We prove a pointwise characterization result for combinations of Bernstein polynomials. The main result of this paper includes an equivalence theorem of H. Berens and G. G. Lorentz as a special case.
Belief functions theory is an important tool in the field of information fusion. However, when the cardinality of the frame of discernment becomes large, the high computational cost of evidence combination will become...Belief functions theory is an important tool in the field of information fusion. However, when the cardinality of the frame of discernment becomes large, the high computational cost of evidence combination will become the bottleneck of belief functions theory in real applications. The basic probability assignment （BPA） approximations, which can reduce the complexity of the BPAs, are always used to reduce the computational cost of evidence combination. In this paper, both the cardinalities and the mass assignment values of focal elements are used as the criteria of reduction. The two criteria are jointly used by using rank-level fusion. Some experiments and related analyses are provided to illustrate and justify the proposed new BPA approximation approach.展开更多
文摘We prove a pointwise characterization result for combinations of Bernstein polynomials. The main result of this paper includes an equivalence theorem of H. Berens and G. G. Lorentz as a special case.
基金co-supported by Grant for State Key Program for Basic Research of China(No.2013CB329405)National Natural Science Foundation of China(Nos.61104214,61203222)+3 种基金Foundation for Innovative Research Groups of the National Natural Science Foundation of China(No.61221063)Specialized Research Fund for the Doctoral Program of Higher Education(No.20120201120036)China Postdoctoral Science Foundation(No.20100481337),China Postdoctoral Science Foundation-Special fund(No.201104670)Fundamental Research Funds for the Central Universities
文摘Belief functions theory is an important tool in the field of information fusion. However, when the cardinality of the frame of discernment becomes large, the high computational cost of evidence combination will become the bottleneck of belief functions theory in real applications. The basic probability assignment （BPA） approximations, which can reduce the complexity of the BPAs, are always used to reduce the computational cost of evidence combination. In this paper, both the cardinalities and the mass assignment values of focal elements are used as the criteria of reduction. The two criteria are jointly used by using rank-level fusion. Some experiments and related analyses are provided to illustrate and justify the proposed new BPA approximation approach.
