The concept of conditional fuzzy measure

In this article a concept of conditional fuzzy measure is presented, which is a generalization of conditional probability measure. Its properties are studied in the general case and in some particular types of fuzzy measures as representable measures, capacities of order two, and belief-plausibility measures. In the case of capacities of order two it coincides with the concept given by Dempster for representable measures. However, it differs from the Dempster's rule for conditioning belief-plausibility measures. As it is shown, Dempster's rule of conditioning is based on the idea of combining information and our definition is based on a restriction in the set of possible worlds.     

Credibility decay model in temporal evidence combination

Data fusion in time domain is sequential and dynamic. Methods to deal with evidence conflict in spatial domain may not suitable in temporal domain. It is significant to determine the dynamic credibility of evidence in time domain. The Markovian requirement of time domain fusion is analyzed based on Dempster's combination rule and evidence discount theory. And the credibility decay model is presented to get the dynamic evidence credibility. Then the evidence is discounted by dynamic discount factor. It's illustrated that such model can satisfied the requirement of data fusion in time domain. Proper and solid decision can be made by this approach.     

COMBINING MULTIPLE CLASSIFIERS USING DEMPSTER'S RULE FOR TEXT CATEGORIZATION

In this paper we investigate the combination of four machine learning methods for text categorization using Dempster's rule of combination. These methods include Support Vector Machine (SVM), kNN (Nearest Neighbor), kNN model-based approach (kNNM), and Rocchio. We first present a general representation of the outputs of different classifiers, in particular, modeling it as a piece of evidence by using a novel evidence structure called focal element triplet. Furthermore, we investigate an effective method for combining pieces of evidence derived from classifiers generated by a 10-fold cross-validation. Finally, we evaluate our methods on the 20-newsgroup and Reuters-21578 benchmark data sets and perform the comparative analysis with majority voting in combining multiple classifiers along with the previous result. Our experimental results show that the best combined classifier can improve the performance of the individual classifiers and Dempster's rule of combination outperforms majority voting in combining multiple classifiers.     

一种基于众信度函数的相关证据合成方法

实际应用中,Dempster规则要求的证据独立性可能难以满足.在相关源证据已知的假设条件下,基于证据的众信度函数,提出一种相关证据合成方法. 该方法无需辨识独立证据的过程,可直接得到解析的合成结果,并且对相关源证据的形式没有要求.最后通过算例验证了所提出方法的有效性.     

Handling of Dependence in Dempster–Shafer Theory

Dempster's rule of combination can only be used when the bodies of evidence are assumed to be independent. However, such an assumption is often unrealistic. This paper proposes a systematic approach to handle dependence in evidence theory. It includes both the representation of dependence among information sources and the aggregation of the dependent evidence. For the representation of the dependence, the proposed methodology is able to capture both inner dependence (i.e., dependence among features of a system) and outer dependence (i.e., dependence among the evidence sources during the information propagating and evaluating process). We suggest dealing with the inner dependence by applying the analytic network process model, and modeling the outer dependence based on the intersection situations of the identified influencing factors. Then for the combination of dependent evidence, the strategy is to use discounting aggregation where the discounting coefficients are related to the degree of both outer and inner dependence. The discounting operator helps reduce the duplicate calculations in the fusion of dependent evidence and relax the assumption of independence when using Dempster's rule. A case study of transportation project evaluation is used to illustrate the proposed methodology.     

Implementing Dempster's rule for hierarchical evidence

This article gives an algorithm for the exact implementation of Dempster's rule in the case of hierarchical evidence. This algorithm is computationally efficient, and it makes the approximation suggested by Gordon and Shortliffe unnecessary. The algorithm itself is simple, but its derivation depends on a detailed understanding of the interaction of hierarchical evidence.     

Evidence combination using OWA-based soft likelihood functions

Dempster's combination rule has been widely regarded and applied since it is an effective and rigorous method of synthesizing multisource information with its special information representation (ie, mass function or basic probability assignment). However, it has also been criticized and debated upon regarding some of its unreasonable behaviors and restrictive requirements, such as the counterintuitive results in some cases. To address these issues from different perspectives, in this study, an alternative fusion rule is developed under the framework of Dempster-Shafer evidence theory. A novel evidence combination rule called CR-SLF is proposed based on soft likelihood functions (SLF) considering the ordered weighted average aggregation operator. Some illustrative examples are shown, and the corresponding analyses demonstrate the good performance of CR-SLF to fuse multisource evidence. To extend CR-SLF further, the reliability of multisource evidence is considered from two aspects, subsequently two reliability-based combination rules are presented, including the discount-based rule and the SLF improvement-based rule. The simulation results show that the reliability-based CR-SLF has a better fusion effect than the rule without considering the reliability.     

A new combination function in evidence theory

This article studies the combination of basic probability assignment (bpa) in evidence theory. After introducing an interpretation of the mass function we show that given two bpa Dempster's rule of combination does not build a coherent bpa with respect to the interpretation. Next we give a new combination function that overcomes this problem and study some of its properties. © 1995 John Wiley & Sons, Inc.     

Belief function combination and conflict management

Within the framework of evidence theory, data fusion consists in obtaining a single belief function by the combination of several belief functions resulting from distinct information sources. The most popular rule of combination, called Dempster's rule of combination (or the orthogonal sum), has several interesting mathematical properties such as commutativity or associativity. However, combining belief functions with this operator implies normalizing the results by scaling them proportionally to the conflicting mass in order to keep some basic properties. Although this normalization seems logical, several authors have criticized it and some have proposed other solutions. In particular, Dempster's combination operator is a poor solution for the management of the conflict between the various information sources at the normalization step. Conflict management is a major problem especially during the fusion of many information sources. Indeed, the conflict increases with the number of information sources. That is why a strategy for re-assigning the conflicting mass is essential. In this paper, we define a formalism to describe a family of combination operators. So, we propose to develop a generic framework in order to unify several classical rules of combination. We also propose other combination rules allowing an arbitrary or adapted assignment of the conflicting mass to subsets.     

A PROBABILISTIC-PROPOSITIONAL FRAMEWORK FOR THE O-THEORY INTERSECTION RULE

In a previous paper, O-theory (OT), a hybrid uncertainly theory was proposed for dealing with problems of uncertainty in logical inference. The foundations of one of the concepts introduced, the OT intersection operator, are explored in this paper. The developments rely solely on set-theoretic and probability notions which are the distinguishing features of this operator's role in the theory.

The OT intersection rule has as its basis Dempster's rule of combination which ties it closely to Dempster-Shafer theory. In this paper the OT rule will be shown to be based more fundamentally on classical probability theory. To demonstrate this, possibility sets are interpreted in a propositional framework and mass assignments are converted to the probabilistic form originally proposed by Dempster. These changes are used to show that the OT intersection rule can be derived from first principles in a probability theory of propositions. Since this derivation does not require conditional probabilities, it can be used as alternative to Bayes' theorem for combining conjunctive information consistently. Dempster's rule will be shown to be a special case of the OT intersection rule. It too will be derived using probability theory.

The formal connection between mass and probability presented originally by Dempster and used here in a propositional framework, makes distinctions between DST and probability theory less consequential. DST is still seen to be a generalization of the concept of probability, but it is also seen to fit within a probabilistic-propositiona) framework.     

Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence

Dempster's rule plays a central role in the theory of belief functions. However, it assumes the combined bodies of evidence to be distinct, an assumption which is not always verified in practice. In this paper, a new operator, the cautious rule of combination, is introduced. This operator is commutative, associative and idempotent. This latter property makes it suitable to combine belief functions induced by reliable, but possibly overlapping bodies of evidence. A dual operator, the bold disjunctive rule, is also introduced. This operator is also commutative, associative and idempotent, and can be used to combine belief functions issues from possibly overlapping and unreliable sources. Finally, the cautious and bold rules are shown to be particular members of infinite families of conjunctive and disjunctive combination rules based on triangular norms and conorms.     

About assessing and evaluating uncertain inferences within the theory of evidence

Dealing with uncertainty of facts and rules in an inference system will be discussed. The assessment and evaluation of uncertainties will be done within Dempster's and Shafer's theory of evidence. The relation between this theory and classical probability theory will be stressed.     

A hybrid approach to deductive uncertain inference

Deductive uncertain inference has been one of the most important ways of handling uncertainty. In this paper we report the development of a hybrid approach to such an inference. This approach has been implemented in a system which is based on INFERNO but integrates the strength of probabilisitc logic and Dempster's rule.     

The entailment principle for dempster—shafer granules

We discuss the rule of inference called the entailment principle which plays a significant role in the possibilistic type reasoning used in the theory of approximate reasoning. We extend this principle to situations in which the knowledge is a type of combination of possibilistic and probabilistic information which we call Dempster—Shafer granules. We discuss the conjunction of these D—S granules and show that Dempster's rule of combination is a special application of conjunction followed by a particular implementation of the entailment principle.     

On the dempster-shafer framework and new combination rules

We discuss the basic concepts of the Dempster-Shafer approach, basic probability assignments, belief functions, and probability functions. We discuss how to represent various types of knowledge in this framework. We discuss measures of entropy and specificity for belief structures. We discuss the combination and extension of belief structures. We introduce some concerns associated with the Dempster rule of combination inherent in the normalization due to conflict. We introduce two alternative techniques for combining belief structures. The first uses Dempster's rule, while the second is based upon a modification of this rule. We discuss the issue of credibility of a witness.     

A method for combining conflicting evidences with improved distance function and Tsallis entropy

For the sake of great ability of handling uncertain information, Dempster-Shafer evidence theory is extensively used in information fusion. Nevertheless, when there exists highly inconsistent evidences, using classical Dempster's combination rule may lead to counter-intuitive results. To address this issue, a new conflicting evidences combination method based on distance function and Tsallis entropy is proposed. Numerical examples are used to illustrate the feasibility and efficiency of the proposed method. Further, an fault diagnosis problem is used as an example to show the effectiveness and superiority of the proposed method. The proposed method outperforms other methods that the proposed method recognize the target by the probability 99.49%, which is higher than other methods.     

Evaluation method based on fuzzy relations between Dempster–Shafer belief structure

Many relations in the real world can be described by mathematical language. Fuzzy set theory can transform human language into mathematical language and use membership degree function to describe relations between events. Dempster–Shafer evidence theory provides basic probability assignment (BPA), which can describe the occurrence rate of attributes in basic events. Based on the known membership degree function and BPA distribution, a new evaluation method is proposed in this paper to analyze decision making. Given the relations among relevant events, which are expressed by BPA distribution and membership degree function, the relations among basic events and top event can be obtained. The Dempster's combination rule and pignistic probability transformation are used to transform BPA distribution into probability distribution. The belief measure is applied to deal with these fuzzy relations. Some numerical examples are given in this paper to illustrate the proposed evaluation methodology.     

A new divergence measure for basic probability assignment and its applications in extremely uncertain environments

Information fusion under extremely uncertain environments is an important issue in pattern classification and decision-making problems. The Dempster-Shafer evidence theory (D-S theory) is more and more extensively applied in dealing with uncertain information. However, the results contrary to common sense are often obtained when combining different evidence using Dempster's combination rule. How to measure the difference between different evidence is still an open issue. In this paper, a new divergence is proposed based on the Kullback-Leibler divergence to measure the difference between different basic probability assignments (BPAs). Numerical examples are used to illustrate the computational process of the proposed divergence. Then, the similarity for different BPAs is also defined based on the proposed divergence. The basic knowledge about pattern recognition is introduced, and a new classification algorithm is presented using the proposed divergence and similarity under extremely uncertain environments. The effectiveness of the classification algorithm is illustrated by a small example handling robot sensing. The proposed method is motivated by the urgent need to develop intelligent systems, such as sensor-based data fusion manipulators, which are required to work in complicated, extremely uncertain environments. Sensory data satisfy the conditions (1) fragmentary and (2) collected from multiple levels of resolution.     

实体异构性下证据链融合推理的多属性群决策

针对多属性群决策中可解释性证据融合推理的实体异构性问题,给出了一个实体异构性下证据链融合推理的多属性群决策方法.基于证据推理理论,引入证据链关联的概念,从多数据表提供的数据矩阵中获取可区分的近邻证据集,推导了各数据表的相似度矩阵,并构建半正定矩阵的二次优化模型,共享群决策专家的经验知识.使用Dempster正交规则,论证了异构实体之间可解释性推理中可信度融合的合理性,并使用证据融合规则集成各个数据表的近邻证据中获得的可信度,验证了调和多源异构数据中不一致信息的有效性.通过具有实体异构性的心脏病多决策数据诊断实例说明了方法的可行性与合理性.