CN103078850A - Transitive-trust evaluating method for supporting cooperative security in distributed open environment - Google Patents

Abstract

The invention discloses a subjective-trust transfer-evaluating method for supporting cooperative security in a distributed open environment. The method comprises the following concrete steps of: firstly, defining related base concepts including a trust-value space, a trust-definition space, a trust cloud, a trust-definition cloud, a honesty-value space, a honesty-definition space, a honesty-definition cloud and the like in the form of clouds; then considering p entities E1, E2, ellipsis, and Ep, and calculating the honesty of the E2 for the E1 according to the direct trust of the E1 for the E2; next, calculating the transitive trust of the E1 for the E3 according to the honesty of the E2 for the E1 and the direct trust of the E2 for the E3; and sequentially calculating the honesty of the Ej+1 for the E1 and the transitive trust of the E1 for the Ej+2 according to the steps until obtaining the transitive trust of the E1 for the Ep through calculation, wherein the j is equal to 2, 3, ellipsis, and p-2. Compared with an existing trust-transferring evaluating method, the subjective-trust transfer-evaluating method has the characteristics that the phenomenon of trust attenuation in the process of subjective-trust transferring is actually described, the transitive trust is effectively quantized, and the weak transferring property of subjective trusts is fully embodied.

Description

Support the transmission degree of belief appraisal procedure of cooperation safety in the Distributed Open Environments

Technical field

The invention belongs to the Computer Applied Technology field, the subjective trust that relates in the Distributed Open Environments transmits assessment technology, particularly supports the transmission degree of belief appraisal procedure of cooperation safety in a kind of Distributed Open Environments.

Background technology

Distributed Open Environments is the typical Loosely coupled computing system that is made of the heterogeneous resource that disperses on a large amount of geography, usually needs a plurality of entities jointly to accomplish a task in the mode of cooperation.Yet in the wide-area distribution type environment, the cooperation both sides may be all less than the experience of directly cooperating.For the safety that guarantees to cooperate, need to solve two key issues: the identity of (1) how to confirm cooperation entity; (2) credibility of dynamic evaluation cooperation entity how.The former relates to objective trust, just can confirm mutual both sides' identity by traditional identity identifying technology.And the latter needs subjective trust is estimated.As cooperation both sides during without direct interaction experiences, can be by having the recommendation (transmission of namely trusting of the entity of direct interaction experiences with cooperation part, the credibility assessment that forms by direct interaction becomes direct degree of belief), therefore the credibility (namely transmitting degree of belief) of assessment cooperation part is to support the matter of utmost importance that security cooperation need solve in Distributed Open Environments to the calculating of transmitting degree of belief.

Subjective trust is based on the human cognitive phenomenon of conviction, and certain ability or behavior for assessment of entity have extremely strong uncertainty, is difficult to describe exactly and quantize.By the firm academician of Li De in last century the nineties at the cloud model that the basis of traditional fuzzy mathematics and probability statistics proposes, be the exchange model between qualitative language and its quantificational expression, also be a kind of effective tool of describing uncertain concept.Cloud is this theoretical core, by three numerical characteristics---and expectation Ex, entropy En and super entropy He characterize a concept.Different according to concrete methods of realizing, cloud has polytype.Wherein, normal cloud model is the brand-new model that grows up on normal distribution and bell membership function basis, has preferably universality.

At present, domestic and international trust pass through mechanism research based on cloud model mainly contains:

The people such as the He Rui of BJ University of Aeronautics ﹠ Astronautics ^[1,2,3]The people such as Lu Feng with Institutes Of Technology Of Nanjing ^[4,5]All adopt the Ex after the mode that a plurality of Ex on the trust chain are simply multiplied each other is calculated merging.The people such as the Meng Xiangyi of BJ University of Aeronautics ﹠ Astronautics ^[6,7]Design a kind of wall scroll spare single criterion logical operator and processed the trust transmission that causes by recommending.Passing through special parameter---" accepting the factor " reflection importance of recommendation paths and trust evaluation side are to the degree of recognition of each recommendation paths.The people such as the Zhang Changlun of Beijing Jiaotong University ^[8]Use basic cloud and " the accepting the factor " of trusting processed the recommendation of trusting.

By the analysis of existing trust pass through mechanism based on cloud model is found, although obtained certain achievement in research, but to the quantificational description of trust transfer with transmit on the computational methods of degree of belief still Shortcomings part: (1) uses simple arithmetic to calculate and transmits degree of belief, can't accurately reflect the trust decay that occurs with transmittance process; (2) in the mode of mean value a plurality of transmission trust values are merged into final single degree of belief.Although the method is simple, obviously do not meet reality, particularly can't resist Malicious recommendation; (3) degree of belief among the transmission result is directly got the transmission degree of belief of confidence level smaller on the bang path, and this pessimistic processing mode is conservative and coarse.

List of references

[1]R.He,J.W.Niu,M.Yuan,et?al.A?novel?cloud-based?trust?model?for?pervasive?computing.Proceedings?of?the?4th?International?Conference?on?Computer?and?Information?Technology(CIT’04),Wuhan,China,September14-16,2004,IEEE?Press,693-700

[2]R.He,J.W.Niu?and?G.W.Zhang.CBTM:A?trust?model?with?uncertainty?quantification?and?reasoning?for?pervasive?computing.Proceedings?of?the?3rd?International?Symposium?on?Parallel?and?Distributed?Processing?and?Applications(ISPA’05),Nanjing,China,November2-5,2005,LNCS?3758,Springer-Verlag,541-552

[3]R.He,J.W.Niu?and?K.Hu.A?novel?approach?to?evaluate?trustworthiness?and?uncertainty?of?trust?relationships?in?Peer-to-Peer?computing.Proceedings?of?the?5th?International?Conference?on?Computer?and?Information?Technology(CIT’05),Shanghai,China,September21-23,2005,IEEE?Press,382-388

[4] peak, road, Wu Huizhong. based on the trust evaluation research of cloud model, Chinese engineering science, 2008,10 (10): 84-90

[5] peak, road, Wu Huizhong. under the grid environment based on trust evaluation and the Research of Decision of cloud model. Journal of System Simulation, 2009,21 (2): 421-426

[6] Meng Xiangyi, Zhang Guangwei, Liu Changyu etc. based on the Subjective Trust Management Model research of cloud model. Journal of System Simulation, 2007,19 (14): 3310-3317

[7]X.Y.Meng,G.W.Zhang,J.C.Kang,et?al.A?new?subjective?trust?model?based?on?cloud?model.Proceedings?of?the?5th?International?Conference?on?Networking,Sensing?and?Control(ICNSC’08),Hainan,China,April?6-8,2008,IEEE?Press,1125-1130

[8]C.L.Zhang?and?Y.Liu.A?cloud-based?discrete?metric?trust?management?model?in?open?networks.Journal?of?Internet?Technology，2009,10(1):79-82

Summary of the invention

The purpose of this invention is to provide a kind of trust relaxation phenomenon that can truly describe in the subjective trust transmittance process, can effectively quantize to transmit degree of belief again, support the transmission degree of belief appraisal procedure of cooperation safety in the Distributed Open Environments of the weak transitivity of embodiment subjective trust, to overcome the deficiencies in the prior art.

To achieve these goals, technical scheme of the present invention is:

Support the transmission degree of belief appraisal procedure of cooperation safety in a kind of Distributed Open Environments, may further comprise the steps:

Step 1: definition trust value space TV, trust concept space T, trust cloud TC (Ex, En, He), trust concept cloud TCC (Ex, En, He), honest value space S V, honest concept space S and honest concept cloud SCC (Ex, En, He) basic conception;

Step 2: consider p entity E ₁, E ₂..., E _pThe trust transitive relation, only have adjacent two entities to know well (experience that direct interaction is namely arranged), i.e. E _iWith E _I+1Know well, 1≤i≤p-1, other entities be strange (experience that does not namely have direct interaction) mutually, works as E _pRequest and E ₁During cooperation, E ₁Need to pass through by E ₂, E ₃..., E _P-1The information evaluation E that the recommendation paths that consists of provides _pCredibility, E _iWith E _I+1The experience that direct interaction is arranged, E _iTo E _I+1Direct degree of belief Known, E then _iCan be according to trusting cloud

How decision treats E _I+1To E _I+2Recommendation, for convenience of description, at first according to E ₁To E ₂Direct degree of belief calculate E ₂With respect to E ₁Honest degree;

Step 3: according to E ₂To E ₁Honest degree and E ₂To E ₃Direct degree of belief calculate E ₁To E ₃The transmission degree of belief;

Step 4: according to the method for step 2 and step 3, calculate successively E _J+1With respect to E ₁Honest degree and E ₁To E _J+2The transmission degree of belief, j=2,3 ... p-2, until calculate E ₁To E _pThe transmission degree of belief.

Described step 2 is according to following process computation E ₂With respect to E ₁Honest degree σ _1,2:

(2.1) with E ₁To E ₂Direct degree of belief

Three numerical characteristic Ex, En and He bring equation (1) and equation (2) repeatedly into, it is different to calculate N

1≤i≤N;

$\widetilde{\mathrm{En}}~N(\mathrm{En},{\left(\mathrm{He}\right)}^2)---\left(1\right)$

$v~N(\mathrm{Ex},{\left(\widetilde{\mathrm{En}}\right)}^2)---\left(2\right)$

(2.2) will trust the concept cloud

With

It is different repeatedly to bring N of equation (1) generation into

(2.3) will

With Repeatedly bring equation (3) into and generate N different ud _Ki, this value has embodied Water dust

To cloud

The degree of certainty of the honest concept of representative;

$\mathrm{ud}=\exp [-\frac{1}{2}{(v-\mathrm{Ex})}^2/{\left(\widetilde{\mathrm{En}}\right)}^2]---\left(3\right)$

At last, calculate N different ud according to formula (4) _KiArithmetic mean σ _k:

${\mathrm{\σ}}_k=\frac{1}{N}{\mathrm{\Σ}}_{i=1}^{N}u{d}_{\mathrm{ki}}---\left(4\right)$

σ _kIt is larger,

More can embody

Feature, then make σ _1,2=max{ σ ₁, σ ₂..., σ _L, i.e. E ₂With respect to E ₁Honest degree.

Described step 3 is according to following process computation E ₁To E ₃The transmission degree of belief:

(3.1) according to E ₂To E ₁Honest degree σ _1,2And E ₂To E ₃Direct degree of belief

Calculate E ₁To E ₃The transmission degree of belief

In

${\mathrm{Ex}}^{E_1{\mathrm{<figure-callout\; id="3"\; label="E"\; filenames="HDA00002675178200021.png"\; state="\{\{state\}\}">E</figure-callout>}}_3}={\mathrm{\&sigma;}}_{\mathrm{1,2}}{\mathrm{Ex}}_2^{\mathrm{TC}};$

(3.2) according to E ₂To E ₁Honest degree σ _1,2And E ₂To E ₃Direct degree of belief Calculate E ₁To E ₃The transmission degree of belief In ${\mathrm{En}}^{E_1{\mathrm{<figure-callout\; id="3"\; label="E"\; filenames="HDA00002675178200021.png"\; state="\{\{state\}\}">E</figure-callout>}}_3}=(1+{\mathrm{\&sigma;}}_{\mathrm{1,2}}){\mathrm{En}}_2^{\mathrm{TC}};$

(3.2) according to E ₂To E ₁Honest degree σ _1,2And E ₂To E ₃Direct degree of belief

Calculate E ₁To E ₃The transmission degree of belief

In

${\mathrm{He}}^{E_1{\mathrm{<figure-callout\; id="3"\; label="E"\; filenames="HDA00002675178200021.png"\; state="\{\{state\}\}">E</figure-callout>}}_3}=(1+{\mathrm{\&sigma;}}_{\mathrm{1,2}}){\mathrm{He}}_2^{\mathrm{TC}}.$

Described step 4 is according to following process computation E ₁To E _pThe transmission degree of belief

(4.1) honest degree computational methods according to claim 2 are calculated E successively _J+1With respect to E ₁Honest degree σ _{1, j+1}, j=2,3 ... p-2;

(4.2) transmission degree of belief computational methods according to claim 3 are calculated E successively ₁To E _J+2The transmission degree of belief

Concrete grammar is:

${\mathrm{Ex}}^{E_1{E}_{j+2}}={\mathrm{\&sigma;}}_{1,j+1}{\mathrm{Ex}}_{j+1}^{\mathrm{TC}},$ ${\mathrm{En}}^{E_1{E}_{j+2}}=(1+{\mathrm{\&sigma;}}_{1,j+1}){\mathrm{En}}_{j+1}^{\mathrm{TC}},$ ${\mathrm{He}}^{E_1{E}_{j+2}}=(1+{\mathrm{\&sigma;}}_{1,j+1}){\mathrm{He}}_{j+1}^{\mathrm{TC}},j=\mathrm{2,3},...p-2$

Until calculate E ₁To E _pThe transmission degree of belief

The present invention has following three characteristics.At first, the present invention with the formal definition of cloud with trust relevant some concepts.The application of cloud model has embodied its uncertain feature preferably so that these definition can consider ambiguity and the randomness of subjective trust, has explained rightly subjective trust.Secondly, by cloud tolerance trusting relationship, very naturally realize the mutual conversion between qualitativing concept and the quantitative expression, supported for the transmission with quantification manner research subjective trust provides effectively, reasonably solved the metric question that transmits trusting relationship.At last, the transmission degree of belief appraisal procedure of proposition utilizes the honest degree factor to reflect the decay in the trust transfer, has described more realistically the weak transitivity of trusting.The transmission degree of belief appraisal procedure that theory analysis and the present invention of the simulation experiment result proof propose can obtain the result in linear session, be efficiently, rationally and effectively.

Description of drawings

Fig. 1 is that the present invention is from entity E ₁To entity E _pTrust transmission (p among the figure 〉=3) scene schematic diagram.

Fig. 2 is method flow diagram of the present invention (p among the figure 〉=4).

Embodiment

The present invention is described in further detail below in conjunction with accompanying drawing.

Step 1: with the formal definition of the cloud some concepts relevant with trust.

Definition 1(trust value space) establishing TV is a quantitative domain, available perfect number value representation.Tv ∈ TV is a trust value, presentation-entity E ₁To entity E ₂The qualitative assessment of credibility.Claim that TV is a trust value space.The present invention sets TV ∈ [0,1].Tv is a real number, tv ∈ [0,1].The value of tv is larger, expression E ₁More trust E ₂

Definition 2(trust concept space) a trust concept space T is a qualitativing concept set on the TV of trust value space.T ∈ T is one and trusts concept, represents a kind of qualitatively reliability rating.The present invention sets T={ and distrusts, weak trust is trusted, and trusts, and trusts very much utmost good faith }.Each element among the set T is one and trusts concept.

Based on definition 1 and definition 2, the subjective trust that the present invention adopts definition 3 to describe based on cloud model.

Definition 3(trust cloud) establishing TV is a trust value space, and tv ∈ TV.T is one and trusts concept space, and t ∈ T.If trust value tv is a Stochastic implementation of trusting concept t, and tv is the random number that steady tendency is arranged to degree of certainty μ (tv) ∈ [0,1] of t, namely

μ:TV→[0,1]

$\&ForAll;\mathrm{tv}\&Element;\mathrm{TV},\mathrm{tv}\&RightArrow;\mathrm{\&mu;}\left(\mathrm{tv}\right)$

Then claim tv on TV, to be distributed as the trust cloud, claim that each tv is a water dust.For simplicity of exposition, tv is designated as ud to the degree of certainty μ (tv) of t.

Based on definition 3, the present invention adopts One-Dimensional Normal to trust cloud

Presentation-entity E ₁To entity E ₂Subjective trust.

Normal state is trusted cloud also can be used for the trust concept that concept space is trusted in quantificational description.Claim this trust cloud for trusting the concept cloud, be designated as TCC (Ex, En, He).Ex among the TCC (Ex, En, He), the implication of En and He and presentation-entity trusting relationship

Similar.

The honest value of definition 4(space) establishing SV is a quantitative domain, can use the perfect number value representation.Sv ∈ SV is a honest value, embodies entity E ₁To entity E ₂The qualitative assessment of recommendation information.Claim that SV is a honest value space.The present invention sets SV ∈ [0,1].Sv is the real number of value between 0 to 1.The value of sv is larger, expression E ₁More can accept E ₂The recommendation information that provides.

The honest concept space of definition 5() a honest concept space S is a qualitativing concept set on the honest value space S V.S ∈ S is a honest concept, represents a kind of qualitatively honest grade.It is dishonest that the present invention sets S={, and weak honesty is honest, and honesty is very honest, and is absolute honest }.Each element in the S set is a honest concept.

With trust the concept varieties of clouds seemingly, the present invention represents honest concept with honest concept cloud SCC (Ex, En, He).Usually, if honest concept space S is made of L honest concept, then wherein certain concept can be used

Expression, 1≤k≤L, and

According to definition 5, herein L=6.

Step 2: consider p entity E ₁, E ₂..., E _p, it trusts transitive relation as shown in Figure 1.In this scene, only have adjacent two entities to know well (experience that direct interaction is namely arranged), i.e. E _iWith E _I+1Know well 1≤i≤p-1.Other entities are strange (experience that does not namely have direct interaction) mutually.Work as E _pRequest and E ₁During cooperation, E ₁Need to pass through by E ₂, E ₃..., E _P-1The information evaluation E that the recommendation paths that consists of provides _pCredibility.Obviously, E _iTo E _I+1Degree of belief be E _iEstimate E _I+2The important evidence of credibility.E _iWith E _I+1The experience that direct interaction is arranged, E _iTo E _I+1Direct degree of belief Known, E then _iCan be according to trusting cloud

How decision treats E _I+1To E _I+2Recommendation.Similar with " trust ", E _iTo E _I+1The attitude of recommendation information also is a kind of probabilistic qualitativing concept of being with.The present invention adopts language word " honesty " to describe this concept, the honest value of definition space S V, honest concept space S and honest concept cloud SCC (Ex, En, He), E _iTo E _I+1The attitude of recommendation information is called E _I+1With respect to E _iHonest degree.

For convenience of description, at first according to E ₁To E ₂Direct degree of belief Calculate E ₂With respect to E ₁Honest degree σ _1,2, need to be with cloud

Be converted to certain the honest concept among the S.Because the degree of certainty of a water dust can reflect that it is under the jurisdiction of the degree of certain qualitativing concept, utilization of the present invention Definite degree of middle water dust is realized above-mentioned conversion, and detailed process is as follows:

At first, will

Three numerical characteristic Ex, En and He bring equation (1) and equation (2) repeatedly into, it is different to calculate N

Wherein, equation (1) expression as expected value and standard deviation, utilizes statistical calculation method to produce a normal random number with En and He

Equation (2) expression with Ex and

As expected value and standard deviation, utilize statistical calculation method to produce a normal random number v.

$\widetilde{\mathrm{En}}~N(\mathrm{En},{\left(\mathrm{He}\right)}^2)---\left(1\right)$

$v~N(\mathrm{Ex},{\left(\widetilde{\mathrm{En}}\right)}^2)---\left(2\right)$

Then, will

With It is different repeatedly to bring N of equation (1) generation into

(1≤i≤N).

Then, will With

Repeatedly bring equation (3) into and generate N different ud _Ki, this value has embodied

Water dust

To cloud

The degree of certainty of the honest concept of representative.

$\mathrm{ud}=\exp [-\frac{1}{2}{(v-\mathrm{Ex})}^2/{\left(\widetilde{\mathrm{En}}\right)}^2]---\left(3\right)$

At last, calculate N different ud according to formula (4) _KiArithmetic mean σ _k:

${\mathrm{\&sigma;}}_k=\frac{1}{N}{\mathrm{\&Sigma;}}_{i=1}^N{\mathrm{ud}}_{\mathrm{ki}}---\left(4\right)$

σ _kIt is larger,

More can embody

Feature, then make σ _1,2=max{ σ ₁, σ ₂..., σ _L, i.e. E ₂With respect to E ₁Honest degree.

Step 3: according to E ₂To E ₁Honest degree σ _1,2And E ₂To E ₃Direct degree of belief Calculate E ₁To E ₃The transmission degree of belief

Concrete grammar is,

${\mathrm{Ex}}^{E_1{\mathrm{<figure-callout\; id="3"\; label="E"\; filenames="HDA00002675178200021.png"\; state="\{\{state\}\}">E</figure-callout>}}_3}={\mathrm{\&sigma;}}_{\mathrm{1,2}}{\mathrm{Ex}}_2^{\mathrm{TC}},$ ${\mathrm{En}}^{E_1{\mathrm{<figure-callout\; id="3"\; label="E"\; filenames="HDA00002675178200021.png"\; state="\{\{state\}\}">E</figure-callout>}}_3}=(1+{\mathrm{\&sigma;}}_{\mathrm{1,2}}){\mathrm{En}}_2^{\mathrm{TC}},$ ${\mathrm{He}}^{E_1{\mathrm{<figure-callout\; id="3"\; label="E"\; filenames="HDA00002675178200021.png"\; state="\{\{state\}\}">E</figure-callout>}}_3}=(1+{\mathrm{\&sigma;}}_{\mathrm{1,2}}){\mathrm{He}}_2^{\mathrm{TC}}$

Step 4: repeated execution of steps two and step 3, calculate successively E _J+1With respect to E ₁Honest degree σ _{1, j+1}And E ₁To E _J+2The transmission degree of belief

Concrete grammar is,

${\mathrm{Ex}}^{E_1{E}_{j+2}}={\mathrm{\&sigma;}}_{1,j+1}{\mathrm{Ex}}_{j+1}^{\mathrm{TC}},$ ${\mathrm{En}}^{E_1{E}_{j+2}}=(1+{\mathrm{\&sigma;}}_{1,j+1}){\mathrm{En}}_{j+1}^{\mathrm{TC}},$ ${\mathrm{He}}^{E_1{E}_{j+2}}=(1+{\mathrm{\&sigma;}}_{1,j+1}){\mathrm{He}}_{j+1}^{\mathrm{TC}},j=\mathrm{2,3},...p-2$

Until calculate E ₁To E _pThe transmission degree of belief

The content that is not described in detail in this specification belongs to the known prior art of this area professional and technical personnel.

Claims (1)

1. support the transmission degree of belief appraisal procedure that cooperation is safe in a Distributed Open Environments, specifically may further comprise the steps:

Step 1: definition trust value space TV, trust concept space T, trust cloud TC (Ex, En, He), trust concept cloud TCC (Ex, En, He), the basic conception of honest value space S V, honest concept space S and honest concept cloud SCC (Ex, En, He);

Step 2: consider p entity E ₁, E ₂..., E _pThe trust transitive relation, only have adjacent two entities to know well, i.e. E _iWith E _I+1Know well, 1≤i≤p-1, other entities are mutually strange, work as E _pRequest and E ₁During cooperation, E ₁Need to pass through by E ₂, E ₃..., E _P-1The information evaluation E that the recommendation paths that consists of provides _pCredibility, E _iWith E _I+1The experience that direct interaction is arranged, E _iTo E _I+1Direct degree of belief

Known, E then _iAccording to trusting cloud

How decision treats E _I+1To E _I+2Recommendation, at first according to E ₁To E ₂Direct degree of belief calculate E ₂With respect to E ₁Honest degree σ _1,2, be specially:

(2.1) with E ₁To E ₂Direct degree of belief

Three numerical characteristic Ex, En and He bring equation (1) and equation (2) repeatedly into, it is different to calculate N

$\widetilde{\mathrm{En}}~N(\mathrm{En},{\left(\mathrm{He}\right)}^2)---\left(1\right)$

$v~N(\mathrm{Ex},{\left(\widetilde{\mathrm{En}}\right)}^2)---\left(2\right)$

(2.2) will trust the concept cloud

With

It is different repeatedly to bring N of equation (1) generation into

(2.3) will

With

Repeatedly bring equation (3) into and generate N different ud _Ki, this value has embodied

Water dust

To cloud

The degree of certainty of the honest concept of representative;

$\mathrm{ud}=\exp [-\frac{1}{2}{(v-\mathrm{Ex})}^2/{\left(\widetilde{\mathrm{En}}\right)}^2]---\left(3\right)$

At last, calculate N different ud according to formula (4) _KiArithmetic mean σ _k:

${\mathrm{\&sigma;}}_k=\frac{1}{N}{\mathrm{\&Sigma;}}_{i=1}^{N}u{d}_{\mathrm{ki}}---\left(4\right)$

σ _kIt is larger,

More can embody

Feature, then make σ _1,2=max{ σ ₁, σ ₂..., σ _L, i.e. E ₂With respect to E ₁Honest degree;

Step 3: according to E ₂To E ₁Honest degree and E ₂To E ₃Direct degree of belief calculate E ₁To E ₃The transmission degree of belief, be specially:

(3.1) according to E ₂To E ₁Honest degree σ _1,2And E ₂To E ₃Direct degree of belief

Calculate E ₁To E ₃The transmission degree of belief

In

${\mathrm{Ex}}^{E_1{E}_3}={\mathrm{\&sigma;}}_{\mathrm{1,2}}{\mathrm{Ex}}_2^{\mathrm{TC}};$

(3.2) according to E ₂To E ₁Honest degree σ _1,2And E ₂To E ₃Direct degree of belief Calculate E ₁To E ₃The transmission degree of belief

In

${\mathrm{En}}^{E_1{E}_3}=(1+{\mathrm{\&sigma;}}_{\mathrm{1,2}}){\mathrm{En}}_2^{\mathrm{TC}};$

(3.2) according to E ₂To E ₁Honest degree σ _1,2And E ₂To E ₃Direct degree of belief

Calculate E ₁To E ₃The transmission degree of belief

In

${\mathrm{He}}^{E_1{E}_3}=(1+{\mathrm{\&sigma;}}_{\mathrm{1,2}}){\mathrm{He}}_2^{\mathrm{TC}};$

Step 4: according to the method for step 2 and step 3, calculate successively E _J+1With respect to E ₁Honest degree and E ₁To E _J+2The transmission degree of belief, j=2,3 ... p-2, until calculate E ₁To E _pThe transmission degree of belief

Be specially:

(4.1) according to the described honest degree computational methods of step 2, calculate successively E _J+1With respect to E ₁Honest degree σ _{1, j+1}, j=2,3 ... p-2;

(4.2) according to the described transmission degree of belief of step 3 computational methods, calculate successively E ₁To E _J+2The transmission degree of belief

Concrete grammar is:

${\mathrm{Ex}}^{E_1{E}_{j+2}}={\mathrm{\&sigma;}}_{1,j+1}{\mathrm{Ex}}_{j+1}^{\mathrm{TC}},$ ${\mathrm{En}}^{E_1{E}_{j+2}}=(1+{\mathrm{\&sigma;}}_{1,j+1}){\mathrm{En}}_{j+1}^{\mathrm{TC}},$ ${\mathrm{He}}^{E_1{E}_{j+2}}=(1+{\mathrm{\&sigma;}}_{1,j+1}){\mathrm{He}}_{j+1}^{\mathrm{TC}},j=\mathrm{2,3},...p-2$

Until calculate E ₁To E _pThe transmission degree of belief

Images