Fuzzy comprehensive evaluation method based on digital signature

Abstract

The invention discloses a digital signature-based fuzzy comprehensive evaluation method, and aims to solve the problems of data security, score transparency and evaluation result fairness in a multi-expert evaluation process. The method comprises the following steps: determining an evaluation factor set and a weight thereof, scoring each evaluation factor by an expert, and encrypting and signing a scoring result through an RSA key. And the decision maker decrypts the score data through the private key and verifies the integrity and authenticity of the score. And finally, constructing a fuzzy evaluation matrix according to the scoring data, and carrying out weighted comprehensive evaluation to obtain a final evaluation result. According to the method, fuzzy comprehensive evaluation and digital signature technologies are combined, so that the security and privacy protection of the scoring data are ensured, the transparency and fairness of the evaluation process are improved, and the method is suitable for complex scenes of multi-factor and multi-expert evaluation.

Description

Technical Field

[0001] The invention relates to the field of digital signatures, and in particular to a fuzzy comprehensive evaluation method based on digital signatures. Background Art

[0002] In modern information processing technology, multi-factor evaluation and expert scoring methods have been widely used in different fields, such as educational examinations, corporate performance evaluation, project bidding, etc. However, such methods often face many challenges in practical application, especially in ensuring data security, transparency of the evaluation process, and the credibility and integrity of expert scoring. In order to solve these problems, many technical solutions have emerged in recent years, such as data processing methods combined with blockchain technology and fuzzy comprehensive evaluation methods.

[0003] Fuzzy Comprehensive Evaluation (FCE) is a classic multi-factor evaluation method that generates the final evaluation result by weighted comprehensive processing of multiple fuzzy factors. FCE has unique advantages in dealing with uncertainty and fuzzy information, so it is widely used in education, medical care, environmental assessment and other fields.

[0004] However, the traditional fuzzy comprehensive evaluation method still has the following shortcomings: offline scoring is costly and inefficient; online evaluation has poor data security, and expert scoring and evaluation data are easily leaked or tampered with during transmission and storage, resulting in the evaluation results losing fairness and security, and once a problem occurs, it is difficult to clarify the responsibility; the process lacks transparency, and the calculations in the evaluation process and the transparency of expert scoring are low, making it difficult to verify the authenticity of the scoring; the credibility of expert scoring is low. In traditional methods, expert scoring is easily affected by subjective factors, and there is no effective mechanism to verify the integrity of the scoring data. Summary of the invention

[0005] The purpose of the present invention is to provide a fuzzy comprehensive evaluation method based on digital signature to solve the problems raised by the above background technology in view of the defects of the prior art.

[0006] To achieve the above object, the present invention provides the following technical solution: a fuzzy comprehensive evaluation method based on digital signature, the method comprising the following steps:

[0007] S1: Determine the evaluation factor set and its weight; where the evaluation factor set U = {u1, u2, u3, u4} and the weight set W = {a1, a2, a3, a4};

[0008] S2: Establish a review set and conduct expert scoring of evaluation factors;

[0009] S3: Generate RSA keys, sign and encrypt expert scores;

[0010] S4: Send the encrypted data to the decision maker, who decrypts and verifies the data using the private key;

[0011] S5: Construct a fuzzy evaluation matrix based on the experts’ evaluation results and conduct a comprehensive evaluation of multiple factors.

[0012] As a technical preferred solution of the present invention, the comment set in step S2 specifically includes the following features:

[0013] The review set V consists of five predefined evaluation levels, i.e., V = {v1, v2, v3, v4, v5};

[0014] The evaluation level reflects the evaluation results of each evaluation factor, wherein v1 represents "good", v2 represents "better", v3 represents "average", v4 represents "poor", and v5 represents "bad";

[0015] Each evaluation grade is associated with a corresponding fuzzy membership value, which is used to indicate the degree of applicability of a grade to a specific evaluation factor;

[0016] The evaluation of the kth expert on the evaluation factor described in step S1 is m k =(d 1k ,d 2k ,d 3k ,d 4k ), where d ik represents the evaluation result of the kth expert on the i-th factor, d ik The calculation formula is:

[0017]

[0018] Wherein, K = {1, 2, ..., k} is the number set of experts.

[0019] As a technical preferred solution of the present invention, the RSA key generation in step S3 specifically includes the following steps:

[0020] S3-1: Each expert generates a pair of RSA keys, and the decision maker also generates a pair of RSA keys. The RSA keys include a public key and a private key. The private key of each expert is used to encrypt the generated hash value, and the public key is used to verify the signature.

[0021] S3-2: Select two large prime numbers p and q, calculate the modulus n = pq, and calculate the Euler function

[0022] S3-3: Randomly select an integer e, where (1<e<φ(n)), e satisfies the following conditions:

[0023] gcd(e,φ(n))=1

[0024] Among them, gcd(e,φ(n))=max{r|r divides both e andφ(n)},

[0025] r represents the largest integer that divides both e and φ(n);

[0026] S3-4: Solve the private key to d, where the public key is (n, e), p and q are secret parameters, and the private key calculation formula is as follows:

[0027]

[0028] The public key of the kth expert is (n k ,e k ), the corresponding private key is d k ; The decision maker's public key is (n,e), and the corresponding private key is d; mod is the modular operation, that is, the operation of finding the remainder.

[0029] As a technical preferred solution of the present invention, the signing in step S3 includes the following steps:

[0030] S3-5: Hash value generation, the evaluation result of each expert is message m k ∈Z n , the evaluation result m k Perform hash operation to generate message digest h(m k ), the hash operation specifically uses the standard SHA-256 algorithm;

[0031] S3-6: Signature generation, using the expert private key d to sign the message digest h(m k ) to encrypt and generate a digital signature s k , the signature calculation formula is:

[0032]

[0033] The evaluation result of each expert is message m k ∈Z n , where s k is the hash value h(m k )’s signature.

[0034] As a technical preferred solution of the present invention, the encryption in step S3 includes the following steps:

[0035] S3-7: Rating data grouping: evaluation results m k The grouping is a message group of length L (L<log2 n),

[0036] m k =m'1||m'2||...||m' i ;

[0037] S3-8: Encryption processing: Use the decision maker's public key (n, e) to encrypt each message block to generate ciphertext c i , the encryption formula is:

[0038]

[0039] Among them, c i is the ciphertext, m' i is the i-th message block, e is the public key exponent, and n is the modulus;

[0040] S3-9: Signature s k 、Ciphertext C k =c1c2…c t Transmitted to decision makers to form encrypted scoring data.

[0041] As a technical preferred solution of the present invention, the private key decryption and verification in step S4 includes the following steps:

[0042] S4-1: The decision maker receives the encrypted ciphertext C k =c1c2...c i After that, use your own private key d to decrypt the ciphertext. The decryption formula is:

[0043]

[0044] That is m' i ≡c i d modn;

[0045] Among them, m' i is the decrypted rating data, n is the modulus, and the evaluation result m is obtained by decrypting and connecting in sequence k =m'1||m'2||...||m' i ; The original evaluation result obtained by decryption is recorded as m' below;

[0046] S4-2: The decision maker receives the expert’s signature k Then, use the public key (n k ,e k ) to restore the signature, the restoration formula is:

[0047]

[0048] Among them, s is the digital signature, d k is the expert’s private key;

[0049] S4-3: Calculate the hash value of the original evaluation result m' obtained by decryption using the hash function used when signing, obtain the hash value h(m'), and compare it with the original hash value h(m) of the signature;

[0050] S4-4: If the theoretical original hash value h(m') and the real original hash value h(m) are the same, it proves that the data has not been tampered with and the verification passes; otherwise, the verification fails.

[0051] As a technical optimization scheme of the present invention, in step S5, a fuzzy evaluation matrix is ​​constructed according to the evaluation results of experts, and a multi-factor comprehensive evaluation is performed, which includes the following steps:

[0052] S5-1: Based on the expert scoring data, a fuzzy membership matrix is ​​constructed. For each evaluation factor, the evaluation level is mapped to its corresponding fuzzy membership value according to the expert's evaluation results. Each expert's score on the evaluation factor will be reflected in the fuzzy matrix in the form of membership.

[0053] S5-2: For a certain factor set U and the expert group's scoring result V, the following formula is used for calculation:

[0054] Assume that the expert group consists of 10 people, K = {1, 2, ..., k, ..., 10} is the number set of experts, and the evaluation of the evaluation factors in scheme 1 by the kth expert is m k =(d 1k ,d 2k ,d 3k ,d 4k ), where d ik represents the evaluation result of the kth expert on the i-th factor, and we record

[0055] Let c ij (i=1,2,3,4)(j=1,2,3,4,5) is in favor of the i-th factor u i (i=1,2,3,4) is the jth evaluation v j The number of votes, then from the above definition we know make

[0056] The single factor evaluation matrix can be obtained as follows:

[0057]

[0058] Among them, r ij It represents the membership degree of the i-th evaluation factor evaluated by the expert group at the j-th level;

[0059] S5-3: Combine the expert weight set W to perform fuzzy comprehensive evaluation. Use the fuzzy transformation model to perform weighted summation of the fuzzy matrix R and the weight set W to obtain the comprehensive evaluation vector:

[0060]

[0061] in, It is a comprehensive evaluation result vector, and each element represents the membership degree of each element in the evaluation set of the evaluation object.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] Data security and integrity are effectively guaranteed: by using RSA digital signature technology, each expert's scoring data is encrypted and signed to ensure the integrity and security of the scoring data during transmission and prevent data tampering and leakage. This mechanism significantly improves the reliability of the multi-expert evaluation method and avoids the risk of malicious data modification.

[0064] The security, transparency and fairness of the evaluation process are improved: Compared with the existing technology, the present invention ensures the non-tamperability of the scoring data and the authenticity of the scoring results through digital signature and encryption technology during the multi-expert scoring process. At the same time, the encryption and decryption mechanism in the evaluation process provides decision makers with the anti-leakage of the scoring data, ensuring that the entire evaluation process is more secure and confidential.

[0065] Combined with fuzzy comprehensive evaluation, the accuracy of evaluation results is improved: The present invention combines the fuzzy comprehensive evaluation method with the digital signature technology, which can effectively deal with the subjectivity and uncertainty in expert scoring. Through the fuzzy matrix and weighted calculation method, multiple evaluation factors are comprehensively evaluated to generate more accurate and reliable evaluation results. Compared with simple blockchain technology or other encryption methods, the present invention is more suitable for multi-dimensional complex evaluation methods.

[0066] Enhanced privacy protection of rating data: The expert rating data in the present invention is encrypted, and only the decision maker with the corresponding private key can decrypt the rating data, which ensures the privacy of the expert's personal rating. Compared with the openness and transparency in the existing technology, this feature further strengthens the protection of personal information and avoids the leakage of rating privacy.

[0067] Applicable to a variety of complex evaluation scenarios: Compared with the existing blockchain-based evaluation methods, this invention is not only applicable to test scoring methods, but can also be widely used in complex scenarios with multiple experts and multi-dimensional factors such as expert review, project evaluation, and performance appraisal. The combination of fuzzy comprehensive evaluation and digital signature makes this method more widely applicable and flexible.

[0068] The method has strong scalability and versatility: the present invention adopts the standard RSA encryption algorithm and fuzzy evaluation model, has strong scalability, can be seamlessly integrated with existing information methods and expert evaluation platforms, and can be easily adjusted according to different needs, thereby improving the practicability and versatility of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 A method flow chart of a fuzzy comprehensive evaluation method based on digital signature provided by the present invention;

[0070] Figure 2 A hash function anti-two-primitive property graph is provided for an embodiment of the present invention;

[0071] Figure 3 A comprehensive determination implementation flow chart of an embodiment of the present invention is provided. DETAILED DESCRIPTION

[0072] The present invention is further described below in conjunction with the accompanying drawings and examples. However, the present invention can be implemented in many different ways and should not be construed as being limited to the embodiments shown; on the contrary, these embodiments provide those skilled in the art with implementation methods that meet applicable legal requirements.

[0073] Example 1: Figure 1 As shown, this embodiment describes a fuzzy comprehensive evaluation method based on digital signature, which includes the following steps:

[0074] S1: Determine the evaluation factor set and its weight; where the evaluation factor set U = {u1, u2, u3, u4} and the weight set W = {a1, a2, a3, a4};

[0075] S2: Establish a review set and perform expert scoring on the evaluation factors; among which:

[0076] The review set V consists of five predefined evaluation levels, i.e., V = {v1, v2, v3, v4, v5};

[0077] The evaluation level reflects the evaluation results of each evaluation factor, wherein v1 represents "good", v2 represents "better", v3 represents "average", v4 represents "poor", and v5 represents "bad";

[0078] Each evaluation grade is associated with a corresponding fuzzy membership value, which is used to indicate the degree of applicability of a grade to a specific evaluation factor;

[0079] The evaluation of the kth expert on the evaluation factor described in step S1 is m k =(d 1k ,d 2k ,d 3k,d 4k ), where d ik represents the evaluation result of the kth expert on the i-th factor, d ik The calculation formula is:

[0080]

[0081] Where, K = {1, 2, ..., k} is the number set of experts;

[0082] S3: Generate RSA keys, sign and encrypt expert scores;

[0083] RSA key generation specifically includes the following steps:

[0084] S3-1: Each expert generates a pair of RSA keys, and the decision maker also generates a pair of RSA keys. The RSA keys include a public key and a private key. The private key of each expert is used to encrypt the generated hash value, and the public key is used to verify the signature.

[0085] S3-2: Select two large prime numbers p and q, calculate the modulus n = pq, and calculate the Euler function

[0086] S3-3: Randomly select an integer e, where (1<e<φ(n)), e satisfies the following conditions:

[0087] gcd(e,φ(n))=1

[0088] Among them, gcd(e,φ(n))=max{r∣r divides both e andφ(n)},

[0089] r represents the largest integer that divides both e and φ(n);

[0090] S3-4: Solve the private key to d, where the public key is (n, e), p and q are secret parameters, and the private key calculation formula is as follows:

[0091]

[0092] The public key of the kth expert is (n k ,e k ), the corresponding private key is d k ; The public key of the decision maker is (n,e), and the corresponding private key is d; mod is the modular operation, that is, finding the equivalence class;

[0093] Signing involves the following steps:

[0094] S3-5: Hash value generation, the evaluation result of each expert is message m k ∈Z n , the evaluation result mk Perform hash operation to generate message digest h(m k ), the hash operation specifically uses the standard SHA-256 algorithm;

[0095] S3-6: Signature generation, using the expert private key d to sign the message digest h(m k ) to encrypt and generate a digital signature s k , the signature calculation formula is:

[0096]

[0097] The evaluation result of each expert is message m k ∈Z n , where s k is the hash value h(m k )’s signature;

[0098] Encryption involves the following steps:

[0099] S3-7: Rating data grouping: evaluation results m k The grouping is a message group of length L (L<log2 n),

[0100] m k =m'1||m'2||...||m' i ;

[0101] S3-8: Encryption processing: Use the decision maker's public key (n, e) to encrypt each message block to generate ciphertext c i , the encryption formula is:

[0102]

[0103] Among them, c i is the ciphertext, m' i is the i-th message block, e is the public key exponent, and n is the modulus;

[0104] S3-9: Signature s k 、Ciphertext C k =c1c2…c t Transmitted to decision makers to form encrypted scoring data;

[0105] S4: Send the encrypted data to the decision maker, who decrypts and verifies the data using the private key;

[0106] Private key decryption and verification consists of the following steps:

[0107] S4-1: The decision maker receives the encrypted ciphertext C k =c1c2...c iAfter that, use your own private key d to decrypt the ciphertext. The decryption formula is:

[0108]

[0109] That is m' i ≡c i d modn;

[0110] Among them, m' i is the decrypted rating data, n is the modulus, and the evaluation result m is obtained by decrypting and connecting in sequence k =m'1||m'2||...||m' i ; The original evaluation result obtained by decryption is recorded as m' below;

[0111] S4-2: The decision maker receives the expert’s signature k Then, use the public key (n k ,e k ) to restore the signature, the restoration formula is:

[0112]

[0113] Among them, s is the digital signature, d k is the expert’s private key;

[0114] S4-3: Calculate the hash value of the original evaluation result m' obtained by decryption using the hash function used when signing, obtain the hash value h(m'), and compare it with the original hash value h(m) of the signature;

[0115] S4-4: If the theoretical original hash value h(m') and the real original hash value h(m) are the same, it proves that the data has not been tampered with and the verification passes; otherwise, the verification fails.

[0116] S5: Construct a fuzzy evaluation matrix based on the expert evaluation results and conduct a comprehensive evaluation of multiple factors;

[0117] The following steps are involved:

[0118] S5-1: Based on the expert's scoring data, a fuzzy membership matrix is ​​constructed. For each evaluation factor, the evaluation level is mapped to its corresponding fuzzy membership value according to the expert's evaluation results. Each expert's score on the evaluation factor will be reflected in the fuzzy matrix in the form of membership;

[0119] S5-2: For a certain factor set U and the expert group's scoring result V, the following formula is used for calculation:

[0120] Assume that the expert group consists of 10 people, K = {1, 2, ..., k, ..., 10} is the number set of experts, and the evaluation of the evaluation factors in scheme 1 by the kth expert is m k =(d 1k ,d 2k ,d 3k ,d 4k ), where d ik represents the evaluation result of the kth expert on the i-th factor, and we record

[0121] Let c ij (i=1,2,3,4)(j=1,2,3,4,5) is in favor of the i-th factor u i (i=1,2,3,4) is the jth evaluation v j The number of votes, then from the above definition we know make

[0122] The single factor evaluation matrix can be obtained as follows:

[0123]

[0124] Among them, r ij It represents the membership degree of the i-th evaluation factor evaluated by the expert group at the j-th level;

[0125] S5-3: Combine the expert weight set W to perform fuzzy comprehensive evaluation. Use the fuzzy transformation model to perform weighted summation of the fuzzy matrix R and the weight set W to obtain the comprehensive evaluation vector:

[0126]

[0127] in, It is a comprehensive evaluation result vector, and each element represents the membership degree of each element in the evaluation set of the evaluation object.

[0128] Among them, Figure 2 As shown, the hash function of the present invention has the following basic properties:

[0129] (1) Compression: H can compress information of any length or data blocks of any size and generate fixed-length output;

[0130] (2) Efficiency: For a message x of any length, the present invention can easily calculate H(x) using computer software;

[0131] (3) Anti-image property: it cannot be reversibly calculated. If the hash value h is known, it is very difficult to find x such that H(x) = h.

[0132] (4) Resistance to second preimage: Given H(x) = h, it is not feasible to find x' that satisfies x≠x' and H(x) = H(x');

[0133] (5) Anti-collision: It is not feasible to find two strings x, x' such that H(x) = H(x').

[0134] Example 2: Figure 3 As shown, in order to verify the effect of the present invention, a simulation experiment was conducted, and specific data was used to demonstrate the application process and effect of the fuzzy comprehensive evaluation method based on digital signature. This simulation example shows how to use the fuzzy comprehensive evaluation method to encrypt, sign, decrypt, and verify the evaluation results of multiple experts, and finally obtain a comprehensive evaluation result.

[0135] S1: Determine the evaluation factor set U and weight set W

[0136] Assume that the evaluation factor set U is U={u1,u2,u3,u4}, and determine the weight of each factor through expert scoring, market research or discussion of relevant departments. The present invention assumes that the weight set of these four indicators is W={0.2,0.3,0.3,0.2}.

[0137] S2: Determine the comment set V and make relevant evaluations

[0138] The comment set V includes five levels, namely V = {v1, v2, v3, v4, v5}, where v1 represents "good", v2 represents "better", v3 represents "average", v4 represents "poor", and v5 represents "poor". These levels are used to quantitatively evaluate the performance of various factors in different project plans. Assume that the expert group consists of 10 people, K = {1, 2, ..., k, ..., 10} is the numbered set of experts, and the evaluation of the evaluation factor in plan 1 by the kth expert is m. k =(d 1k ,d 2k ,d 3k ,d 4k ), where d ik It represents the evaluation result of the k-th expert on the i-th factor. Meanwhile, the present invention records:

[0139]

[0140] Table 1: Evaluation criteria for each factor

[0141]

[0142] As shown in Table 1, c ij (i=1,2,3,4)(j=1,2,3,4,5) is in favor of the i-th factor u i (i=1,2,3,4) is the jth evaluation vj The number of votes, then from the above definition, the present invention can know and

[0143] S3: RSA sign and encrypt the expert opinion

[0144] (1) RSA key generation

[0145] Each expert needs to generate a pair of RSA keys, and the decision maker also has a pair of keys, including a public key and a private key. The private key must be kept confidential and only known by the expert, while the public key must be made public so that the other party can obtain it when encrypting or signing the evaluation results.

[0146] Select two large prime numbers p and q, calculate n = pq, and calculate its Euler function at the same time Then randomly select an integer satisfy That is, the greatest common divisor is 1. Calculate d as follows:

[0147]

[0148] The public key is (n, e), and the private key is d, where p and q are secret parameters that need to be kept confidential. After calculating d, p and q can be directly decrypted. The present invention assumes that the public key of the kth expert is (n k ,e k ), the corresponding private key is d k ; The decision maker’s public key is (n,e) and the corresponding private key is d.

[0149] (2) Encryption algorithm and signature algorithm

[0150] Signature algorithm: record each expert’s evaluation result as message m k ∈Z n , select a secure Hash function h to evaluate the result m k Generate a message digest, i.e. a hash value h(m k ), the expert group calculates the signature using the following algorithm:

[0151]

[0152] Then k is the hash value h(m k )’s signature.

[0153] Encryption algorithm: Each expert needs to give his or her evaluation result m k To encrypt:

[0154] The evaluation results k The group is a message group of length L (L < log2 n), mk =m'1||m'2||...||m' i ;

[0155] Using the decision maker's public key (n,e) using an encryption algorithm Calculate the ciphertext:

[0156] C k =c1c2...c i

[0157] After the signature algorithm and encryption algorithm are completed, the signature s k 、Ciphertext C k Sent to decision makers.

[0158] S4: Decrypt ciphertext and verify signature algorithm

[0159] The decision maker receives the hash value signature s of the evaluation result k 、Ciphertext C k After that, the next step is to decrypt the ciphertext and verify the digital signature.

[0160] Decrypted ciphertext: The decision maker receives the ciphertext C k =c1c2...c i Then, use your own private key d to restore the plaintext packets m one by one i , the decryption algorithm is verified as follows: Knowing c i ≡m i e (modn)(1≤i≤t), then we can get the equation:

[0161]

[0162] That is m' i ≡c i d modn, the plaintext can be gradually restored using the decryption algorithm to obtain the original evaluation result.

[0163] Verify the signature: First, the present invention understands the RSA signature algorithm. The present invention assumes that (n', e') is the public key of the signer and d' is the private key of the signer. The signature algorithm process is:

[0164]

[0165] In other words, anyone who has the signer's public key can theoretically restore the signed object.

[0166] Therefore, the decision maker receives the hash value signature s from the expert k After decrypting the original text m, first use the expert's public key (n k ,e k) restore what was theoretically signed, that is, the theoretical original hash value h'(m), because at this time it is not certain whether the evaluation result has been tampered with on the way; then use the hash function used in the signature to calculate the hash value of the original evaluation result m, and get the real original hash value h(m), and compare the theoretical original hash value h'(m) and the real original hash value h(m) to see if they are the same. If they are the same, it proves that the signature is valid, and the restored evaluation result is the evaluation result sent by the experts at the beginning, and the data has not been tampered with on the way.

[0167] S5: Establish a single factor evaluation matrix

[0168] After verifying the validity of the signature, the decision makers can ensure the authenticity of the expert evaluation results during the transmission process. Next, the fuzzy matrix needs to be constructed based on the evaluation results. After statistics of the expert evaluation results, the present invention assumes that the evaluation results are shown in Table 2.

[0169] Table 2: Evaluation results

[0170]

[0171] From the above evaluation results, we can see The single factor evaluation matrix can be obtained:

[0172]

[0173] In the above process, the present invention has assumed that the evaluation factor weight set W = {0.2, 0.3, 0.3, 0.2}, and also obtained the fuzzy matrix, then the model M = (∧, ∨) is used to calculate the

[0174]

[0175]

[0176] So the result In actual problem solving, in order to make full use of the results brought by fuzzy comprehensive evaluation and decision-making, and for decision makers to make decisions more intuitively, the present invention generally normalizes the vector generated by the evaluation results, and quantifies the level of the evaluation factor set with a 1-point system, and performs weighted average on the evaluation results to obtain a more intuitive score to facilitate the selection of solutions. The review set V = {v1,v2,v3,v4,v5} can be quantified as V = (5,4,3,2,1) T , then the total score of the evaluation result can be calculated as Therefore, the final comprehensive evaluation score of Plan 1 is 3.45 points. The other plans are also evaluated in the same way. Each plan can calculate the final score. The decision maker will finally select the best plan to implement based on the score.

[0177] The above embodiments only express the implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention. It should be pointed out that, for those of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention.

Claims

1. A fuzzy comprehensive evaluation method based on digital signature, characterized by: The method comprises the following steps: S1: Determine the evaluation factor set and its weight; where the evaluation factor set U = {u1, u2, u3, u4} and the weight set W = {a1, a2, a3, a4}; S2: Establish a review set and conduct expert scoring of evaluation factors; S3: Generate RSA keys, sign and encrypt expert scores; S4: Send the encrypted data to the decision maker, who decrypts and verifies the data using the private key; S5: Construct a fuzzy evaluation matrix based on the experts’ evaluation results and conduct a comprehensive evaluation of multiple factors.

2. The fuzzy comprehensive evaluation method based on digital signature according to claim 1 is characterized in that: The comment set in step S2 specifically includes the following features: The review set V consists of five predefined evaluation levels, i.e., V = {v1, v2, v3, v4, v5}; The evaluation level reflects the evaluation results of each evaluation factor, wherein v1 represents "good", v2 represents "better", v3 represents "average", v4 represents "poor", and v5 represents "bad"; Each evaluation grade is associated with a corresponding fuzzy membership value, which is used to indicate the degree of applicability of a grade to a specific evaluation factor; The evaluation of the kth expert on the evaluation factor in step S1 is m k =(d 1k ,d 2k ,d 3k ,d 4k ), where d ik represents the evaluation result of the kth expert on the i-th factor, d ik The calculation formula is: Wherein, K = {1, 2, ..., k} is the number set of experts.

3. The fuzzy comprehensive evaluation method based on digital signature according to claim 1 is characterized in that: The RSA key generation in step S3 specifically includes the following steps: S3-1: Each expert generates a pair of RSA keys, and the decision maker also generates a pair of RSA keys. The RSA keys include a public key and a private key. The private key of each expert is used to encrypt the generated hash value, and the public key is used to verify the signature. S3-2: Select two large prime numbers p and q, calculate the modulus n = pq, and calculate the Euler function S3-3: Randomly select an integer e, where (1<e<φ(n)), e satisfies the following conditions: gcd(e,φ(n))=1; Among them, gcd(e,φ(n))=max{r∣r divides both e andφ(n)} r represents the largest integer that divides both e and φ(n); S3-4: Solve the private key d: where the public key is (n, e), p and q are secret parameters, and the private key calculation formula is as follows: The public key of the kth expert is (n k ,e k ), the corresponding private key is d k ; The decision maker’s public key is (n,e), and the corresponding private key is d; mod is the modular operation, that is, finding the equivalence class.

4. The fuzzy comprehensive evaluation method based on digital signature according to claim 1 is characterized in that: The signing in step S3 includes the following steps: S3-5: Hash value generation, the evaluation result of each expert is message m k , the evaluation result m k Perform hash operation to generate message digest h(m k ), the hash operation specifically uses the standard SHA-256 algorithm; S3-6: Signature generation, using the expert private key d to sign the message digest h(m k ) Signature, generate digital signatures k , the signature calculation formula is: The evaluation result of each expert is message m k , where s k is the hash value h(m k )’s signature.

5. The fuzzy comprehensive evaluation method based on digital signature according to claim 1 is characterized in that: The encryption in step S3 includes the following steps: S3-7: Rating data grouping: evaluation results m k The grouping is a message group of length L (L<log2 n), m k =m'1||m'2||...||m' i ; S3-8: Encryption processing: Use the decision maker's public key (n, e) to encrypt each message block to generate ciphertext c i , the encryption formula is: Among them, c i is the ciphertext, m' i is the i-th message block, e is the public key exponent, and n is the modulus; S3-9: Signature s k 、Ciphertext C k =c1c2…c t Transmitted to decision makers to form encrypted scoring data.

6. The fuzzy comprehensive evaluation method based on digital signature according to claim 1 is characterized in that: The private key decryption and verification in step S4 includes the following steps: S4-1: The decision maker receives the encrypted ciphertext C k =c1c2...c i After that, use your own private key d to decrypt the ciphertext. The decryption formula is: That is m' i ≡c i d mod n; Among them, m' i is the decrypted rating data, n is the modulus, and the evaluation result m is obtained by decrypting and connecting in sequence k =m'1||m'2||...||m' i ; The original evaluation result obtained by decryption is recorded as m' below; S4-2: The decision maker receives the expert’s signature k Then, use the public key (n k ,e k ) to restore the signature, the restoration formula is: Among them, s is the digital signature, d k is the expert’s private key; S4-3: Calculate the hash value of the original evaluation result m' obtained by decryption using the hash function used when signing, obtain the hash value h(m'), and compare it with the original hash value h(m) of the signature; S4-4: If the theoretical decrypted original hash value h(m') and the signed original hash value h(m) are the same, it proves that the data has not been tampered with and the verification passes; otherwise, the verification fails.

7. The fuzzy comprehensive evaluation method based on digital signature according to claim 1 is characterized in that: In step S5, a fuzzy evaluation matrix is ​​constructed based on the evaluation results of the experts, and the process of performing a multi-factor comprehensive evaluation includes the following steps: S5-1: Based on the expert's scoring data, a fuzzy membership matrix is ​​constructed. For each evaluation factor, the evaluation level is mapped to its corresponding fuzzy membership value according to the expert's evaluation results. Each expert's score on the evaluation factor will be reflected in the fuzzy matrix in the form of membership; S5-2: For a certain factor set U and the expert group's scoring result V, the following formula is used for calculation: Assume that the expert group consists of 10 people, K = {1, 2, ..., k, ..., 10} is the number set of experts, and the evaluation of the evaluation factors in scheme 1 by the kth expert is m k =(d 1k ,d 2k ,d 3k ,d 4k ), where d ik represents the evaluation result of the kth expert on the i-th factor, and records Let c ij (i=1,2,3,4)(j=1,2,3,4,5) is in favor of the i-th factor u i (i=1,2,3,4) is the jth evaluation v j The number of votes is known from the above definition. make The single factor evaluation matrix can be obtained as follows: Among them, r ij It represents the membership degree of the i-th evaluation factor evaluated by the expert group at the j-th level; S5-3: Combine the expert weight set W to perform fuzzy comprehensive evaluation. Use the fuzzy transformation model to perform weighted summation of the fuzzy matrix R and the weight set W to obtain the comprehensive evaluation vector: in, It is a comprehensive evaluation result vector, and each element represents the membership of the evaluation object to each element in the evaluation set.

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