Block chain consensus protocol selection method based on fuzzy multi-criterion decision

By constructing a probability language term set and using the VIKOR method, combining hierarchical analysis method and entropy weight method, the problem of processing non-numerical evaluation indicators in blockchain consensus protocol selection is solved, and a more accurate and direct protocol selection effect is achieved.

CN120128512APending Publication Date: 2025-06-10CHONGQING UNIV OF POSTS & TELECOMM
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Patent Information

Application Number
CN202510337196.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-03-21
Publication Date
2025-06-10

AI Technical Summary

Technical Problem

When choosing a blockchain consensus protocol, it is difficult to effectively deal with non-numerical evaluation indicators such as security and sustainability, and most of them use numerical multi-criteria decision-making frameworks, so these indicators cannot be accurately expressed.

Method used

The method based on fuzzy multi-criteria decision-making is adopted, and the weight of each standard is calculated by constructing a set of probabilistic language terms and using the VIKOR method, combining hierarchical analysis method and entropy weight method, and then protocol selection is made.

Benefits of technology

A broad consensus protocol evaluation framework that more directly reflects expert opinions is provided, solving the standard problem that cannot or should not be converted to numerical values, and achieving more accurate protocol selection.

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Abstract

The invention relates to the technical field of block chain consensus protocols, in particular to a block chain consensus protocol selection method based on fuzzy multi-criterion decision, which comprises the following steps: acquiring a target scene alternative protocol data set, and extracting key attributes of each alternative protocol scheme in the target scene alternative protocol data set; constructing a probability language term set according to the alternative protocol schemes and the key attributes thereof, constructing an evaluation matrix according to the probability language term set, and performing standardization processing; calculating the comprehensive weight of each key attribute by adopting a subjective and objective method; based on the comprehensive weight of the key attribute, processing by adopting a VIKOR method to obtain an alternative protocol scheme score; according to the invention, the alternative scheme can be accurately selected.
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Description

Technical Field

[0001] The present invention relates to the technical field of blockchain consensus protocols, and specifically relates to a method for selecting a blockchain consensus protocol based on fuzzy multi-criteria decision-making. Background Art

[0002] The blockchain consensus protocol is the core mechanism for multiple nodes in a distributed system to reach an agreement on transactions and block states, solving the problem of "decentralized trust". Currently, there are multiple consensus protocols, and their working principles are different, and thus there are also differences in terms of decentralization, security, and efficiency. It is very important to select an appropriate consensus protocol in different application scenarios, and the selection of the consensus protocol needs to be weighed according to specific requirements.

[0003] Multi-Criteria Decision Making (MCDM) is a method for dealing with complex decision-making problems. By quantifying multiple conflicting criteria (such as cost, benefit, risk, etc.), it helps decision-makers find the optimal solution among multiple alternative solutions. MCDM provides a structured analysis framework for the complex problem of consensus protocol selection. The TOPSIS method is a classical multi-attribute decision-making method proposed in 1981. The core idea of the TOPSIS method is to calculate the distances of each solution to the ideal solution and the negative ideal solution, and select the solution with the smallest distance to the ideal solution and the largest distance to the negative ideal solution. The VIKOR method is another commonly used multi-attribute decision-making method proposed in 1998. Different from the TOPSIS method, the VIKOR method emphasizes compromise selection, and obtains a comprehensive ranking by comprehensively considering the multi-attribute performance of each solution. However, in the current research on the selection of consensus protocols, most use numerical MCDM frameworks for evaluation, which is difficult to accurately express some evaluation indicators such as security and sustainability in numerical values. Summary of the Invention

[0004] To solve the above problems, the present invention provides a method for selecting a blockchain consensus protocol based on fuzzy multi-criteria decision-making, including the following steps:

[0005] S1. Collect the alternative protocol dataset for the target scenario, and extract the key attributes of each alternative protocol solution in the alternative protocol dataset for the target scenario;

[0006] S2. Construct a probabilistic linguistic term set according to the alternative protocol solutions and their key attributes, construct an evaluation matrix according to the probabilistic linguistic term set, and perform normalization processing;

[0007] S3. Based on the normalized evaluation matrix, use the subjective and objective method to calculate the comprehensive weight of each key attribute;

[0008] S4. Combine the standardized evaluation matrix and the comprehensive weights of the key attributes, and use the VIKOR method to process and obtain the scores of the alternative protocol solutions.

[0009] Advantages of the present invention:

[0010] The present invention combines the probabilistic linguistic term set and the VIKOR method to construct a generalized consensus protocol evaluation framework based on multi-criteria decision-making, improves the previous numerical-based calculation methods, provides a more direct reflection of expert opinions, and solves the criteria that cannot or should not be converted into numerical values.

[0011] In order to more accurately represent the weights of each criterion, we adopt the analytic hierarchy process and the entropy weight method. This method provides an accurate description of the weights of each criterion from both subjective and objective perspectives. Brief description of the drawings

[0012] Figure 1 It is a schematic diagram of the overall framework structure of the present invention;

[0013] Figure 2 It is a criterion diagram for the evaluation of the present invention. Detailed implementation manners

[0014] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0015] The present invention provides a method for selecting a blockchain consensus protocol based on fuzzy multi-criteria decision-making, as Figure 1 shown, including the following steps:

[0016] S1. Collect the alternative protocol data set for the target scenario, and extract the key attributes of each alternative protocol solution in the alternative protocol data set for the target scenario.

[0017] Specifically, in the embodiments of the present invention, according to the specific application scenario, research the consensus protocols that appear in various literature studies and open-source projects in similar scenarios, obtain the actual blockchain system data, and then obtain the alternative protocol data set for the target scenario. The alternative protocol data set for the target scenario contains multiple alternative protocol solutions, and each alternative protocol solution is the application data of a consensus protocol obtained from existing research in an actual blockchain system.

[0018] Specifically, when evaluating different consensus protocols, the selection of evaluation criteria is particularly important. The present invention designs from different perspectives as Figure 2The evaluation criteria shown extract nine key attributes for each alternative protocol solution in the alternative protocol dataset for the target scenario, including:

[0019] (1) From the perspective of throughput

[0020] Transaction volume (TPS): The number of transactions per second is used to measure the ability of the consensus protocol to process transactions within one second;

[0021] Transaction latency: The time required from submitting a transaction until the transaction is confirmed and verified as part of the ledger.

[0022] (2) From the perspective of decentralization

[0023] The number of consensus nodes: The number of participants involved in the consensus process;

[0024] The number of network nodes: Represents the number of nodes in the blockchain system.

[0025] (3) From the perspective of the incentive mechanism

[0026] Transaction fees: The cost incurred by nodes for submitting transactions to the ledger network;

[0027] Rewards: The total average daily monetary reward for all consensus nodes.

[0028] (4) From the perspective of sustainability

[0029] Power consumption: The resources such as electricity consumed by the consensus protocol in the blockchain system.

[0030] (5) From the perspective of security

[0031] 51% attack: Used to measure the vulnerability of the consensus protocol to attacks;

[0032] Double spending: Represents the situation where dishonest nodes attempt to spend their currency multiple times in a transaction.

[0033] S2. Construct a probabilistic linguistic term set based on the alternative protocol solution and its key attributes, construct an evaluation matrix according to the probabilistic linguistic term set, and perform normalization processing.

[0034] Specifically, a linguistic term set (LTS) is a set of discrete, non-numerical linguistic labels (such as {low, medium, high}, {bad, average, good, very good}), which is used to qualitatively express fuzzy semantics and is an abstraction of human subjective judgment. A probabilistic linguistic term set (PLTS) is a probabilistic extension of LTS, which assigns probability weights to each linguistic label to form a combination such as {s i (p i )} (such as {high(0.6), medium(0.3), low(0.1)}), which is used to quantify the uncertainty of semantics. In the present invention, a linguistic term set S t = {s 0 , s 1 , s 2 , …, s 2t} is defined, and each element in the linguistic term set S t is a quantitative representation of a term, where t represents the number of linguistic term sets. On this basis, a probabilistic linguistic term set L(p) = {L t (p (1) ), L (1) (p (2) ), …, L (2) (p (n) )} defined on the linguistic term set S (n) is defined, where n represents the number of terms included in the probabilistic linguistic term set L(p); L (1) , L (2) , …, L (n) correspond one by one to the parameters in the linguistic term set S t , and are also quantitative representations of a term; p (1) , p (2) , …, p (n) respectively represent the probability distributions of a term.

[0035] Specifically, terms such as "not good", "average", and "very good" can be defined, and then these terms are quantified to obtain S = {s 0 , s 1 , s 2}, where s 0 , s 1 , s 2 correspond to "not good", "average", and "very good" respectively. In the present invention, multiple alternative protocol schemes are evaluated on multiple key attributes. On this basis, the probabilistic linguistic term set of a certain alternative protocol scheme on a certain key attribute may be L(p) = {s 0 (0.2), s 1(0.8)}, Note that the sum of probabilities may not be equal to one, but all are greater than zero. An evaluation matrix is constructed based on the probability linguistic term sets of all alternative protocol solutions on all key attributes. Subsequent standardization is carried out. The main content of the standardization is as follows:

[0036] (1) Uniformly convert the attributes in the evaluation matrix into positivity.

[0037] Suppose there is a probability linguistic term set on S t ={s 0 ,s 1 ,s 2}, and t = 1. This probability linguistic term set is expressed as L(p) = {s 0 (0.3),s 1 (0.7)}, but this is a term set on a negative attribute (such as energy consumption, where s 2 represents high energy consumption), so it is necessary to convert it into data on a positive attribute. According to the conversion rule, other terms in the probability linguistic term set are all in accordance with this rule. After conversion, it is L(p) = {s 2 (0.3),s 1 (0.7)}.

[0038] (2) Order the data in the PLTS.

[0039] Suppose there is a probability linguistic term set L(p) = {s 0 (0.3),s 1 (0.7)}, and order it. The following rules are required: Sort in descending order, that is, the product of the term set subscript and the corresponding probability distribution. Then, after standardization, it is L(p) = {s 1 (0.7),s 0 (0.3)}.

[0040] (3) Unify the number of terms in all PLTS.

[0041] There are two probability linguistic term sets, L 1 (p) = {s 0 (0.3),s 1 (0.7)} and L 2 (p) = {s 0 (0.3),s 1 (0.6),s 2 (0.1)}, because the number of terms in these two probability linguistic term sets is different and distance calculation cannot be performed, so it is necessary to make L 1(p) Expand to three term sets according to the rule: First, order the probabilistic linguistic term set, then set the smaller one of them as the new term set, and the probability distribution is 0.

[0042] Then L 1 (p) = {s 1 (0.7), s 0 (0.3), S 0 (0.0)}.

[0043] S3. Use the subjective and objective method to assign weights to each key attribute.

[0044] Specifically, the existing weight calculation methods can be divided into three main types: subjective weight calculation method, objective weight calculation method, and comprehensive weight calculation method.

[0045] The subjective weight calculation method requires decision-makers (DMs) to have in-depth understanding of the decision problem and rich experience in specific issues. Therefore, usually a group of experts from related fields act as decision-makers. In this case, the commonly used method is the Analytic Hierarchy Process (AHP) to obtain weights.

[0046] The objective weight calculation method is only based on attribute data and derives weights by applying relevant mathematical techniques (such as the entropy method). The main advantage of this method is that the calculated weights do not depend on the opinions of decision-makers. However, the results may sometimes be inconsistent with the standard actual importance and may be affected by data.

[0047] The comprehensive weight calculation method combines subjective and objective weight calculations. It is not limited to expert opinions and also evaluates based on the actual performance data of the criteria.

[0048] Based on the above analysis, in order to effectively determine the weights of the criteria, the present invention uses a method that combines subjective and objective weight calculations, specifically including:

[0049] S31. Calculate the objective weights of each key attribute using PLTS fuzzy entropy.

[0050] Specifically, step S31 calculating the objective weights of each key attribute using PLTS fuzzy entropy includes:

[0051] S311. Construct a PLTS set according to the normalized evaluation matrix; specifically, take each element in the normalized evaluation matrix as a probabilistic linguistic term set, and form a PLTS set with all probabilistic linguistic term sets For processing multi-dimensional or multi-source fuzzy information. Among them:

[0052]

[0053] Among them, M represents the number of key attributes, and K represents the number of alternative protocol solutions. represents the combination of probability linguistic term sets corresponding to the m-th (m = 1, 2,..., M) key attribute, L k,m (p) represents the k-th (k = 1, 2,..., K) probability linguistic term set in represents L k,m (p) the i-th (i = 1, 2,..., n) k,m term, represents the corresponding probability distribution; n k,m represents the number of terms in L k,m (p); S312. Calculate the fuzzy entropy of each key attribute according to the PLTS set which is expressed as

[0054]

[0055] Among them, represents the PLTS fuzzy entropy of the m-th key attribute, and c(k, m) represents;

[0056] S313. Calculate the objective weight of each key attribute according to the PLTS fuzzy entropy, which is expressed as

[0057]

[0058] Among them, w m represents the objective weight of the m-th key attribute.

[0059] Specifically, if the probability linguistic term set only includes one term, that is, n k,m = 1, then

[0060]

[0061] If the probability linguistic term set includes multiple terms, that is, n k,m > 1, then

[0062]

[0063] Among them, is the subscript representation function, s t represents a linguistic term set, represents the difference between the sum of the probability distribution in the probability linguistic term set L k,m (p) and 1; cot() represents the trigonometric function. represents the subscript value of the corresponding term,

[0064] Based on the above content, assume that in the linguistic term set S1 = {s 0 , s 1 , s 2}}, there exists a probabilistic linguistic term set L 1,2 (p) = {s 0 (0.4), s 1 (0.3)}, then n 1,2 = 2, is 0.3, corresponds to the first term in L 1,2 (p), and the first term is s 0 , so it is the subscript representing this, so

[0065] S32. Use the Analytic Hierarchy Process (AHP) to calculate the subjective weight of each key attribute.

[0066] Specifically, the Analytic Hierarchy Process (AHP) is a systematic multi-criteria decision-making analysis method. It decomposes complex problems into multiple levels, combines qualitative and quantitative analysis, and helps decision-makers make rational choices under multiple objectives and criteria. The specific steps are as follows:

[0067] Construct a hierarchical structure, decompose the decision problem into multiple levels, including the goal level, criterion level, and alternative level; conduct pairwise comparisons, in each level, make pairwise comparisons for each criterion to evaluate their relative importance to the upper-level goal;

[0068] Construct a comparison matrix, based on the results of pairwise comparisons, construct a comparison matrix, and each element of the matrix represents the relative importance between two criteria;

[0069] Calculate the weights, calculate the weight vector of the comparison matrix through eigenvalue method or other methods to obtain the relative weights of each criterion;

[0070] Conduct a consistency test to ensure the rationality and consistency of the comparisons. If the consistency ratio (CR) exceeds a certain threshold, it is necessary to re-evaluate the pairwise comparisons;

[0071] Summarize the weights, sum up the weights of each criterion to obtain the final weight distribution.

[0072] S33. For each key attribute, sum and average its objective weight and subjective weight to obtain the comprehensive weight.

[0073] Specifically, use W, W o , W s to represent the comprehensive weight, objective weight, and subjective weight of a key attribute respectively, and the relationship among the three is

[0074]

[0075] S4. Based on the comprehensive weights of the key attributes, the VIKOR method is used to process and obtain the scores of the alternative protocol solutions.

[0076] Specifically, step S4 specifically includes:

[0077] S41. Construct a normalized decision matrix: The set of alternative protocol solutions A = {a 1 , a 2 , …, a K}, where a k represents the k-th (k = 1, 2, …, K) alternative protocol solution; the set of key attributes C = {c 1 , c 2 , …, c M}, where c m represents the m-th (m = 1, 2, …, M) key attribute; use the standardized evaluation matrix as the normalized decision matrix, and let the normalized decision matrix P’ = [p’ km K×M , where p’ km represents the normalized evaluation value of the alternative protocol solution k under the key attribute m, that is, the element in the k-th row and m-th column of the standardized evaluation matrix.

[0078] S42. According to the normalized decision matrix P’, determine the positive ideal solution and the negative ideal solution.

[0079] Specifically, the positive ideal solution The negative ideal solution

[0080] Among them, It represents the best normalized evaluation value of the key attribute c m ; It represents the worst normalized evaluation value of the key attribute c m .

[0081] S43. Calculate the group utility value and the individual regret value of each alternative protocol solution, expressed as

[0082]

[0083]

[0084] Among them, S k represents the group utility value of the k-th alternative protocol solution, R k represents the individual regret value of the k-th alternative protocol solution, w m ​denotes the comprehensive weight of the m-th key attribute, and ded(,) represents the Euclidean distance between two probabilistic linguistic membership sets.

[0085] Specifically,

[0086]

[0087] The objective function min i S i means finding a solution with the maximum group utility. The objective function min i R i represents minimizing the individual regret of the opponent. To find a compromise solution, we should minimize both of these objective functions simultaneously.

[0088] S45. Calculate the score of each alternative protocol solution, denoted as

[0089]

[0090] where Q k denotes the compromise value of the k-th alternative protocol solution, S + = min k S k , S - = max k S k ,, R + = min k R k , R - = max k R k , and v is the strategy weight representing group utility and individual regret. For convenience, it can be set to 0.5. The smaller Q k , the better the corresponding alternative solution performs.

[0091] S46. Arrange all alternative protocol solutions in ascending order according to the scores, and select the alternative protocol solution corresponding to the minimum score.

[0092] In one embodiment, according to Filatovas E, Marcozzi M, Mostarda L, et al. AMCDM-based framework for blockchain consensus protocol selection[J]. Expert Systems with Applications, 2022, 204: 117609, nine alternative protocol solutions, namely Nakamoto, Algorand, Tendermint, EOSIO, PoC, PoI, PoA probabilistic, SCP, and Tangle, are collected and represented by A 1 -A 9 For the nine key attributes of transaction volume, transaction latency, number of consensus nodes, number of network nodes, transaction fees, reward mechanism, energy consumption, 51% attack, and double spending, they are respectively represented by C 1 -C 9 The constructed evaluation matrix is shown in Table 1. Table 1 Evaluation Matrix

[0093]

[0094] In the embodiment of the present invention, seven terms are defined and represented by the linguistic term set S t ={s 0 , s 1 , s 2 , …, s 6}. By obtaining the probability distribution of each alternative protocol solution on each key attribute through the evaluation of multiple experts, multiple probability linguistic term sets are obtained. The data in each blank in Table 1 represents a probability linguistic term set.

[0095] The data normalization process is performed on the evaluation matrix, and the result is shown in Table 2.

[0096] Table 2 Normalized Evaluation Matrix

[0097]

[0098]

[0099] The data in each blank in Table 2 represents a normalized probability linguistic term set. In the embodiment of the present invention, the comprehensive weights calculated based on the data given in Table 2 are shown in Table 3.

[0100] Table 3 Comprehensive Weights

[0101]

[0102] The sorting results finally obtained by using the VIKOR method are shown in Table 4.

[0103] Table 4 Sorting Results

[0104]

[0105]

[0106] The numbers in the figure represent the ranking order numbers, and the smaller the number, the more worthy of selection.

[0107] In the present invention, unless otherwise clearly specified and defined, terms such as "installation", "setting", "connection", "fixation", "rotation", etc. shall be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or integrated; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the internal communication of two components or the interaction relationship between two components. Unless otherwise clearly defined, for those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0108] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A blockchain consensus protocol selection method based on fuzzy multi-criteria decision making, characterized in that: The following steps are involved: S1. Collect the target scenario alternative protocol data set, and extract the key attributes of each alternative protocol scheme in the target scenario alternative protocol data set; S2. Construct a probabilistic language term set based on the alternative protocol schemes and their key attributes, construct an evaluation matrix based on the probabilistic language term set and perform standardization; S3. Based on the standardized evaluation matrix, the comprehensive weight of each key attribute is calculated using subjective and objective methods; S4. Combining the standardized evaluation matrix and the comprehensive weights of key attributes, the VIKOR method is used to obtain the scores of alternative protocol options.

2. According to a method for selecting a blockchain consensus protocol based on fuzzy multi-criteria decision-making according to claim 1, it is characterized in that: For each alternative protocol scheme in the target scenario alternative protocol dataset, 9 key attributes are extracted, including transaction volume, transaction delay, number of consensus nodes, number of network nodes, transaction fees, reward mechanism, energy consumption, 51% attack and double payment.

3. According to a method for selecting a blockchain consensus protocol based on fuzzy multi-criteria decision-making according to claim 1, it is characterized in that: Step S3 specifically includes: S31. Use PLTS fuzzy entropy to calculate the objective weight of each key attribute; S32. Use the analytic hierarchy process to calculate the subjective weight of each key attribute; S33. For each key attribute, the objective weight and the subjective weight are summed and averaged to obtain the comprehensive weight.

4. According to a method for selecting a blockchain consensus protocol based on fuzzy multi-criteria decision-making according to claim 3, it is characterized in that: Step S31 uses PLTS fuzzy entropy to calculate the objective weight of each key attribute, including: S311. Construct PLTS set based on normalized evaluation matrix Among them, M represents the number of key attributes, K represents the number of alternative protocol solutions, represents the combination of probabilistic language term sets corresponding to the m=1, 2, …, M key attributes, L k,m (p) means The k-th = 1, 2, ..., K probabilistic language term sets in; Indicates L k,m (p) where i=1,2,…,n k,m term, express The corresponding probability distribution; n k,m Indicates L k,m The number of terms in (p); S312. According to PLTS collection Calculate the PLTS fuzzy entropy of each key attribute, expressed as in, The PLTS fuzzy entropy of the mth key attribute is represented by c(k,m); S313. Calculate the objective weight of each key attribute based on PLTS fuzzy entropy, expressed as Among them, w m Represents the objective weight of the mth key attribute.

5. According to a method for selecting a blockchain consensus protocol based on fuzzy multi-criteria decision-making according to claim 4, it is characterized in that: If the probability language term set contains only one term, that is, n k,m =1, then If the probability language term set includes multiple terms, that is, n k,m >1, then Among them, φ() is a subscript indicating a function, s t represents a language term set, Represents the probabilistic language term set L k,m (p) is the difference between the sum of the probability distribution and 1; cot() represents the trigonometric function, express The subscript value of the corresponding term, 6. According to a method for selecting a blockchain consensus protocol based on fuzzy multi-criteria decision-making according to claim 1, it is characterized in that: Step S4 specifically includes: S41. Construct a standardized decision matrix: Use the standardized evaluation matrix as the standardized decision matrix, and let the standardized decision matrix P'=[p' km ] K×M , p' km represents the standardized evaluation value of alternative protocol scheme k under key attribute m, that is, the element in the kth row and mth column in the standardized evaluation matrix; S42. According to the standardized decision matrix P', determine the positive ideal solution and the negative ideal solution; S43. Based on the positive ideal solution and the negative ideal solution, calculate the group utility value and individual regret value of each alternative protocol solution; S44. Calculate the score of each alternative protocol solution based on the group utility value and the individual regret value; S45. Arrange all the alternative protocol schemes in ascending order according to their scores, and select the alternative protocol scheme corresponding to the smallest score.

7. According to claim 6, a blockchain consensus protocol selection method based on fuzzy multi-criteria decision-making is characterized in that: The group utility value and individual regret value of each alternative protocol solution are calculated as Among them, S k represents the group utility value of the kth alternative protocol, R k represents the individual regret value of the kth alternative protocol solution, w m represents the comprehensive weight of the mth key attribute, ded(,) represents the Euclidean distance between two probability language sets, and its calculation formula is Among them, L 1,m (p) represents the k=1,2,…,Kth probabilistic language term set; Indicates i=1,2,…,n 1,m term, express The corresponding probability distribution; n 1,m Indicates L 1,m The number of terms in (p).

8. According to claim 6, a blockchain consensus protocol selection method based on fuzzy multi-criteria decision-making is characterized in that: Calculate the score of each alternative agreement solution, expressed as Among them, Q k represents the compromise value of the kth alternative protocol solution, S + =min k S k , S - =max k S k ,,R + =min k R k ,R - =max k R k , v is the strategy weight representing group utility and individual regret.