CN103577664A - Comprehensive evaluation system for combination rules under mixed Dezert-Smarandache (DSm) model - Google Patents
Comprehensive evaluation system for combination rules under mixed Dezert-Smarandache (DSm) model Download PDFInfo
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- CN103577664A CN103577664A CN201210258255.9A CN201210258255A CN103577664A CN 103577664 A CN103577664 A CN 103577664A CN 201210258255 A CN201210258255 A CN 201210258255A CN 103577664 A CN103577664 A CN 103577664A
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Abstract
The invention discloses a comprehensive evaluation system for combination rules under a mixed DSm model. A comprehensive evaluation index system of combination rules is established, first-grade indexes of the index system are composed of synthetic properties, timing properties and engineering usable properties. Second indexes of the synthetic properties are high-conflict resistance and low-conflict adaptability, second indexes of the timing properties are interchangeability and quasi associativity, second indexes of the engineering usable properties are complexity and robustness, and the index system is shown in figure 1. Besides, the evaluation indexes are defined and modeled. According to the comprehensive evaluation system, properties of the combination rules under the mixed DSm model are analyzed comprehensively, the evaluation index system is established, and bases are provided for evaluation and selection of the combination rules; definitions and models of the evaluation indexes are given, so that the combination rules can be evaluated objectively and specifically; the combination rules under the mixed DSm model can be evaluated, and a free DSm model and a Shafer model can be evaluated by adding corresponding constraint conditions, so that the system has wide application values.
Description
Technical field
The present invention has created the overall evaluation system of rule of combination under a kind of DSm of mixing model, can, for the multianalysis to rule of combination, realize the comprehensive evaluation of rule of combination, practical application and improved definite.
Background technology
Dezert-Smarandache theoretical (DSm is theoretical) is a kind of important Uncertain Reasoning Theory, and it can either be processed traditional mutual exclusion and merges problem, can process again fuzzy in actual fused, uncertain, conflict etc. more complicated problem.The Shafer model that not only has Dempster-Shafer theoretical (DS is theoretical) in DSm theory, has also increased free DSm model and has mixed DSm model.The deficiency of Shafer model on representing of having mixed DSm model extension, and do not exist free DSm model because a lot of parts of segmentation cause the defects that there is no physical significance.Mixing DSm model can have fuzzy concept and discrete hypothesis simultaneously, has added constraint condition, makes DSm theory under mixing DSm model, to process the dynamic fusion problem in reality.Therefore, mixing DSm model is the universal model that can be applicable to various conditions, and other two models can be regarded as the special case of mixing DSm model.Good nature due to DSm theory, a lot of experts and scholars have carried out more deep research to it, many rules of combination based on DSm theory have been proposed, these rules are processed evidence from different angles, as processed rule of combination of the rule of combination of conflicting evidence, the rule of combination of considering evidence order, calculated amount control etc.But how rule of combination being evaluated, and also do not generally acknowledged effective method for the applicable rule of combination of different application How to chooses, is problem demanding prompt solution.Therefore, need to be for the overall evaluation system of rule of combination under the intension of DSm theory and characteristic systematic study mixing DSm model.
Summary of the invention
Object of the present invention proposes for the weak point in above-mentioned background technology just.The present invention has built the overall evaluation system that mixes rule of combination under DSm model.Model the System of Comprehensive Evaluation of rule of combination, the first class index of index system can consist of by three of character synthesising property, sequential character and engineering, wherein the two-level index of synthesising property is anti-high conflict property and low conflict adaptability, the two-level index of sequential character is exchangeability and accurate associativity, engineering can be complicacy and robustness with the two-level index of character, and index system as shown in Figure 1.Secondly evaluation index is defined, has set up model.By setting up such overall evaluation system, the feature of rule of combination is evaluated, can be provided foundation for engineering technical personnel's evaluation, selection and improvement.Engineering technical personnel can be according to specific tasks and actual requirement, and in conjunction with evaluation conclusion, reasonably evaluation, Selection and Constitute rule, make effect reach best.
In order to realize above-mentioned goal of the invention, the invention provides the overall evaluation system of rule of combination under a set of mixing DSm model.
The overall evaluation system that mixes rule of combination under DSm model is two-level index system, the first class index of index system can consist of by three of character synthesising property, sequential character and engineering, wherein the two-level index of synthesising property is anti-high conflict property and low conflict adaptability, the two-level index of sequential character is exchangeability and accurate associativity, engineering can be complicacy and robustness with the two-level index of character, and index system as shown in Figure 1.
(1) synthesising property, whether synthetic result meets people's reasoning from logic.The two-level index of synthesising property is anti-high conflict property and low conflict adaptability, represents respectively whether reasonable to high and low conflicting evidence result.Conventional combination rule is main considers anti-high conflict property, and two kinds of character of rule of combination of evaluating based on mixing DSm model all will be considered.
1. anti-high conflict property
Anti-high conflict property, the i.e. rationality of rule of combination to high combination of conflicting evidence result.If rule of combination can not effectively be processed high conflicting evidence, obtain the conclusion different with intuition, be referred to as antinomy.According to the conflict spectrum of evidence and feature, can be divided into three kinds: the antinomy of entirely conflicting, 0 is trusted antinomy, 1 and trusted antinomy.The character so anti-high conflict property is also divided three classes accordingly.
Full conflict antinomy.If distributing, the basic reliability of any two evidences under framework of identification conflicts completely, i.e. k=1 between the two, even if the consistance that the basic reliability of other most of evidences is distributed is fine, can not use Dempster composition rule, be called full conflict antinomy.
0 trusts antinomy.If the basic reliability of a certain burnt unit of an evidence in a plurality of evidences under framework of identification is assigned as 0, and in this Jiao unit and same evidence, to distribute the common factor of Jiao unit that is not 0 be not itself to other basic reliability, no matter other evidence is assigned much to the basic reliability of this Jiao unit, in synthetic result, the basic reliability distribution of this Jiao unit is always 0, is called 0 trust antinomy.
1 trusts antinomy.Suppose framework of identification Θ={ θ
1, θ
2..., θ
nunder have l evidence, the basic reliability of i evidence is assigned as m
i(E
j), E
jfor burnt unit, i=1,2 ..., l, j=1,2 ..., N, N is the number of burnt unit, N≤2
n-1, if existed
Wherein
and k=1-a
l, m (A)=1 after synthesizing.Even when a value is very little, there will be the false inference that synthetic result is 1, be called 1 trust antinomy.
Mixing under DSm model, when rule of combination is synthetic to evidence, conflict determines its reservation or redistributes according to constraint condition.Constraint condition can be divided into two classes: a class is the repellency constraint between proposition; Another kind of is that proposition is compatible but learn in practice also non-existent non-existence constraint according to priori.According to the relation between constraint condition and high conflicting evidence, to mix DSm model and can be divided into conflicting associations mixing DSm model, part conflicting associations mixing DSm model and standard are mixed DSm model.Even two class constraints are irrelevant with the high proposition that conflicts, and model is that standard is mixed DSm model.If two class constraints exist part relevant to high conflict proposition, model is part conflicting associations mixing DSm model.If two class constraints are all relevant to high conflict proposition, model is conflicting associations mixing DSm model.
2. low conflict adaptability
Low conflict adaptability, the i.e. rationality of rule of combination to low combination of conflicting evidence result.Owing to having added the focal element of conflict, the rule of combination based on mixing DSm model can better be processed high conflicting evidence, but the feature that exists burnt unit to disperse when processing low conflicting evidence.So will the adaptability to low conflicting evidence analyze it the rule of combination based on mixing DSm model.
Define main burnt unit, Jiao unit that main burnt unit is basic reliability apportioning cost maximum in this belief function.When like this two first belief functions of same main Jiao are synthesized, main burnt unit should not change, and keeps low conflict adaptability.
To mixing the analysis to low conflicting evidence handling property normally of DSm model group, consider the relation of main burnt unit and constraint condition.Seemingly, but in low conflict analysis, main burnt unit only has one to the analysis classes of low conflict analysis and high conflict situations, does not have the problem of partial association.According to the relation of main burnt unit and constraint condition, model is divided into associated DSm model and the first dereferenced mixing of the main Jiao DSm model of mixing of main burnt unit.The associated DSm model that mixes of main burnt unit refers to that the constraints limit the focal element of conflict associated with main burnt unit is sky.Otherwise be the first dereferenced mixing of main Jiao DSm model.
(2) sequential character, the synthetic order of evidence to synthetic result whether influential and effect.The two-level index of sequential character is exchangeability and associativity.Sequencing problem when two evidences of exchangeability consideration are synthetic, when many evidences of associativity consideration are synthetic, order is synthesized between two with non-order and is synthesized between two the relation of result.
1. exchangeability
Exchangeability is illustrated in the situation of synthetic evidence without any priori, thinks that two evidences are equality, and the order of transposing combination does not change combined result.
2. accurate associativity
Associativity is illustrated in the situation of combined evidence without any priori, and the combined result of many evidences is not affected by the combination order of evidence completely,
meet
Mixing under DSm model, due to the existence of various boundary conditions, its associativity is difficult to meet, and in order to evaluate the synthetic impact on proof results of the sequential of mixing under DSm model, introduces the concept of accurate associativity.
Mixing under DSm model, use certain rule of combination to synthesize evidence, if evidence obtains identical final decision according to the synthetic result of different orders, think that so this rule of combination has accurate associativity.
(3) engineering can be used character, and whether rule of combination possesses practicality in actual engineering application.Engineering can be complicacy and robustness with the two-level index of character.Complicacy is that rule of combination carries out the calculated amount of evidence when synthetic.When robustness is the subtle change of evidence, the intensity of variation of result.When many evidences are synthetic, two kinds of character all need to consider.
1. complicacy
In DSm theory, added the focal element of conflict, burnt first quantity is obviously increased, calculated amount is the key factor of its application of restriction.The complicacy of rule of combination need to be analyzed to main calculated amount (main calculated amount refers to the number of times that need to carry out multiplication or division arithmetic).Defined and mixed the complicacy under DSm model.
Mixing under DSm model, having n dimension framework of identification Θ={ θ
1, θ
2..., θ
n, according to respective limits condition, the burnt metaset of maximum possible is D
Θ, burnt first number is | D
Θ|, to k bar evidence
j=1,2 ..., k, l=1,2 ..., | D
Θ|,
the complicacy that is called this rule of combination with the synthetic multiplication of the required computing of this k bar evidence of certain rule of combination and the number of times of division, is expressed as O
dSmT(f (n, k)).
2. robustness
Robustness refers to that, when the little variation of belief function generation of the burnt unit of evidence, the variation of matter can not occur its combined result or in allowed limits, main burnt unit does not have to change before and after combination.
The invention has the advantages that:
(1) character of rule of combination under mixing DSm model has been carried out to comprehensive analysis and set up assessment indicator system, to the evaluation of rule of combination and selection, provide foundation;
(2) provided detailed evaluation index definition and corresponding model, rule of combination has been carried out to objective, evaluation particularly.Can not only effectively to the rule of combination mixing under DSm model, evaluate, add corresponding constraint condition to evaluate free DSm model and Shafer model.
Accompanying drawing explanation
Fig. 1 is the overall evaluation system entire block diagram of rule of combination under mixing DSm model of the present invention.
The overall evaluation system that mixes rule of combination under DSm model is two-level index system, the first class index of index system can consist of by three of character synthesising property, sequential character and engineering, wherein the two-level index of synthesising property is anti-high conflict property and low conflict adaptability, the two-level index of sequential character is exchangeability and accurate associativity, engineering can be complicacy and robustness with the two-level index of character, and index system as shown in Figure 1.
Claims (2)
1. mix the overall evaluation system of rule of combination under DSm model, be specially:
The overall evaluation system that mixes rule of combination under DSm model is two-stage index system, the first class index of index system can consist of by three of character synthesising property, sequential character and engineering, wherein the two-level index of synthesising property is anti-high conflict property and low conflict adaptability, the two-level index of sequential character is exchangeability and accurate associativity, and engineering can be complicacy and robustness with the two-level index of character.
2. the overall evaluation system of rule of combination under mixing according to claim 1 DSm model, specific targets are defined as:
1) synthesising property, whether synthetic result meets people's reasoning from logic.The two-level index of synthesising property is anti-high conflict property and low conflict adaptability, represents respectively whether reasonable to high and low conflicting evidence result.
2) sequential character, the synthetic order of evidence to synthetic result whether influential and effect.The two-level index of sequential character is exchangeability and associativity.Sequencing problem when two evidences of exchangeability consideration are synthetic, when many evidences of associativity consideration are synthetic, order is synthesized between two with non-order and is synthesized between two the relation of result.
3) engineering can be used character, and whether rule of combination possesses practicality in actual engineering application.Engineering can be complicacy and robustness with the two-level index of character.Complicacy is that rule of combination carries out the calculated amount of evidence when synthetic.When robustness is the subtle change of evidence, the intensity of variation of result.
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|---|---|---|---|---|
| CN101639864A (en) * | 2009-08-18 | 2010-02-03 | 东南大学 | Multi-level hierarchical DSmT rapid approximate reasoning fusion method |
| CN102222240A (en) * | 2011-06-29 | 2011-10-19 | 东南大学 | DSmT (Dezert-Smarandache Theory)-based image target multi-characteristic fusion recognition method |
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Patent Citations (2)
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|---|---|---|---|---|
| CN101639864A (en) * | 2009-08-18 | 2010-02-03 | 东南大学 | Multi-level hierarchical DSmT rapid approximate reasoning fusion method |
| CN102222240A (en) * | 2011-06-29 | 2011-10-19 | 东南大学 | DSmT (Dezert-Smarandache Theory)-based image target multi-characteristic fusion recognition method |
Non-Patent Citations (3)
| Title |
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| ROLF HAENNI: "Letter to the Editor Are alternatives to Dempster’s rule of combination real alternatives? Comments on"About the belief function combination and the conflict management problem"–Lefevre et al", 《INFORMATION FUSION》 * |
| 侯俊: "证据推理的组合方法_评价体系与应用研究", 《中国博士学位论文全文数据库 信息科技辑》 * |
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Application publication date: 20140212 |