CN106447044A - Risk assessment method based on Shapley value and interaction index - Google Patents
Risk assessment method based on Shapley value and interaction index Download PDFInfo
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Abstract
The invention discloses a risk assessment method based on a Shapley value and an interaction index and belongs to the technical field of network fuzzy comprehensive risk assessment. The method includes the following steps: (1) introducing the Shapley value in the cooperative game theory to a fuzzy comprehensive risk assessment method to provide a more accurate weight value input for evaluation factors; (2) calculating a systematic risk value by using Choquet fuzzy integral synthesis, wherein not only the relative importance of each evaluation factor is considered, but also the interaction among the evaluation factors is taken into account. The risk assessment method has the advantages that by introduction of the Shapley value and interaction index in the cooperative game theory to the fuzzy comprehensive risk assessment method and by two times of weight value correction, a more accurate weight value is provided for the fuzzy comprehensive risk assessment method, interaction effects among the indexes are reduced, and therefore, the obtained system risk value more conforms to an actual situation.
Description
Technical field
The present invention relates to online fuzzy integrated risk assessment technology field, show in particular a kind of based on Shapley value with
The methods of risk assessment of reciprocal action index.
Background technology
Risk, just refers to potential danger.In other words, risk just refers to the general of the adverse events generation avoided by people
Rate.Management of risk of information security is to recognize, evaluate the loss risk that various Information Security Risk factors are brought, and risk is controlled
System, mitigates the negative effect that risk may be brought, the process that loss is preferably minimized.At present, how to increasingly complicated network
Risk status carries out scientific and reasonable risk assessment, to take corresponding safety measure to carry out reduce risk, has become as the Internet
One of popular research content of security fields.Existing methods of risk assessment divided from Evaluation property mainly include qualitative
Analysis and quantitative analyses, this two classes appraisal procedure respectively has the pluses and minuses of oneself.Simple qualitative analyses or quantitative analyses are due to which
The limitation being individually present, the information that can all cause risk assessment disappearance certain, causes the inaccurate of assessment result.So, only
Have the advantages that, with reference to the two, can just draw relatively reliable assessment result.And fuzzy overall evaluation algorithm is exactly one kind combines
The appraisal procedure of qualitative analyses and quantitative analyses, for fuzzy overall evaluation algorithm, which is based primarily upon fuzzy mathematics and fuzzy set
Rationally discuss, a kind of integrated evaluating method being widely used in various evaluation problems.
Fuzzy theory and fuzzy overall evaluation algorithm have in-depth study and application in China, and fuzzy system is also
Become better and approaching perfection day by day, experts and scholars are mainly focused on the improvement of fuzzy overall evaluation algorithm and application.Such as Zhao Gang etc. pass through entropy weight
Theory is applied in multi-layer fuzzy comprehensive, establishes improved comprehensive artificial intelligence's risk analysis method.Wu Zihan with
Factorial analyses are core, fuzzy overall evaluation algorithm is improved, combines the two common advantage.Li Ji is true etc. to be directed to
Network safety pre-warning corresponding model lacks initiative and is not introduced into the problem of corresponding opportunity decision-making mechanism, establishes based on dual dynamic
The active forewarning response decision modle of the asymmetric Triangle Model fuzzy matrix game of state.
In sum, fuzzy overall evaluation algorithm is incorporated on evaluating information system risk with good effect, so
And, also there is a problem of certain, be mainly manifested in factor of evaluation concentrate the weight of each factor be to each factor relative importance
Quantitative description, for fuzzy overall evaluation algorithm it is critical that, Chinese scholars are carried out for this problem
Substantial amounts of exploration and practice, but there is presently no unified standard to be determined which, therefore there is very big researching value.
The existing fuzzy overall evaluation algorithm applied in evaluating information system risk maximally related with the present invention is main
Have：Liu Wenbin is in its master thesis《Comprehensive evaluation system research and realization》In comprehensive evaluation system is carried out
In-depth study simultaneously achieves related prototypical system, describe in detail fuzzy overall evaluation algorithm in evaluation system should
With.Thank to luxuriant Lignum Rhamnellae to exist《Application of the fuzzy overall evaluation in information system security class deciding grade and level》Middle by fuzzy overall evaluation application
In information system security class deciding grade and level application, good assessment result is achieved.
The existing fuzzy overall evaluation algorithm that applies in evaluating information system risk mainly has two of above-mentioned introduction
Document, this two documents adopt evaluation procedure of the fuzzy overall evaluation algorithm to evaluating information system risk, specifically mainly
It is divided into 5, as shown in Figure 1：
1. determine overall merit set of factors, i.e., so-called discussion scope for the factors U={ U1 ..., Ui ..., Um }, m be by its shadow
The number of the Type division of criterion is rung, is met
2. opinion rating is set up, determine opinion rating domain V={ v1,...,vi,...,vn, final result is the n
One vector of grade；
3. determine membership function, set up opinion rating.If to i-th index UiEvaluation Ri={ r11,...,r1j,...,
r1n, it is the fuzzy subset on V, wherein rijRepresent degree of membership of i-th index for j-th grade, the evaluation square of composition
Battle array is as follows：
4. determine its weight for each factor in set of factors, build corresponding weight vectors W=w1 ...,
wi,...,wk}；
5. attribute weights are calculated using fuzzy operator ο with Evaluations matrix, final appraisal results B=W ο R are obtained,
System final risk value R=w is worth to specific to being estimated with reference to relative set by each factor of evaluation weights in risk assessmento×
μ({P,L,O})+(wp-wo)×μ({P,L})+(wl-wp)×μ({L}).
The deficiency of the fuzzy synthesis methods of risk assessment of this two documents, can be summarized as the following aspects：
1. the overlapping phenomenon between evaluation index, is likely to result in the inaccurate of assessment result
The selection of evaluation index is artificial, exactly because the impact of the subjective factorss of people, the selection of index will not be two
Two repel each other, and there may be interactional relation between index, and these relations are summarized to get up to be divided three classes：(1) redundancy or disappear
Pole is cooperated；(2) complementary or enthusiastic cooperation；(3) independence.And with increasing for evaluation index quantity, the weight between index
Folded phenomenon can be more and more, and it is often indiscoverable for people that these overlap, and these overlapping phenomenons are to final evaluation
As a result large effect can be produced.
2. the structure of weight vectors is affected by artificial subjective or calculation, does not account for each factor in factor
The relative contribution of concentration
In current fuzzy synthesis methods of risk assessment, the construction method of factor of evaluation weight vectors mainly has following several：
Expert's estimation technique：By expert, factor of evaluation weight vectors are estimated, expert's number generally should
More than 1 people；Delphi method：Need also exist in field authoritative sources to assist, different from be in place of expert's appraisal method be not by special
Family directly gives the weights of determination, but calculates concrete weights by expertise.Can be existed according to expert when being embodied as
Professional standards in industry determine different authoritative coefficients, obtain after expert opinion and authoritative coefficient are combined the weight revised to
Amount；The statistic frequency method of fractional steps：The method belongs to quantitative statistical analysis technique, is not related to expert, needs sampling, as a result depends on
Sample；Matrix matching method：Method i.e. by being mutually compared between factor, obtains weight；Analytic hierarchy process AHP：Core
Part is similar with comparator matrix method, only difference is that, AHP is suitable for for the multi-level, destructuring of multi objective
Challenge.Each factor weights that above-mentioned each method is determined all do not consider Relative Contribution of each factor in whole set of factors
Degree, therefore be present based on the assessment result of this gained inaccurate.
The selection of the weight of factor of evaluation collection is the core of whole fuzzy synthesis risk evaluating method, and directly influences
The determiner of interpretation of result, therefore, should be double cautious to the determination of weight, to reduce the impact of anthropic factor, accomplish section
, correct risk assessment.
In summary, Related domestic documents have all carried out certain spy to the application of fuzzy overall evaluation algorithm and research
Rope, is concentrated mainly in fuzzy overall evaluation algorithm in the determination problem of each factor weights, but these documents all do not consider because
Impact of the reciprocal action between element to final appraisal results.Due to the particularity of evaluating information system risk, in assessment system wind
Generally require when dangerous with reference to the subjective suggestion of expert and the statistical data of sample, therefore by the application of fuzzy overall evaluation algorithm its
When middle, need to the relative importance between each key element of risk assessment and its between the relation of influencing each other carry out finer
Excavate and combing, this is also the most important contribution part of the inventive method.
Content of the invention
Goal of the invention
Present invention is primarily targeted at providing a kind of based on Shapley value and the risk assessment side of reciprocal action index
Method, solves the problems, such as impact of the reciprocal action between current non-Consideration to final appraisal results.
Technical scheme
A kind of based on Shapley value and the methods of risk assessment of reciprocal action index, it is characterised in that including following step
Suddenly：
S1. factor of evaluation collection is determined；
S2. the opinion rating of system evaluation is set up；
S3. according to the different attribute of factor of evaluation and its between dependency be that each sets of factors provides the fuzzy of each set
Degree of membership；
S4. the weights of each factor of evaluation are determined；
S5. the weights for each factor of S4 determination are modified, and calculate each factor of evaluation U according to formula (2)i's
After Shapley value, further according to following formula, first time correction is carried out to the weights of each factor of evaluation：
Wherein, i ∈ N+, represents i-th factor of evaluation, n ∈ N+, the sum of expression factor of evaluation；
S6. carried out according to the reciprocal action index between each factor that formula (3) reciprocal action index definition is calculated
Second correction of the weights of each factor, the foundation of correction is I between each factorijSize, to all positive with other each factors
The factor of cooperation improves its weights, and reduces its weights to the factor with all passive cooperations of other each factors；
S7. after obtaining the weights of revised each factor, further according to formula (1) composite formula R=wo×μ({P,L,O})+
(wp-wo)×μ({P,L})+(wl-wp) × μ ({ L }) calculates the value-at-risk of the system of needs assessment, and wherein w represents each attribute
Weights, μ represents the measure value of each set.
Preferably, the factor of evaluation collection described in S1, threat, the vulnerability of system and the system for being faced including system
Asset level.
Preferably, the system evaluation grade described in S2, according to the related standard of assets assessment both at home and abroad by system evaluation etc.
Level is set as Pyatyi.
From the above it can be seen that the present invention has advantages below：The present invention is introduced in cooperation interactive theory respectively
Shapley value and reciprocal action index.Wherein it is introduced into Shapley value to be mainly used in solving in fuzzy synthesis methods of risk assessment
Second Problem, embody contribution degree of each assessment factor in whole set of factors by Shapley value；Introduce reciprocal action
Index solving the first problem in fuzzy synthesis methods of risk assessment, by calculating the reciprocal action between each assessment factor
Index is being modified to each factor weights.Shapley value and reciprocal action index of the method by each factor of evaluation of calculating
Relative importance and the reciprocal action of factor of evaluation is showed, the interaction problems between factor of evaluation are efficiently solved, is obtained
To more accurately each factor of evaluation weights, evaluation result is finally caused to more conform to actual situation.
Description of the drawings
Fig. 1 is the flow chart of former method fuzzy synthesis methods of risk assessment.
Fig. 2 is the flow chart of fuzzy synthesis methods of risk assessment of the present invention.
Specific embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present application, the technical scheme in the embodiment of the present application is carried out clear, complete
Site preparation is described, it is clear that described embodiment is only some embodiments of the present application, rather than whole embodiments.It is based on
Embodiment in the application, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of the application protection.
In order to better illustrate to the present invention, be firstly introduced into some concepts in fuzzy synthesis methods of risk assessment and
Definition.
(1) membership function and degree of membership
If element portions degree ground belongs to this set in domain U, this collection is claimed to be combined into fuzzy set.If domain is
X, x are the element in X, forMap given following：
x→μA(x)∈[0,1]
Then claim following set：A=(x | μA(x))},For the fuzzy set on X.
Wherein, μAMembership function for fuzzy subset A.The selection of membership function uses different sides according to particular problem
Method, common method has point system, fuzzy statistical method, trapezoidal fuzz method, triangle fuzz method etc., and the present invention is mainly using fuzzy system
Meter method.
It is a concept in mathematics to estimate, and classics are estimated with additivity, such as, the total length of two connected line segments
Sum equal to this two lines segment length.However, additivity is difficult to meet in the realistic case, the work efficiency that such as two people cooperate
It is not to be simply equal to two people's work efficiency sums.Japanese scholars Segeno proposed fuzzy mearue in 1974, and which is mainly thought
It is a kind of set function that additivity is substituted with weaker monotonicity to think.Fuzzy mearue is defined as follows：
Defining 1 and (X, F) being set for a measurable space, F is the σ-algebraically of all subsets composition of X.If μ：F → [0,1] is on F
A fuzzy mearue, then μ meet：
1. boundary condition μ (Φ)=0, μ (X)=1；
2. monotonicityIfThen μ (B) >=μ (A)；
If 3. serialityThen
By fuzzy mearue, the interaction between factor of evaluation can be symbolized, evaluation result more science can be caused to close
Reason.The Aggregation Operators of correlative factor adopt fuzzy integral, and fuzzy integral has a variety of forms, including Sugeno integration, Choquet
Integration, (N) fuzzy integral, Zhenyuan integration etc., mainly introduce Choquet fuzzy integral below, and it is mainly used in multi input
The system model of single output type, with being widely applied scene very much.
(2) Choquet fuzzy integral definition
Define 2 and set X={ x1,x2,…,xn, P (X) represents the power set of X, is made up of all subsets of X, and μ is definition
Fuzzy mearue on X, f is defined in the set function f on X:X → [0,1], then f is as follows with regard to the Choquet Definitions On Integration of μ：
Wherein Ai={ xi,xi+1,…,xn, if f (x can not be met1)≤f(x2)…≤f(xn), then need to enter the element of X
Row rearrangementSo that the element after rearranging meets
(3) Shapley value definition
Shapley value embodies the relative importance in property set of an attribute from cooperative game theory,
More reasonable than individually consideration measure value, it is that the correction of attribute weights provides help well[6].If K represents that X's is individual containing k
The subset of element, note μ (K) is μK, μ ({ xi) it is μi, μ ({ xi∪ K) it is μiK.
Define the fuzzy mearue that 3 μ are defined on X, attribute xiShapley value with regard to fuzzy mearue μ is defined as：
Wherein,| K | represents the gesture of set K, and specifies 0！=1.
(4) reciprocal action index definition
Attribute xiWith attribute xjInteractivity only by μ ({ xi,xj})-μ({xi})-μ({xj) determining and imperfection
, it should while calculate covering { xi,xjThe estimating of all subsets, Grabisch gives the definition of reciprocal action index.
Define 4 attribute xi,xjBetween reciprocal action index definition be:
Iij<0 shows it is to weaken between two attributes, i.e., the two is passive cooperation；Iij>0 shows between two attributes
It is to strengthen, i.e., the two is enthusiastic cooperation.Can be according to the I for calculatingijEach factor of evaluation in risk assessment is adjusted.
Shapley value and reciprocal action index consider significance level of the attribute in whole property sets and global friendship
Interaction, more reasonable than simple consideration measure value.
Embodiment：Flow process Fig. 2 for fuzzy synthesis methods of risk assessment
S1. factor of evaluation collection is determined, according to concerned countries standard, the set of factors in average risk assessment is system institute face
The factors such as the asset level of threat, the vulnerability of system and system that faces.
S2. the opinion rating of system evaluation is set up, can be by system evaluation according to related domestic and international assets assessment Standard General
Grade is set as Pyatyi.
S3. according to the different attribute of factor of evaluation and its between dependency be that each sets of factors provides the fuzzy of each set
Degree of membership.
S4. the weights of each factor of evaluation are determined；
S5. the weights for each factor of S4 determination are modified, and calculate each factor of evaluation U according to formula (2)i's
After Shapley value, first time correction is carried out to each factor of evaluation weights according to following formula：
Wherein, i ∈ N+, represents i-th factor of evaluation, n ∈ N+, expression factor of evaluation sum.
Revised weights can embody contribution degree of each factor in whole set of factors, be fuzzy synthesis risk assessment
Method provides more accurate weights input so that final evaluation result more conforms to real situation.
S6. carried out according to the reciprocal action index between each factor that formula (3) reciprocal action index definition is calculated
Second correction of the weights of each factor, the foundation of correction is I between each factorijSize, to all positive with other each factors
The factor of cooperation improves its weights, and reduces its weights to the factor with all passive cooperations of other each factors.
S7. after obtaining the weights of revised each factor, further according to formula (1) composite formula R=wo×μ({P,L,O})+
(wp-wo)×μ({P,L})+(wl-wp) × μ ({ L }) calculates the value-at-risk of the system of needs assessment, and wherein w represents each attribute
Weights, μ represents the measure value of each set.
Claims (3)
1. a kind of based on Shapley value and the methods of risk assessment of reciprocal action index, it is characterised in that to comprise the following steps：
S1. factor of evaluation collection is determined；
S2. the opinion rating of system evaluation is set up；
S3. according to the different attribute of factor of evaluation and its between dependency be fuzzy membership that each sets of factors provides each set
Degree；
S4. the weights of each factor of evaluation are determined；
S5. the weights for each factor of S4 determination are modified, and calculate each factor of evaluation U according to formula (2)iShapley
After value, further according to following formula, first time correction is carried out to the weights of each factor of evaluation：
Wherein, i ∈ N+, represents i-th factor of evaluation, n ∈ N+, the sum of expression factor of evaluation；
S6. carried out according to the reciprocal action index between each factor that formula (3) reciprocal action index definition is calculated each because
Second correction of the weights of element, the foundation of correction is I between each factorijSize, to other each factor all enthusiastic cooperations
Factor improve its weights, and its weights is reduced to the factor with all passive cooperations of other each factors；
S7. after obtaining the weights of revised each factor, further according to formula (1) composite formula R=wo×μ({P,L,O})+(wp-
wo)×μ({P,L})+(wl-wp) × μ ({ L }) calculates the value-at-risk of the system of needs assessment, and wherein w represents the power of each attribute
Value, μ represents the measure value of each set.
2. want a kind of described in 1 based on Shapley value and the methods of risk assessment of reciprocal action index according to right, its feature exists
In, the factor of evaluation collection described in S1, the asset level of the threat, the vulnerability of system and the system that are faced including system.
3. a kind of according to right wants 1 or 2 is based on Shapley value and the methods of risk assessment of reciprocal action index, and which is special
Levy and be, the system evaluation grade described in S2, according to related assets assessment standard both at home and abroad, system evaluation grade is set as five
Level.
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Application publication date: 20170222 |