CN114996897B - Multi-attribute group ship anti-settling capacity evaluation decision method based on cloud model joint coefficient - Google Patents
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Abstract
The invention relates to the technical field of multi-attribute group decision-making methods, in particular to a multi-attribute group ship anti-settling capacity assessment decision-making method based on cloud model joint coefficients. Based on the cloud model joint coefficient, a novel multi-attribute group decision method based on the cloud model joint coefficient is provided. Finally, the method is applied to an evaluation example of the ship fire fighting capacity, and the practicability and the scientificity of the method are verified.
Description
Technical Field
The invention relates to the technical field of multi-attribute group decision-making methods, in particular to a multi-attribute group ship anti-settling capacity assessment decision-making method based on cloud model joint coefficients.
Background
The cloud theory is a theory for solving the coexistence problem of ambiguity and randomness, which is proposed by the Lideyi institute, forms the conversion between the qualitative concept and the quantitative representation thereof through a specially constructed algorithm, and reveals the inherent relevance of the ambiguity and the randomness. The cloud model consists of three numerical features (E) x ，E n ，H e ) Is expressed in which E x Is the central value of the concept in the domain of discourse and is the value that best represents this qualitative concept. Entropy E n Is a measure of qualitative conceptual ambiguity, reflecting what can be done in the theoretical domainThe range of values accepted for this concept. Hyper entropy H e I.e. the entropy E n The entropy of (a) reflects the degree of dispersion of cloud droplets. At present, the cloud model is widely applied to aspects such as comprehensive evaluation, system decision, data mining and the like.
Set-pair analysis is a systematic mathematical theory proposed in 1989 by Zhao Ke Li to deal with uncertain problems, wherein a joint coefficient is a main tool for set-pair analysis of uncertainty of processed things, and the system development is researched from the viewpoint of unity of determinism and uncertainty opposition. In recent years, researchers in many engineering and economic fields apply the joint coefficient method to multi-attribute decision in the field, and all the results are good. The construction of the joint coefficients and the sorting method of the joint coefficients are always an important direction in the research of the analytical theory. Wann et al, by constructing the degree of closeness of the joint coefficients, provide a interval number multiattribute decision method; the Liuxiu plum constructs a connection coefficient in the form of a + bi according to the obtained triangular fuzzy number, proposes the concept of a quadratic connection coefficient, and provides an interval number multi-attribute decision method based on the quadratic connection coefficient by the assignment change of i in the binary connection coefficient; the Wanwanjun gives a new interval number ordering method according to the concept of the potential in the joint coefficient.
With the rapid development of big data and corresponding computer technologies, group assessment and decision making on big data scale become possible. In the decision making process for dealing with practical problems, various uncertain and fuzzy information is often faced. The cloud theory is an effective theory which can well embody the group opinions under a large sample. The set pair analysis can well deal with the uncertainty of things through a dialectical method. The invention provides a quaternion joint coefficient construction method based on a cloud model on the theoretical basis of a cloud model and a set pair analysis joint coefficient, wherein the joint coefficient covers three digital characteristics (E) of the cloud model x ，E n ，H e ) Fuzzy information contained in the cloud model is expressed more completely, and a weighted arithmetic mean closeness of the four-element coefficient is given, and the definition meets three conditions of the closeness definition. Based on the cloud model joint coefficient, the multi-attribute group ship resistance based on the cloud model joint coefficient is providedAnd (4) a sinking capability evaluation decision method. The method can completely express the fuzzy information of the expert group under large data scale, and can make comprehensive judgment of the expert group through a set pair analysis middle connection coefficient tool.
Disclosure of Invention
Based on the technical problems in the background art, the invention provides a cloud model joint coefficient-based multi-attribute group ship anti-settling capacity assessment decision method, which can completely express fuzzy information of an expert group under large data scale and make comprehensive judgment of the expert group through a joint coefficient tool in pair analysis.
The invention provides the following technical scheme: the multi-attribute group ship anti-settling capacity assessment decision method based on the cloud model joint coefficient comprises the following steps:
s1, respectively scoring each scheme by an expert group according to a judgment index system and a judgment standard to give cloud drops, and generating cloud drops into a cloud model by using a reverse cloud generator to give characteristic numbers;
s2, constructing a quaternary coefficient of the cloud model generated by expert scoring to obtain a coefficient decision matrix;
s3, giving an ideal cloud model of each index in an index system by an expert, and constructing an ideal quadruple coefficient;
s4, respectively calculating the closeness of each scheme and the corresponding index of the ideal scheme by using a quadric-union coefficient closeness formula, and setting mu 1 ，μ 2 Is a quadruple coefficient, mu 1 ＝a 1 +b 1 i 1 +c 1 i 2 +d 1 i 3 ，μ 2 ＝a 2 +b 2 i 1 +c 2 i 2 +d 2 i 3 Wherein a is 1 +b 1 +c 1 +d 1 ＝1，a 2 +b 2 +c 2 +d 2 ＝1，i 1 ，i 2 ，i 3 ∈[-1，1]Definition of μ 1 ，μ 2 The closeness of (A) is:
T(μ 1 ，μ 2 )＝1-{w a ||a 1 -a 2 ||+w b ||b 1 -b 2 ||+w c ||c 1 -c 2 ||+w d ||d 1 -d 2 ||}
wherein w a ，w b ，w c ，w d The normalization weight of importance degree of identity and dissimilarity in the four-element coefficient in the comprehensive evaluation result, and w a +w b +w c +w d ＝1；
And calculating the total closeness T of each scheme and the ideal scheme according to the following formula jp ：
Wherein j =1,2, Λ M, M is total number of schemes, t is total number of evaluation indexes, w i Is the weight of each index, mu pi The four-element coefficient of each index of the ideal scheme;
s5, total closeness T of the pair scheme jp And sorting and outputting the optimal scheme.
Preferably, the inputs of the inverse cloud generator in step S1 are: the quantitative positions of N cloud drops in a number domain space, and the certainty that each cloud drop represents the concept; the output is: expectation E of a certain qualitative concept x Entropy E n And entropy H e 。
Preferably, the specific algorithm of the inverse cloud generator is as follows:
s11, according to the known cloud droplets, using a cloud expectation curve equation through a least square method
Fitting, directly obtaining
And
s12, removing points with y being larger than 0.999, and recording the number of the remaining cloud drops as m;
s13, according to
Find out
S14, according to standard deviation function
Find out
S15, outputting
I.e. the expected value E of a certain qualitative concept x Entropy E n And entropy H e 。
Preferably, the cloud model joint coefficient constructing step in step S2 is as follows:
s21, determining three digital characteristics of the cloud model (E) x ，E n ，H e )；
S22, passing
Corresponding abscissa values are processed, corresponding intervals of the cloud model reflecting fuzzy concepts are given, and an equation aiming at inner and outer envelope lines of the cloud model is given, namely
Calculate out
And the horizontal coordinate values corresponding to the time inner envelope line and the time outer envelope line are as follows:
the coordinate of the point D is x D ＝E x +3E n ；
S23, determining the quadruple coefficient mu = A 1 +B 1 i 1 +C 1 i 2 +D 1 i 3 Let i 1 ，i 2 ，i 3 ∈[-1，1]And wherein
After normalization is carried out by using the formula, the coefficient of the cloud model is obtained to be mu = a + bi 1 +ci 2 +di 3 ，i 1 ，i 2 ，i 3 ∈[-1，1]：
The invention provides a cloud model connection coefficient-based multi-attribute group ship anti-settling capacity assessment decision method, wherein the connection coefficient covers three digital characteristics of a cloud model, can completely express information judged by an expert group, and provides a weighted proximity definition of quaternary connection, so that the proximity is more objective and reasonable. Based on the cloud model joint coefficient, a novel multi-attribute group decision method based on the cloud model joint coefficient is provided. The method embodies the practicability and scientificity in the evaluation of the ship fire fighting capacity.
Drawings
Fig. 1 is a schematic diagram of a cloud model.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a technical scheme that: the cloud model joint coefficient-based multi-attribute group ship anti-settling capacity evaluation decision method comprises the following steps:
s1, respectively scoring each scheme by an expert group according to a judgment index system and a judgment standard, giving out cloud droplets, generating the cloud droplets into a cloud model by using a reverse cloud generator, and giving out characteristic numbers;
s2, constructing a quaternary coefficient of the cloud model generated by expert scoring to obtain a coefficient decision matrix;
s3, giving an ideal cloud model of each index in an index system by an expert, and constructing an ideal quadruple coefficient;
s4, respectively calculating the closeness of each scheme and the corresponding index of the ideal scheme by using a quadric-union coefficient closeness formula, and setting mu 1 ，μ 2 Is a quadruplex coefficient, mu 1 ＝a 1 +b 1 i 1 +c 1 i 2 +d 1 i 3 ，μ 2 ＝a 2 +b 2 i 1 +c 2 i 2 +d 2 i 3 Wherein a is 1 +b 1 +c 1 +d 1 ＝1，a 2 +b 2 +c 2 +d 2 ＝1，i 1 ，i 2 ，i 3 ∈[-1，1]Definition of μ 1 ，μ 2 The closeness of (A) is:
T(μ 1 ，μ 2 )＝1-{w a ||a 1 -a 2 ||+w b ||b 1 -b 2 ||+w c ||c 1 -c 2 ||+w d ||d 1 -d 2 ||}
wherein w a ，w b ，w c ，w d The normalization weight of importance degree of identity and dissimilarity in the four-element coefficient in the comprehensive evaluation result, and w a +w b +w c +w d ＝1；
And calculating the total closeness T of each scheme and the ideal scheme according to the following formula jp ：
Wherein j =1,2, Λ M, M is total number of schemes, t is total number of evaluation indexes, w i Is the weight of each index, mu pi The four-element coefficient of each index of the ideal scheme;
s5, total closeness T of the pair scheme jp And sorting and outputting the optimal scheme.
The cloud model is an uncertainty model for researching the interconversion between the qualitative concept and the quantitative representation of the natural language.
Let U be a quantitative universe of discourse U = { X } expressed in precise numerical values, C be the linguistic value associated with U, and the degree of membership μ of the element X in U to the qualitative concept expressed by C C (x) Is a random number with stable tendency, and the membership degree mu C (x) The distribution of U on the domain of discourse is called membership cloud, cloud for short, that is:
the normal cloud is the most important one of the cloud model styles and is most useful in expressing language values.
If the random variable x satisfies:
wherein
Degree of membership to qualitative concepts mu C (x) Satisfies the following conditions:
then the membership cloud of X on the domain is called normal cloud when E n Not equal to 0, then call
Is the expected curve of a normal cloud.
Since normal clouds satisfy the "3 σ rule" of normal distribution, more than 99.73% of the clouds of normal random number fall into the interval [ E ] x -3E n ，E x +3E n ]In this zone, ignoreCloud droplets outside the interval do not affect the overall characteristics of the cloud model.
The numerical characteristics of the attached clouds include the following meanings, respectively, in FIG. 1
(1) Centroid of area under membership cloud coverage
The corresponding discourse domain value reflects the information center value of the fuzzy concept;
(2) The bandwidth of the membership cloud expectation curve reflects the fuzzy degree of the fuzzy concept;
(3) Points on the membership cloud's expected curve
The variance of the corresponding membership degree random distribution, namely the super entropy H e Reflecting the degree of membership cloud dispersion.
A reverse cloud generator:
the inverse cloud generator is used for solving the cloud model according to the given cloud droplets (E) x ，E n ，H e ) Three numerical features. With respect to the algorithm of the inverse cloud generator, many scholars have given different ideas. Considering the data scale of multi-attribute group decision in practical problems, an adjusted reverse cloud generator algorithm is provided by combining the prior art:
inputting: the quantitative positions of N cloud droplets in the number domain space, and each cloud droplet represents the certainty of the concept.
And (3) outputting: expectation E of a certain qualitative concept x Entropy E n And entropy H e 。
The specific algorithm is as follows:
the first step is as follows: according to the known cloud droplets, using a cloud expectation curve equation by a least square method
Fitting, directly obtaining
And
the second step: points with y larger than 0.999 are removed, and the number of the remaining cloud drops is recorded as m;
the third step: according to
Find out
The fourth step: according to the standard deviation function
Find out
The fifth step: output of
I.e. the expected value E of a certain qualitative concept x Entropy E n And entropy H e 。
The coupling coefficient is as follows:
the joint coefficient is a characteristic function of the set pair and is also a main mathematical tool for set pair analysis, and has different expression forms, wherein the general form of the triple joint coefficient is as follows: μ = a + bi + cj, where a, b, c ∈ R, a + b + c =1, i ∈ [ -1,1], j = -1 (1)
If a + b + c ≠ 1, then equation (1) can be obtained after equation (2):
in the decision of the actual problem, the distribution of the identity and the dissimilarity can be determined according to the actual situation, so that various normalized connection coefficients, such as a quadruple connection coefficient, a quintuple connection coefficient and the like, can be generated.
Proximity:
closeness is a concept in fuzzy mathematics that is used to represent a measure of the degree of similarity between two fuzzy subsets.
Defining, setting A, B, C epsilon to F (U), if mapping
T：F(U)×F(U)→[0，1]
The conditions are satisfied:
(1)T(A，B)＝T(B，A)；
(2)T(A，A)＝1，T(U，φ)＝0；
(3) If it is
Then T (A, C) ≦ T (A, B) and T (A, C) ≦ T (B, C).
Let T (A, B) be the closeness of fuzzy sets A and B, and T be the closeness function on F (U)
According to the definition of the closeness of the fuzzy set, the following definition of the closeness of the quaternion coefficient is given by considering the importance degree of fuzzy information contained in the quaternion coefficient.
Definition, let u 1 ，μ 2 Is a quadruple coefficient, mu 1 ＝a 1 +b 1 i 1 +c 1 i 2 +d 1 i 3 ，μ 2 ＝a 2 +b 2 i 1 +c 2 i 2 +d 2 i 3 Wherein a is 1 +b 1 +c 1 +d 1 ＝1，a 2 +b 2 +c 2 +d 2 ＝1，i 1 ，i 2 ，i 3 ∈[-1，1]. Definition of mu 1 ，μ 2 The closeness of (A) is:
T(μ 1 ，μ 2 )＝1-{w a ||a 1 -a 2 ||+w b ||b 1 -b 2 ||+w c ||c 1 -c 2 ||+w d ||d 1 -d 2 ||}，
wherein w a ，w b ，w c ，w d Is a coefficient of quaternionThe degree of similarity and difference in the central data are normalized to the importance degree of the comprehensive evaluation result, and w a +w b +w c +w d ＝1。
Obviously, this definition satisfies three conditions of the proximity definition.
Example (b):
among the vessel damage control capabilities, the sink resistance of the vessel occupies an important position. The evaluation index of the anti-sinking capability of the ship comprises four aspects, namely cabin plugging capability, cabin supporting capability, cabin drainage capability and cabin balancing capability.
The organization expert group scores the anti-sinking capability of three ships and requires each expert to give an ideal anti-sinking capability state of the ships and each index of the actual three ships and gives scores and corresponding membership degrees. Applying a reverse cloud generator to generate a cloud model from cloud droplets given by an expert, wherein the obtained characteristic numbers are shown in table 1, wherein S0 is the number of a ship with ideal anti-sinking capability:
TABLE 1 Ship anti-sinking capability assessment cloud model characteristic number
And constructing a quaternary coefficient of the cloud model generated by expert scoring by using a cloud model coefficient construction method to obtain a coefficient decision matrix as follows:
setting the identity and three difference weights of the connection coefficient as w a ＝0.40，w b ＝0.30，w c ＝0.20，w d The weights of the four indexes of the anti-sinking capability of the ship are w = [0.27,0.21,0.28 and 0.24 ] respectively]Respectively calculating the closeness between the anti-sinking capability of the three ships and the ideal anti-sinking capability, which are respectively T 1 ＝0.026，T 2 ＝0.017，T 3 =0.021, which indicates that the sink resistance of the ship S1 is strongest, and the ship S has to be carried out for 2 timesThe ship S3 is relatively worst.
Quantitative analysis of uncertain information and fuzzy information is always an important research direction in information processing. Cloud theory and the collection both make great contributions to the analysis in this direction of research. The quantitative processing of uncertain information and fuzzy information in group decision determines the reasonability and scientificity of decision results. According to the cloud model and the theory of the joint coefficient of set pair analysis, the invention provides a quaternary joint coefficient construction method based on the cloud model, the joint coefficient covers three digital characteristics of the cloud model, the information for evaluation by an expert group can be expressed more completely, and a weighted proximity definition of quaternary joint is provided, so that the proximity is more objective and more reasonable. Based on the cloud model joint coefficient, a novel multi-attribute group decision method based on the cloud model joint coefficient is provided. The method embodies the practicability and scientificity of the method in the evaluation of the ship fire fighting capacity.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered as the technical solutions and the inventive concepts of the present invention within the technical scope of the present invention.
Claims (3)
1. A multi-attribute group ship anti-settling capacity assessment decision method based on cloud model joint coefficients is characterized by comprising the following steps: the method comprises the following steps:
s1, respectively scoring each scheme by an expert group according to a ship anti-settling capacity evaluation index system and an evaluation standard, giving cloud droplets, generating the cloud droplets into a cloud model by using a reverse cloud generator, and giving characteristic numbers, wherein evaluation indexes of ship anti-settling capacity comprise four aspects, namely cabin leakage blocking capacity, cabin supporting capacity, cabin drainage capacity and cabin balance capacity;
s2, constructing a quaternary coefficient of the cloud model generated by expert scoring to obtain a coefficient decision matrix;
the cloud model joint coefficient construction method comprises the following steps:
s21, determining three digital characteristics of the cloud model (E) x ，E n ，H e )；
S22, passing
The corresponding abscissa value is processed, the corresponding interval of the cloud model reflecting the fuzzy concept is given, and an equation aiming at the inner and outer envelope lines of the cloud model is given, namely
Calculate out
Horizontal coordinate values corresponding to the inner envelope and the outer envelope:
the coordinate of the point D is x D ＝E x +3E n ；
S23, determining quadruplex coefficient mu = A 1 +B 1 i 1 +C 1 i 2 +D 1 i 3 Let i 1 ，i 2 ，i 3 ∈[-1，1]And wherein
After normalization is carried out by using the formula, the coefficient of the cloud model is mu = a + bi 1 +ci 2 +di 3 ，i 1 ，i 2 ，i 3 ∈[-1，1]：
S3, giving an ideal cloud model of each index in an index system by an expert, and constructing an ideal quadruple coefficient;
s4, respectively calculating the closeness of each scheme and the corresponding index of the ideal scheme by using a quadric-union coefficient closeness formula, and setting mu 1 ,μ 2 Is a quadruple coefficient, mu 1 ＝a 1 +b 1 i 1 +c 1 i 2 +d 1 i 3 ，μ 2 ＝a 2 +b 2 i 1 +c 2 i 2 +d 2 i 3 Wherein a is 1 +b 1 +c 1 +d 1 ＝1，a 2 +b 2 +c 2 +d 2 ＝1，i 1 ，i 2 ，i 3 ∈[-1，1]Definition of μ 1 ,μ 2 The closeness of (A) is:
T(μ 1 ，μ 2 )＝1-{w a ||a 1 -a 2 ||+w b ||b 1 -b 2 ||+w c ||c 1 -c 2 ||+w d ||d 1 -d 2 ||}
wherein w a ，w b ，w c ，w d The normalization weight of importance degree of identity and dissimilarity in the four-element coefficient in the comprehensive evaluation result, and w a +w b +w c +w d ＝1；
And calculating the total closeness T of each scheme and the ideal scheme according to the following formula jp ：
Wherein j =1,2, \8230 \ 8230;, M, M is the total number of the schemes, t is the total number of the evaluation indexes, w is the total number of the evaluation indexes i Is the weight of each index, mu pi The quadric-union coefficient of each index of an ideal scheme;
s5, total closeness T of the solution jp And sequencing and outputting the ship number with the strongest anti-sinking capability.
2. The cloud model joint coefficient-based multi-attribute group ship anti-settling capacity assessment decision method according to claim 1, characterized in that: the reverse cloud generator in step S1 has the following inputs: the quantitative positions of N cloud drops in a number domain space and the certainty degree of each cloud drop representing a certain qualitative concept; the output is: expectation E of a certain qualitative concept x Entropy E n And entropy H e 。
3. The cloud model joint coefficient-based multi-attribute group ship anti-settling capacity assessment decision method according to claim 2, characterized in that: the specific algorithm of the reverse cloud generator is as follows:
s11, according to the known cloud drops, using a cloud expectation curve equation through a least square method
Fitting, directly obtaining
And
s12, removing points with y being larger than 0.999, and recording the number of the remaining cloud drops as m;
s13, according to
Find out
S14, according to standard deviation function
Find out
S15, outputting
I.e. the expected value E of a certain qualitative concept x Entropy E n And entropy H e 。
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