to obtain the weights of different users, making the weight determination more scientific. Finally, the TOPSIS method is introduced to calculate the closeness between alternative solutions and ideal solutions to obtain preference information values.

[0144] 1) Construct a solution evaluation matrix based on user preferences

[0145] User U q Based on the degree of preference for each attribute of the scheme, the scheme P is analyzed in the form of a Pythagorean hesitant fuzzy number. i Corresponding attribute F j Assign the value r ij Based on the given evaluation information, construct a user individual evaluation matrix R = (r ij ) m×n The standardized matrix is

[0146]

[0147] In equations (17)-(18), R is the individual user evaluation matrix; r mn This represents the rating given by an individual user to the performance of solution m on attribute n; This is a standardized user individual evaluation matrix; This refers to standardized individual user evaluation information.

[0148] 2) Determine user weight

[0149] Because different users have different needs and priorities, conflicting evaluation information may arise, failing to accurately reflect user satisfaction. Therefore, the similarity of hesitant fuzzy Pythagorean matrices is used to calculate user weights. The Hamming distance is used to calculate the similarity (SIM) between user evaluation matrices to obtain the support (Sup) of a user's preference regarding other users. A higher similarity indicates greater support for the user, and greater support indicates more persuasive evaluation information from the corresponding user, i.e., user weight (γ). Therefore, a larger weight can be assigned to that user. The calculation formula is as follows:

[0150]

[0151]

[0152] In equations (19)-(23), SIM(q,l) represents user U q and U l Evaluate the similarity between matrices. For fuzzy numbers and The similarity, also known as Hamming distance; w j Attribute weights; SIM is the similarity matrix of all users; Sup q User U q Support, Υ q User U q The weights;

[0153] 3) Calculate user preference values ​​for alternative options.

[0154] To comprehensively consider multiple attributes, an approximation-to-ideal-solution ranking method is introduced to take into account the scheme preference information value. Decisions are made based on the degree of closeness between the alternative scheme and the ideal scheme, which can well take into account the attribute values ​​of the scheme indicators.

[0155] ① The standardized decision matrix and user weights are aggregated to obtain the Pythagorean hesitation fuzzy weighted score of each attribute of the alternative solutions;

[0156] ②Based on the Pythagorean hesitant fuzzy distance mapping, the distances between each scheme and the positive and negative ideal schemes are calculated;

[0157]

[0158] In the formula: d + (P i ) and d - (P i These are schemes P and P respectively.i The distance to the positive and negative ideal solutions; and These represent the satisfaction and non-satisfaction of attribute j in the positive ideal solution, respectively. and w represents the satisfaction and non-satisfaction of attribute j in the negative ideal solution, respectively; j It is the weight of the attribute;

[0159] ③ The merits of each scheme are calculated by the ratio of the distances between each scheme and the positive and negative ideal schemes:

[0160]

[0161] In the formula: τ i The final score is based on user preferences, with a larger value indicating the optimal solution [Wang Zhiyuan, Li Guodong & Wang Yonghua. (2017). Decision model for bridge design scheme optimization based on AHP-TOPSIS. Journal of Jilin University (Engineering Science) (02), 478-482].

[0162] Step 5, Crowdsourcing Solution Optimization Method

[0163] To ensure that the decision-making results reflect both the objectivity of the expert group and the preferences of different user groups, a deviation minimization approach is used to fuse expert and user evaluation information for the final decision.

[0164]

[0165] In the formula, the candidate solutions are ranked according to the comprehensive score minη to obtain the final decision result. The larger the value of η, the more balanced the satisfaction of experts and users with the candidate solutions, which is the optimal solution.

[0166] Example

[0167] This invention will use a coffee machine product form design scheme as an application case. In this case, the coffee machine manufacturer proposes product form design requirements. The entire case process simulates a cloud environment, using PCs to simulate decentralized decision-making members, each of whom completes the decision on the product form design scheme in a network-connected environment.

[0168] I. Construct a multi-attribute evaluation system for alternative solutions.

[0169] Based on the form design requirements proposed by the company, eight alternative design schemes P = [P1, P2, ..., P8] were obtained, such as... Figure 3 As shown. Based on the needs of enterprises, five evaluation attributes were determined, represented as F = [F1, F2, F3, F4, F5], representing form (F1), color (F2), material (F3), interactivity (F4), and ergonomics (F5), respectively.

[0170] Among these criteria, aesthetics are evaluated as follows: Aesthetics: This assesses whether each solution meets the user's requirements for simplicity, beauty, and style in appearance, and whether it integrates into modern home design; Color: This evaluates whether the color design of each solution enhances the overall aesthetic appeal of the product and whether it reflects the product's function and purpose (e.g., the use of indicator colors); Material: This evaluates whether the materials used in each solution are durable and whether the combination with surface treatment processes enhances the product's texture and quality; Interactivity: This evaluates whether the intuitive button layout, clear display screen, and user-friendly operation process allow users to easily make coffee; Ergonomics: This evaluates whether each solution conforms to user habits and is convenient to operate during use.

[0171] The expert decision-making group D and the user decision-making group U each have 10 members, denoted as D = [D1, D2, D3, ..., D...]. 10 and U=[U1, U2, U3,...,U 10 Based on the proposed multi-attribute decision-making method for product form design driven by collective intelligence, the above alternative solutions are optimized to select the product form design solution that best balances expert and user satisfaction.

[0172] II. Product form decision-making based on expert knowledge.

[0173] (1) The expert group uses the Pythagorean hesitant fuzzy number to evaluate and assign values ​​to the attributes corresponding to the alternative schemes using the 0-1 score value of the 11-level semantic information evaluation transformation, and constructs a hesitant Pythagorean fuzzy evaluation matrix based on the given decision information. Taking Scheme 1 as an example, it is shown in Table 2.

[0174] Table 2 Initial Matrix of Pythagorean Hesitation and Fuzziness Expert Evaluation

[0175]

[0176]

[0177] (2) Taking a single Pythagorean hesitant fuzzy number <(0.5,0.6)(0.3,0.4)> ​​as an example, it is standardized to <(0.5,0.55,0.6)(0.3,0.4)>, thus obtaining the entire standardized Pythagorean hesitant fuzzy expert evaluation matrix.

[0178] (1) Then, according to the Pythagorean hesitant fuzzy weighted geometric mean operator (1), the membership and non-membership of the expert evaluation of each attribute are aggregated to obtain the score function of each attribute.

[0179] Table 3. Attribute Scores of Each Alternative Solution Based on Expert Knowledge

[0180]

[0181] (2) The grey relation coefficients between each attribute in the expert decision matrix and the ideal solution are calculated according to equations (7)-(9), and the grey relation coefficient decision matrix is ​​formed.

[0182]

[0183] (3) The association weights of each scheme attribute are calculated according to formulas (10)-(11), as shown in Table 4.

[0184] Table 4. Association weights of attributes for each scheme

[0185]

[0186] (4) Calculate the group utility value S for each scheme according to equations (12)-(15). i Individual Regret Value R i Profit ratio Q i Closeness value OV i Finally, the comprehensive score of the scheme is obtained according to formula (16), as shown in Table 5.

[0187] Table 5. Overall Score of Solution Based on Expert Knowledge

[0188]

[0189]

[0190] III. Product form decision-making based on user preferences.

[0191] 1) Consistent with expert decision-making step (1), user evaluation information is collected and standardized. After obtaining the standardized evaluation matrix, the similarity between individual user evaluation matrices is calculated using equations (3)(4)(19)(20), resulting in the following user similarity matrix Sim:

[0192]

[0193] 2) Obtain the support level sup and user weight γ of each user through equations (22)-(23), as shown in Table 6-7.

[0194] Table 6 User Support

[0195]

[0196] Table 7 User Weights

[0197]

[0198] 3) Calculate the score function for each attribute by weighting the standardized decision matrix with the user weights:

[0199] Table 8. Attribute Scores of Each Alternative Solution Based on User Preferences

[0200]

[0201]

[0202] 4) Calculate the solution score τ based on user preferences according to equations (24)-(25):

[0203] Table 9: Overall Score of Solutions Based on User Preferences

[0204]

[0205] IV. Selection of the best collective intelligence solution.

[0206] 5) σ i After performing positive transformation, then σ i and τ i Normalization is performed, and the optimal function is obtained by minimizing the deviation. The values ​​were set to 0.52 for the expert and 0.42 for the user. The comprehensive score of the scheme was calculated according to formula (26), and the results are shown in Table 10.

[0207] Table 10: Overall Score of Product Form Design Scheme Driven by Collective Intelligence

[0208]

[0209] The final ranking of the schemes is: P6→P7→P8→P2→P4→P5→P3→P1, with P6 being the product form design scheme that best balances expert and user satisfaction.

Claims

1. A multi-attribute decision-making method for product form design driven by crowd intelligence in a cloud environment, characterized in that, Includes the following steps: Step 1: Establish a multi-attribute evaluation system for product form design schemes based on Pythagorean hesitant fuzzy sets; Step 2: Based on the multi-attribute evaluation system for product form design schemes established in Step 1, a calculation method for multi-attribute indicators of product form design decision is given, and qualitative product attributes are quantitatively calculated. Step 3: Construct a product form solution decision model based on expert knowledge, establish a multi-attribute decision-making technology framework for product form design based on expert knowledge, and calculate the solution evaluation value based on expert knowledge according to expert evaluation. Step 4: Construct a product form solution decision model based on user preferences, establish a multi-attribute decision-making technology framework for product form design based on user preferences, and calculate the solution evaluation value based on user preferences according to user evaluation. Step 5, the collective intelligence solution selection method, makes a final decision by integrating solution evaluation values ​​based on expert knowledge and solution evaluation values ​​based on user preferences, and obtains the final solution evaluation value.

2. The multi-attribute decision-making method for product form design driven by crowd intelligence in a cloud environment according to claim 1, characterized in that, The specific steps for establishing a multi-attribute evaluation system for product form design based on Pythagorean hesitant fuzzy sets, as described in step 1, are as follows: Based on the characteristics of product form design decisions, and considering the hesitancy and fuzziness of evaluators, a Pythagorean hesitant fuzzy set is used for evaluation to objectively describe the uncertainty and fuzziness of attributes and the relationships between attributes in product form design schemes. Its mathematical description is as follows: Let X be a universe of discourse, and M be a Pythagorean hesitant module set on X: M={<x,Γ M (x),ψ M (x)>|x∈X} (1) In equation (1), X is the set of all alternative product form designs, M is a Pythagorean hesitant fuzzy set on X, used to represent the fuzziness and uncertainty of a certain product form design x in the multi-attribute decision-making process, and Γ M (x) and Ψ M (x) are all non-empty finite sets on [0,1], Γ M (x) represents the membership degree of x to M, reflecting the degree to which the decision-maker believes that the product form design scheme x meets or exceeds the evaluation criteria in a certain attribute; ψ M (x) represents the non-membership degree of x belonging to M, reflecting the degree to which the decision-maker believes that the product form design scheme x does not meet or is inferior to the evaluation criteria in a certain attribute, and μ M ∈Γ M (x), v M ∈ψ M (x), with μ M v M ∈[0,1], 3. The multi-attribute decision-making method for product form design driven by crowd intelligence in a cloud environment according to claim 1, characterized in that, The aforementioned method for calculating multi-attribute indicators for product form design decisions is developed collaboratively by domain experts and users in a cloud environment using the Pythagorean hesitant fuzzy number α=<Γ. α ,Ψ α The algorithm provides evaluations of each attribute of each alternative, and uses the Pythagorean hesitant fuzzy weighted geometric mean operator to aggregate the evaluation information from each attribute, calculating the final comprehensive score. The mathematical description is as follows: Suppose there are m alternative solutions set P = {P1, P2, P3, ..., P...} m }, where n attributes are represented as F = {F1, F2, F3, ..., F}. n }, u sets of experts D = [D1, D2, D3, ..., D u ], q sets of user groups U = [U1, U2, U3, ..., U q Expert D u and user U q Scheme P is evaluated in the form of Pythagorean hesitant fuzzy numbers. i Corresponding attribute F j The satisfaction and dissatisfaction levels are evaluated and assigned values, denoted as α. ij =<Γ ij , ψ ij > and construct a Pythagorean hesitant fuzzy number decision expert individual evaluation matrix. and user individual evaluation matrix in and These represent the opinions of the u-th expert and the q-th user on solution P, respectively. i The value of the j-th attribute in the evaluation matrix is ​​used to obtain the normalized individual decision matrix after standardization of the evaluation matrix based on Pythagorean hesitant fuzzy sets. and By combining the Pythagorean hesitant fuzzy integration operator, the attributes of each scheme are integrated, and the score value of each attribute of the scheme is calculated by Equation (2). The overall score for each attribute in the alternative options is: In equation (2): S α Let Γ be the score function of α, representing the comprehensive score of a certain attribute among the alternatives; α | and |ψ α | respectively represent Γ α , ψ α The number of elements in the attribute is derived from the ratings given by designers and users. In a cloud environment, α1 and α2 represent the evaluation information of two different decision-makers. The Euclidean distance between α1 and α2 is: In equation (3), l(Γ) and l(Ψ) represent the number of elements in the membership set and the non-membership set, This represents the number of membership degrees in α1. This represents the number of membership degrees in α2. This represents the number of non-membership degrees in α1. Let l(∏) represent the number of non-membership degrees in α2, and l(∏) represent the number of elements in the hesitancy set. and Let α1 and α2 represent the degree of hesitation, respectively, and their calculation formulas are as follows: In equation (4), π α This indicates the degree of hesitation among decision-makers during the product form design process.

4. The multi-attribute decision-making method for product form design driven by crowd intelligence in a cloud environment according to claim 1, characterized in that, The product form solution decision model based on expert knowledge described in step 3 is implemented as follows: By combining grey relational analysis, multi-criteria compromise solution ranking, and improved closeness value method, the decision-making process can fully consider the correlation between the evaluation indicators of the alternatives and intuitively express the closeness between the alternatives and the ideal solution, thus achieving multi-angle evaluation. The process also provides an expert evaluation language based on Pythagorean hesitant fuzzy sets and converts it into specific numerical values ​​to construct a preliminary decision matrix. Then, the grey relational analysis method is introduced to construct the grey relational coefficient decision matrix, calculate the association weight of the attributes, and quantify the differences and correlations between different alternatives; finally, the multi-criteria compromise solution ranking method and the improved closeness value method are combined to calculate the evaluation value of the scheme based on expert knowledge. The specific solution is as follows: 1) Constructing an evaluation matrix for solutions based on expert knowledge First, determine the set of alternative solutions P and the set of evaluation attributes F. Experts then evaluate each solution based on its actual performance across all attributes and using Pythagorean hesitation fuzzy numbers, constructing an m×n preliminary decision matrix C = (c ij ) m×n Secondly, the matrix is ​​standardized as follows: In equations (5)-(6), C is the individual expert evaluation matrix; mn This represents the score given by an individual expert to the performance of solution m on attribute n; This is the standardized expert individual evaluation matrix; This refers to standardized individual expert evaluation information; 2) Calculate the overall score of each attribute of the scheme. By integrating the expert evaluation matrix C' using the Pythagorean hesitant fuzzy weighted geometric mean operator, the comprehensive score S of each attribute of the scheme is obtained by calculating it using equation (2). α ; 3) Establish the grey relational coefficient decision matrix and determine the attribute weights. For each attribute in the decision matrix, the grey relational coefficient between it and the ideal sequence C0 is calculated using grey relational analysis. All the calculated grey relational coefficients are used to form a new decision matrix, namely the grey relational coefficient decision matrix ξ. The correlation between each attribute is then calculated to obtain the importance of each attribute to the overall scheme and the degree of influence between attributes. In equation (7), and Let represent the positive and negative ideal solutions for the j-th attribute of the i-th scheme, respectively; In equation (8): ξ ij Let represent the grey relational coefficient between the j-th attribute of the i-th solution and the ideal solution; C0(j) is the j-th attribute value in the ideal solution; x(i,j) is the value of the i-th solution in the matrix with respect to the j-th attribute; ρ is the resolution coefficient, which is 0.5; min and maxmax represent the minimum and maximum operations that take all i and j values ​​respectively. In equation (9): ξ is the grey relational coefficient decision matrix, ξ mn This represents the grey relational coefficient between the nth attribute of the mth solution and the ideal solution. The grey relational degree r of the attribute is: In equation (10), n is the number of attributes. After normalization, the weight w of the j-th attribute is... j for: 4) Obtain the evaluation value of the solution based on expert knowledge. First, the group utility value S of each solution is determined using the multi-criteria compromise solution ranking method. i Individual Regret Value R i And the profit ratio value Q i Furthermore, the improved closeness value method is used to amplify the differences between the alternatives, allowing for a more accurate assessment of their merits. By combining the multi-criteria compromise solution ranking method and the improved closeness value method, a more comprehensive and balanced decision can be made. ① Calculate the group utility value S i Individual Regret Value R i And the profit ratio value Q i In equation (12), v is the decision coefficient, taken as 0.5, and the benefit ratio value Q is used. i The optimal solution is determined by measuring its closeness to the ideal solution, with the benefit ratio value Q. i The smaller the solution, the better; ② Calculate the closeness value (OV) i In equations (13)-(15): This is the worst-case ideal solution in the virtual system. They are respectively and The weighted Euclidean distance; OV i The approximation value (OV) represents the closeness of the product form factor. i Smaller solutions perform better; ③ Aggregate evaluation value In equation (16), and The profit ratio value Q is respectively i And closeness value OV i The normalized value; λ is the distribution coefficient, taken as λ = 0.

5.

5. The multi-attribute decision-making method for product form design driven by crowd intelligence in a cloud environment according to claim 1, characterized in that, Step 4, which describes the construction of a product form solution decision model based on user preferences, is specifically implemented as follows: In the product form solution decision model based on user preferences, a user evaluation language based on Pythagorean hesitant fuzzy sets is given and converted into specific numerical values. The evaluation matrix based on user preferences is constructed using Pythagorean hesitant fuzzy sets. Then, the similarity between user evaluation decision matrices is calculated by Hamming distance to obtain the weights of different users, making the weight determination more scientific. Finally, the approximation of the ideal solution ranking method is introduced to calculate the degree of closeness between the alternative solutions and the ideal solution, thereby obtaining the preference information value; 1) Construct a solution evaluation matrix based on user preferences User U q Based on the degree of preference for each attribute of the scheme, the scheme P is analyzed in the form of a Pythagorean hesitant fuzzy number. i Corresponding attribute F j Assign the value r ij Based on the given evaluation information, construct a user individual evaluation matrix R = (r ij ) m×n The standardized matrix is In equations (17)-(18), R is the individual user evaluation matrix; r mn This represents the rating given by an individual user to the performance of solution m on attribute n; This is a standardized user individual evaluation matrix; This refers to standardized individual user evaluation information. 2) Determine user weight Because different users have different needs and priorities, conflicting evaluation information may arise, failing to accurately reflect user satisfaction. Therefore, the similarity of hesitant fuzzy Pythagorean matrices is used to calculate user weights. The Hamming distance is used to calculate the similarity (SIM) between user evaluation matrices to obtain the support (Sup) of a user's preference regarding other users. A higher similarity indicates greater support for the user, and greater support indicates more persuasive evaluation information from the corresponding user, i.e., user weight (γ). Therefore, a larger weight can be assigned to that user. The calculation formula is as follows: In equations (19)-(23), SIM(q,l) represents user U q and U l Evaluate the similarity between matrices. For fuzzy numbers and The similarity, also known as Hamming distance; w j Attribute weights; SIM is the similarity matrix of all users; Sup q User U q Support, Υ q User U q The weights; 3) Calculate user preference values ​​for alternative options. To comprehensively consider multiple attributes, an approximation-to-ideal-solution ranking method is introduced to take into account the scheme preference information value. Decisions are made based on the degree of closeness between the alternative scheme and the ideal scheme, which can well take into account the attribute values ​​of the scheme indicators. ① The standardized decision matrix and user weights are aggregated to obtain the Pythagorean hesitation fuzzy weighted scores of each attribute of the alternative solutions; ②Based on the Pythagorean hesitant fuzzy distance mapping, the distances between each scheme and the positive and negative ideal schemes are calculated; In the formula: d + (P i ) and d - (P i These are schemes P and P respectively. i The distance to the positive and negative ideal solutions; and These represent the satisfaction and non-satisfaction of attribute j in the positive ideal solution, respectively. and w represent the satisfaction and non-satisfaction of attribute j in the negative ideal solution, respectively; j It is the weight of the attribute; ③ The merits of each scheme are calculated by the ratio of the distances between each scheme and the positive and negative ideal schemes: In the formula: τ i The final score is based on user preferences, with a higher value indicating the optimal solution.

6. The multi-attribute decision-making method for product form design driven by crowd intelligence in a cloud environment according to claim 1, characterized in that, The method for optimizing the collective intelligence solution described in step 5 is as follows: To ensure that the decision-making results reflect both the objectivity of the expert group and the preferences of different user groups, a deviation minimization approach is used to integrate expert and user evaluation information for the final decision. The alternative solutions are then ranked based on their comprehensive scores to obtain the final optimal solution. In the formula, the candidate solutions are ranked according to the comprehensive score minη to obtain the final decision result. The larger the value of η, the more balanced the satisfaction of experts and users with the candidate solutions, which is the optimal solution.

Images