In the theory of belief functions, the measure of uncertainty is an important concept, which is used for representing some types of uncertainty incorporated in bodies of evidence such as the discord and the non-specif...In the theory of belief functions, the measure of uncertainty is an important concept, which is used for representing some types of uncertainty incorporated in bodies of evidence such as the discord and the non-specificity. For the non-specificity part, some traditional measures use for reference the Hartley measure in classical set theory; other traditional measures use the simple and heuristic function for joint use of mass assignments and the cardinality of focal elements. In this paper, a new non-specificity measure is proposed using lengths of belief intervals, which represent the degree of imprecision. Therefore, it has more intuitive physical meaning. It can be proved that our new measure can be rewritten in a general form for the non-specificity. Our new measure is also proved to be a strict non-specificity measure with some desired properties. Numerical examples, simulations, the related analyses and proofs are provided to show the characteristics and good properties of the new non-specificity definition. An example of an application of the new non- specificity measure is also presented.展开更多
Dempster-Shafer evidence theory, also called the theory of belief function, is widely used for uncertainty modeling and reasoning. However, when the size and number of focal elements are large, the evidence combinatio...Dempster-Shafer evidence theory, also called the theory of belief function, is widely used for uncertainty modeling and reasoning. However, when the size and number of focal elements are large, the evidence combination will bring a high computational complexity. To address this issue,various methods have been proposed including the implementation of more efficient combination rules and the simplifications or approximations of Basic Belief Assignments(BBAs). In this paper,a novel principle for approximating a BBA into a simpler one is proposed, which is based on the degree of non-redundancy for focal elements. More non-redundant focal elements are kept in the approximation while more redundant focal elements in the original BBA are removed first. Three types of degree of non-redundancy are defined based on three different definitions of focal element distance, respectively. Two different implementations of this principle for BBA approximations are proposed including a batch and an iterative type. Examples, experiments, comparisons and related analyses are provided to validate proposed approximation approaches.展开更多
In the theory of belief functions,the evidence combination is a kind of decision-level information fusion.Given two or more Basic Belief Assignments(BBAs)originated from different information sources,the combination r...In the theory of belief functions,the evidence combination is a kind of decision-level information fusion.Given two or more Basic Belief Assignments(BBAs)originated from different information sources,the combination rule is used to combine them to expect a better decision result.When only a combined BBA is given and original BBAs are discarded,if one wants to analyze the difference between the information sources,evidence de-combination is needed to determine the original BBAs.Evidence de-combination can be considered as the inverse process of the information fusion.This paper focuses on such a defusion of information in the theory of belief functions.It is an under-determined problem if only the combined BBA is available.In this paper,two optimization-based approaches are proposed to de-combine a given BBA according to the criteria of divergence maximization and information maximization,respectively.The new proposed approaches can be used for two or more information sources.Some numerical examples and an example of application are provided to illustrate and validate our approaches.展开更多
In information fusion,the uncertain information from different sources might be modeled with different theoretical frameworks.When one needs to fuse the uncertain information represented by different uncertainty theor...In information fusion,the uncertain information from different sources might be modeled with different theoretical frameworks.When one needs to fuse the uncertain information represented by different uncertainty theories,constructing the transformation between different frameworks is crucial.Various transformations of a Fuzzy Membership Function(FMF)into a Basic Belief Assignment(BBA)have been proposed,where the transformations based on uncertainty maximization and minimization can determine the BBA without preselecting the focal elements.However,these two transformations that based on uncertainty optimization emphasize the extreme cases of uncertainty.To avoid extreme attitudinal bias,a trade-off or moderate BBA with the uncertainty degree between the minimal and maximal ones is more preferred.In this paper,two moderate transformations of an FMF into a trade-off BBA are proposed.One is the weighted average based transformation and the other is the optimization-based transformation with weighting mechanism,where the weighting factor can be user-specified or determined with some prior information.The rationality and effectiveness of our transformations are verified through numerical examples and classification examples.展开更多
基金supported by the Grant for State Key Program for Basic Research of China(No.2013CB329405)National Natural Science Foundation of China(No.61573275)+3 种基金Foundation for Innovative Research Groups of the National Natural Science Foundation of China(No.61221063)Science and Technology Project of Shaanxi Province of China(No.2013KJXX-46)Specialized Research Fund for the Doctoral Program of Higher Education of China(20120201120036)Fundamental Research Funds for the Central Universities of China(No.xjj2014122)
文摘In the theory of belief functions, the measure of uncertainty is an important concept, which is used for representing some types of uncertainty incorporated in bodies of evidence such as the discord and the non-specificity. For the non-specificity part, some traditional measures use for reference the Hartley measure in classical set theory; other traditional measures use the simple and heuristic function for joint use of mass assignments and the cardinality of focal elements. In this paper, a new non-specificity measure is proposed using lengths of belief intervals, which represent the degree of imprecision. Therefore, it has more intuitive physical meaning. It can be proved that our new measure can be rewritten in a general form for the non-specificity. Our new measure is also proved to be a strict non-specificity measure with some desired properties. Numerical examples, simulations, the related analyses and proofs are provided to show the characteristics and good properties of the new non-specificity definition. An example of an application of the new non- specificity measure is also presented.
基金the National Natural Science Foundation of China (Nos. 61671370, 61573275)Postdoctoral Science Foundation of China (No. 2016M592790)+1 种基金Postdoctoral Science Research Foundation of Shaanxi Province, China (No. 2016BSHEDZZ46)Fundamental Research Funds for the Central Universities, China (No. xjj201066)
文摘Dempster-Shafer evidence theory, also called the theory of belief function, is widely used for uncertainty modeling and reasoning. However, when the size and number of focal elements are large, the evidence combination will bring a high computational complexity. To address this issue,various methods have been proposed including the implementation of more efficient combination rules and the simplifications or approximations of Basic Belief Assignments(BBAs). In this paper,a novel principle for approximating a BBA into a simpler one is proposed, which is based on the degree of non-redundancy for focal elements. More non-redundant focal elements are kept in the approximation while more redundant focal elements in the original BBA are removed first. Three types of degree of non-redundancy are defined based on three different definitions of focal element distance, respectively. Two different implementations of this principle for BBA approximations are proposed including a batch and an iterative type. Examples, experiments, comparisons and related analyses are provided to validate proposed approximation approaches.
基金supported by the National Natural Science Foundation of China(No.61671370)Project supported by joint foundation of X Lab–the 2~(nd)Academy of CASIC+1 种基金the Postdoctoral Science Foundation of China(No.2016M592790)the Postdoctoral Science Research Foundation of Shaanxi Province,China(No.2016BSHEDZZ46)。
文摘In the theory of belief functions,the evidence combination is a kind of decision-level information fusion.Given two or more Basic Belief Assignments(BBAs)originated from different information sources,the combination rule is used to combine them to expect a better decision result.When only a combined BBA is given and original BBAs are discarded,if one wants to analyze the difference between the information sources,evidence de-combination is needed to determine the original BBAs.Evidence de-combination can be considered as the inverse process of the information fusion.This paper focuses on such a defusion of information in the theory of belief functions.It is an under-determined problem if only the combined BBA is available.In this paper,two optimization-based approaches are proposed to de-combine a given BBA according to the criteria of divergence maximization and information maximization,respectively.The new proposed approaches can be used for two or more information sources.Some numerical examples and an example of application are provided to illustrate and validate our approaches.
基金supported by the Grant for State Key Program for Basic Research of China (No. 2013CB329405)National Natural Science Foundation of China (No. 61573275)+3 种基金Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 61221063)Science and Technology Project of Shaanxi Province (No. 2013KJXX-46)Postdoctoral Science Foundation of China (No. 2016M592790)Fundamental Research Funds for the Central Universities of China (No. xjj2014122)
基金supported by the National Natural Science Foundation of China(No.61671370)Postdoctoral Science Foundation of China(No.2016M592790)Postdoctoral Science Research Foundation of Shaanxi Province,China(No.2016BSHEDZZ46)。
文摘In information fusion,the uncertain information from different sources might be modeled with different theoretical frameworks.When one needs to fuse the uncertain information represented by different uncertainty theories,constructing the transformation between different frameworks is crucial.Various transformations of a Fuzzy Membership Function(FMF)into a Basic Belief Assignment(BBA)have been proposed,where the transformations based on uncertainty maximization and minimization can determine the BBA without preselecting the focal elements.However,these two transformations that based on uncertainty optimization emphasize the extreme cases of uncertainty.To avoid extreme attitudinal bias,a trade-off or moderate BBA with the uncertainty degree between the minimal and maximal ones is more preferred.In this paper,two moderate transformations of an FMF into a trade-off BBA are proposed.One is the weighted average based transformation and the other is the optimization-based transformation with weighting mechanism,where the weighting factor can be user-specified or determined with some prior information.The rationality and effectiveness of our transformations are verified through numerical examples and classification examples.
