CN108763793A - A kind of Weighted Fuzzy type D-S evidence theory frame - Google Patents
A kind of Weighted Fuzzy type D-S evidence theory frame Download PDFInfo
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Abstract
The present invention proposes a kind of Weighted Fuzzy type D-S evidence theory frame.For D-S evidence theory, BPA obtains difficult problem in the application of data fusion, the frame is based on D-S evidence theory, data to be fused are subjected to Attribute transposition first, then class method will be generated to be combined with differentiation class method, respectively using fuzzy naive Bayesian and FCM algorithm construction models；The BPA stages are being generated, uncertain information is expressed by defining uncertain region, is recycling fuzzy membership and the distance between sample and barycenter to obtain respectively and generates class BPA and differentiate class PBA, compound BPA is obtained finally by believable mathematical model；The compound BPA from each model is merged using the composite formula of D-S evidence theory, final decision is obtained after being converted finally by Pignstic probability.The frame can efficiently complete data fusion task, and fusion accuracy is high, mean difference is small, and can clearly handle it is different classes of between uncertainty.
Description
Technical field
The present invention relates to a kind of Weighted Fuzzy type D-S evidence theory frames, belong to information technology field.
Background technology
D-S evidence theory [1] provides a kind of effective method to solve uncertainty and the information from multiple sources
Integration.It does not need prior probability or conditional probability, and the difference between " uncertain " and " not knowing " can be good at retouching
It states out, is a kind of extension to probability theory.
The reasoning process of D-S evidence theory is integrally built upon on the basis of identification framework, and basic ideas are as follows：
(1) identification framework is established.Utilize the technique study project of set theory；
(2) initial trust distribution is established.The degree of support that total amount is 1 is distributed to knowledge by the information provided according to evidence
Each subset (i.e. proposition) in other frame is as the degree of support to each subset, but the degree of support cannot be specifically thin again
It assigns in the proper subclass of the subset.
(3) degree of belief of all propositions is calculated.According to causality, if certain evidence supports a proposition, this evidence
To equally support the conclusion obtained by this proposition, thus total degree of belief of a proposition be equal to his all premise propositions just
The sum of beginning degree of belief.
(4) combining evidences.D-S evidence theory provides ripe combining evidences formula, the information that multiple evidences are provided
Synthesis, after fusion, obtain on evidence to total degree of belief of each proposition.
(5) decision.The degree of belief obtained according to combining evidences, using certain selection rule as decision-making foundation, selection is known
Some proposition in other frame is as decision.The maximum proposition of degree of belief is selected under normal circumstances.
Weighted Fuzzy type frame proposed by the invention is exactly to build a kind of fusion from the angle for how constructing BPA
Precision is high, stability is good, can handle the D-S evidence theory frame of uncertain information.
The prior art related to the present invention：
The design of BPA usually will be according to designing in practical application the characteristics of multi-source data, and the construction of BPA is needed based on close
Spend the generation method of estimation and the method for discrimination based on distance function.For generation method, BPA can be simply considered that
It is a probability function, it is usually associated with probability distribution, fuzzy membership or probability function；For method of discrimination, usually
BPA is defined using concept of some relativities, such as distance, feature or similitude etc..
In research at home and abroad, Yager utilizes the concept of intuitionistic Fuzzy Sets, with a set that Imprecise probability is intuitive
Ground shows.In Fuzzy Set Theory, inaccurate membership can be indicated with two different modes：Interval value mould
Paste collection and intuitionistic Fuzzy Sets.It, can be with one by conviction and confidence level with relevant inaccurate probability is gathered under DS frames
The section of definition is measured to indicate.Document [2] uses the normal distribution model of each attribute of data to construct a nesting
BPA structures, avoid the high conflict between evidence.In document [3], Masson and Denoeux are by D-S is theoretical and degree of belief
Division is combined to solve the degree of belief partition problem in computing object data.Denoeux has also been proposed one kind in document [4]
Novel sorting technique, he combines K arest neighbors (KNN, K-Nearest Neighbor) algorithm and D-S evidence theory proposes
K-NN-DST rules.
Therefore these methods each the advantages of having oneself by oneself and disadvantage are inspired by the above author and viewpoint, some scholars attempt
These methods are combined and make new improvement to maximize favourable factors and minimize unfavourable ones.Pal and Ghosh also proposed one kind in document [5] as a result,
The mass function of BPA is determined in conjunction with arest neighbors sort algorithm (RNN, Recurrent Neural Networks) and DS theories
Method.In addition, being suggested in document [6] [7] based on the D-S evidence theory of neural network, in the text, the determination of BPA is
It is realized by regarding the relationship between reference model as the evidence each assumed.Recently, Boudaren and
Pieczynski [8] proposes a kind of broad sense evidence Markov model, it provides wider modeling ability, can locate simultaneously
Manage the fusion of uncertain information and multi-source data.Smets and Kennes [9] establish transitive trust models (TBM,
Tansferable Belief Model), with a kind of function all unrelated with any elementary probability model come quantization uncertainty.
Invention content
BPA (basic probability assignment, Basic Probability Assignment) in evidence theory represents evidence
To the degree of faith of a proposition, so it is exactly to find one to carry out an important step of data fusion in D-S evidence theory
Suitable Basic probability assignment function, so that evidence is distributed to each possible state.It intuitively, may for each
State, BPA represents a kind of degree of support of evidence for " system belongs to this state " this proposition.And combining evidences exist
It is exactly the combination of several probability numbers substantially on its realization rate, therefore the make and construction of Basic probability assignment function BPA
As a result just directly determine whether the conclusion after Evidence Combination Methods is reliable.The BPA constructed should have robustness, define
The data or parameter of BPA significantly should not generate interference when generating small sample perturbations to the mass functions distributed.
Description of the drawings
Fig. 1 Weighted Fuzzy D-S evidence theory frame algorithm figures；
The uncertain regions Fig. 2 schematic diagram；
Specific implementation mode
D-S evidence theory frame (as shown in Figure 1) proposed by the present invention：
Step 1：Attribute transposition
For a given cube, each single attribute (or feature) can be viewed as one it is independent
Information source can also be considered as multidimensional even if there is multiple attributes to be from same data source.In order to be obtained from evidence
Reliable integrated decision-making first asks the BPA of each attribute that D-S evidence theory is recycled to be synthesized respectively.
After Attribute transposition, the test data set with p attribute is just divided and is converted into the p in text independent moulds
Type.When applied to D-S evidence theory frame, because data are entered as evidence, this part can also be called card
According to division.
Step 2：Compound BPA is generated
Generate BPA functions first have to will set C as identification framework：
Identification framework power set 2θBurnt member be expressed as：
Ω={ { C1..., { CN, { C1, C2..., { Ci, Cj..., { CN-1, CN}} (2)
Wherein, complex element { Ci, Cj(i ≠ j) be uncertain it is assumed that we do not examine in this research in D-S evidence theory
Consider the coke member that radix is more than 2.
In order to more intuitively understand that the complex element in identification framework, each classification are modeled using Gaussian Profile, such as
Shown in Fig. 2, represents kth item attribute and belong to classification CiOr CjSubjection degree.The left side is blackish green and the right blue region generation respectively
Table CiAnd CjGaussian Profile, the region of intermediate coincidence is uncertain region (ROU, Region of Uncertainty),
So the sample fallen in ROU can be difficult to recognize, because they largely have simultaneously, there are two different classes of property, institutes
Classification error may be will produce with the identification mission of this part sample.It is, therefore, apparent that we need to indicate compound vacation using ROU
If { Ci, Cj, uncertain data divided with this.In this way, for each attribute, can obtain N number of Gaussian Profile andA ROU functions carry out the model respectively as single hypothesis and composite hypothesis.
It when calculating the elementary probability for being assigned to each burnt member, is obscured using fuzzy Nae Bayesianmethod and FCM algorithms
It is subordinate to angle valueIt is used to represent each attribute and belongs to different classes of degree.Given input sample
This, for attribute x, the angle value that is subordinate to of calculating is：
For composite hypothesis { Ci, Cj, the variance of the degree of membership under each fuzzy division is calculated after classification:
Wherein, M is it is expected, subordinated-degree matrix is
One variance yields D (u) of setting is used as threshold value, under the division, the side of the degree of membership of every a line of subordinated-degree matrix U
Value of the average value of difference as D (u).As D (ui) < D (u) when think the sample largely while there are two categories
The property of label.
Since the object in uncertain region can belong to CiClass, and C can be belonged tojClass, so using a fuzzy AND
Operator come distribute with the relevant mass function of composite hypothesis, in this way, each of being calculated by fuzzy Nae Bayesianmethod
The Basic probability assignment function of hypothesis is：
Similarly, in the case that appropriate normalized, formula 5 and 6 possibly can not generate effective BPA.In formula 6
In, for ∧ operations, any triangle normal form (T-Norm) can be used, has selected minimum value as triangle model in the present invention
Formula.
Next, according to FCM algorithms, input sample and class centroid vector are utilizedBetween Europe
A few Reed distances differentiate class elementary probability to determine.Therefore, we based on this concept, are defined using ROU as composite hypothesis
CrosspointFor the class centroid of composite hypothesis, its value is to pass through two kinds of different classes of Ci、CjThe calculated tool of distribution
There is the point of minimum AND values：
The method for defining differentiation type BPA functions is the exponential function using sample and class centroid distance：
The frame is more flexible, can more have preferable performance in practical applications in order to make, and proposes a kind of weighting adjustment frame
Different evidences are collected and be integrated.The generation class BPA that fuzzy Nae Bayesianmethod generates：And based on away from
From differentiation class BPA：It can be integrated by following equation：
Wherein, 0≤α, β >=1 are the adaptive adjustment parameters for determining two class evidence importance, this weighting regulation mechanism can be with
Enable us to find the appropriate weighting for different evidence sources from training data, minimizing training using grid search misses
Difference is found optimal adjustment parameter, is not repeated training process herein.In addition, there is still a need for emphasize in formula 5,6,8,9WithAnd non-final BPA itself.
The whole BPA of feature x：mxThe definition of ({ }) is exactly：
Wherein, K is the condition for meeting formula 2-7, so that equation is obtained the normalization factor of effective BPA, for each
A attribute is all corresponding to it there are one optimal collection (α, β)：
Step 3：The synthesis of BPA
Then, the BPA generated by different attribute is combined to obtain comprehensive BPA using Dempster composition rules.
According to D-S combining evidences formula shown in formula 2-13 and formula 2-15, we can obtain one from each independent sources of information
A comprehensive BPA.
The synthesis of (one) two evidence function
A certain proposition A, forProposition A is for two mass functions on the θ on same identification framework：m1, m2,
Their Dempster composition rules are：
Wherein, symbolIndicate it is orthogonal and.It is normaliztion constant to make the sum of mass function be 1, K：
(2) synthesis of multiple evidences
ForAs the limited a mass functions m for needing multiple evidence sources on processing identification framework θ1, m2..., mn
When, equally method orthogonal and as a basic trust function can be sought according to by multiple Basic probability assignment functions,
Dempster composition rules are：
Wherein, normaliztion constant K is：
Step 4：Pignistic probability is converted
Pignistic probability metrics are the maximum distance of each subset using under identification framework Θ as evidence distance.It utilizes
Pignistic probability metrics construct Certainty Factor, can judge the contradiction between evidence well.Therefore, of the invention
Using Pignistic probability metrics as evidence decision foundation.
Pignistic conversions refer to is converted into Pignistic probability functions by mass functions, function Bet PmIt indicates.
ForM (A) is defined in a Basic probability assignment function on identification framework θ, then it is on identification framework θ
Pignistic probability function Bet Pm：θ → [0,1]：
In above formula,Then above-mentioned equation can be reduced to：
After all BPA combinations are completed, comprehensive BPA is converted into one using formula 19 and focuses decision
Pignistic probability.
Step 5：Final decision
Finally, it is made a policy using Pignistic conversions.Hypothesis (classification) with maximum Pignistic probability is selected
Make the prediction classification of sample in test data.
The above method has quantified the evidence from each information source and has constructed its base respectively to single hypothesis and composite hypothesis
This probability distribution function defines composite hypothesis, in order to balance not homologous feature in our method using ROU, uses
Weighting adjusts framework and comes for single and composite hypothesis allocation probability.In practical applications, it is suitable to find that trained mechanism may be used
When weighting coefficient (α, β), they are applied into no evidence classification.
The advantageous effect that technical solution of the present invention is brought
For algorithm proposed by the present invention, partial data of the selection in UCI databases verify and and related algorithm
It is compared, the experimental results showed that, algorithm structure proposed by the present invention mainly enhances data fusion system in a manner of three kinds：
1) clearly handle it is different classes of between uncertainty, uncertainty is intuitively divided by ROU, will " not really
The information with " not knowing " is effectively distinguished calmly ", and obtained BPA is more accurate, therefore also has preferable syncretizing effect；
2) evidence from different data sources is efficiently integrated, data fusion result has higher precision, passes through each mould
The compound BPA of type, the support relationship between being intuitive to see each attribute and assuming, obtains percentage contribution of the evidence to decision
Etc. information.
3) mean difference of fusion accuracy is smaller, and algorithm has certain stability.
Claims (1)
1. proposing a kind of Weighted Fuzzy type D-S evidence theory data fusion frame, it is characterised in that：
A kind of Weighted Fuzzy type D-S evidence theory data fusion frame, comprises the steps of：
For a given multi-source data collection, extraction characteristic information carries out Attribute transposition, after Attribute transposition, has p
The test data set of attribute is just divided and is converted into p independent model in text；
Generation method is combined with method of discrimination, constructs BPA functions, detailed process is：First define uncertain region, generation side
Method calculates the elementary probability for being assigned to each burnt member using fuzzy Nae Bayesianmethod and FCM algorithms, and method of discrimination utilizes
Sample constructs basic probability function to the Euclidean distance of the distance of barycenter；
The BPA generated by different attribute is combined to obtain comprehensive BPA using Dempster composition rules；
Certainty Factor is constructed using Pignistic probability metrics, as evidence decision foundation；
The prediction classification of sample in test data is selected as with the hypothesis (classification) of maximum Pignistic probability.
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Cited By (9)
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| CN110046651A (en) * | 2019-03-15 | 2019-07-23 | 西安交通大学 | A kind of pipeline conditions recognition methods based on monitoring data multi-attribute feature fusion |
| CN110070118A (en) * | 2019-04-10 | 2019-07-30 | 广东电网有限责任公司 | A kind of multi-space data fusion method |
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| CN111047173A (en) * | 2019-12-05 | 2020-04-21 | 国网河南省电力公司 | Community credibility evaluation method based on improved D-S evidence theory |
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| CN111563532A (en) * | 2020-04-07 | 2020-08-21 | 西北工业大学 | Unknown target identification method based on attribute weight fusion |
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| CN110046651A (en) * | 2019-03-15 | 2019-07-23 | 西安交通大学 | A kind of pipeline conditions recognition methods based on monitoring data multi-attribute feature fusion |
| CN110070118A (en) * | 2019-04-10 | 2019-07-30 | 广东电网有限责任公司 | A kind of multi-space data fusion method |
| CN111104344B (en) * | 2019-11-06 | 2023-11-03 | 无锡科技职业学院 | D-S evidence theory-based distributed file system data reading method |
| CN111104344A (en) * | 2019-11-06 | 2020-05-05 | 无锡科技职业学院 | Distributed file system data reading method based on D-S evidence theory |
| CN111047173A (en) * | 2019-12-05 | 2020-04-21 | 国网河南省电力公司 | Community credibility evaluation method based on improved D-S evidence theory |
| CN111047173B (en) * | 2019-12-05 | 2022-09-09 | 国网河南省电力公司 | Community credibility evaluation method based on improved D-S evidence theory |
| CN111031042A (en) * | 2019-12-13 | 2020-04-17 | 电子科技大学 | Network anomaly detection method based on improved D-S evidence theory |
| CN111563532A (en) * | 2020-04-07 | 2020-08-21 | 西北工业大学 | Unknown target identification method based on attribute weight fusion |
| CN111563532B (en) * | 2020-04-07 | 2022-03-15 | 西北工业大学 | Unknown target identification method based on attribute weight fusion |
| CN113657429A (en) * | 2021-06-30 | 2021-11-16 | 北京邮电大学 | Data fusion method and device for digital twin city Internet of things |
| CN113657429B (en) * | 2021-06-30 | 2023-07-07 | 北京邮电大学 | Data fusion method and device for digital twin city Internet of things |
| CN117056827A (en) * | 2023-08-15 | 2023-11-14 | 合肥中科自动控制系统有限公司 | Asynchronous multi-mode target level information fusion method based on time sequence DS theory |
| CN117407833A (en) * | 2023-10-30 | 2024-01-16 | 山东农业大学 | Automatic monitoring system and method for identifying pathogenic spores of crops based on neural network |
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