Basic belief assignment approximations using degree of non-redundancy for focal element

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.

An improved α-cut approach to transforming fuzzy membership function into basic belief assignment

In practical applications, pieces of evidence originated from different sources might be modeled by different uncertainty theories. To implement the evidence combination under the Dempster–Shafer evidence theory (DST) framework, transformations from the other type of uncertainty representation into the basic belief assignment are needed. α-Cut is an important approach to transforming a fuzzy membership function into a basic belief assignment, which provides a bridge between the fuzzy set theory and the DST. Some drawbacks of the traditional α-cut approach caused by its normalization step are pointed out in this paper. An improved α-cut approach is proposed, which can counteract the drawbacks of the traditional α-cut approach and has good properties. Illustrative examples, experiments and related analyses are provided to show the rationality of the improved α-cut approach. © 2016 Chinese Society of Aeronautics and Astronautics

A new non-specificity measure in evidence theory based on belief intervals

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.

Periodic acoustic source tracking using propagation delayed measurements

There exist a large class of acoustic sources which have an underlying periodic phenomenon. Unlike the well-studied Bearings-Only Tracking(BOT) of an aperiodic acoustic source,this paper considers the problem of tracking a periodic acoustic source. For periodic acoustic tracking, the signal emission time is known. However, the true measurement reception time is unknown because it is corrupted by noise due to propagation delay. We augment the sensor’s signal reception time onto bearing measurements, and the information of the delay constraint is included in the original bearing measurements to compensate for the propagation delay. A Cubature Kalman Filter(CKF) is used for periodic acoustic source tracking, in which measurement prediction cannot be obtained directly because the sensor’s position at the true measurement reception time is unknown.We solve this problem by using the implicit Gauss-Helmert Sensor Model(GHSM) for estimating the sensor’s position, which consists of the sensor’s motion equation and the known measured sensor’s signal reception time equation related to the state. Then a CKF based on the GHSM(CF-GHSM) is developed for periodic acoustic tracking. Illustrative examples demonstrate that the CF-GHSM algorithm is better than other algorithms for periodic acoustic source tracking.