Analytic hierarchy process for multi-sensor data fusion based on belief function theory

Multi-sensor data fusion is an evolving technology whereby data from multiple sensor inputs are processed and combined. The data derived from multiple sensors can, however, be uncertain, imperfect, and conflicting. The present study is undertaken to help contribute to the continuous search for viable approaches to overcome the problems associated with data conflict and imperfection. Sensor readings, represented by belief functions, have to be fused according to their corresponding weights. Previous studies have often estimated the weights of sensor readings based on a single criterion. Mono-criteria approaches for the assessment of sensor reading weights are, however, often unreliable and inadequate for the reflection of reality. Accordingly, this work opts for the use of a multi-criteria decision aid. A modified Analytical Hierarchy Process (AHP) that incorporates several criteria is proposed to determine the weights of a sensor reading set. The approach relies on the automation of pairwise comparisons to eliminate subjectivity and reduce inconsistency. It assesses the weight of each sensor reading, and fuses the weighed readings obtained using a modified average combination rule. The efficiency of this approach is evaluated in a target recognition context. Several tests, sensitivity analysis, and comparisons with other approaches available in the literature are described.     

Relevance and truthfulness in information correction and fusion

A general approach to information correction and fusion for belief functions is proposed, where not only may the information items be irrelevant, but sources may lie as well. We introduce a new correction scheme, which takes into account uncertain metaknowledge on the source’s relevance and truthfulness and that generalizes Shafer’s discounting operation. We then show how to reinterpret all connectives of Boolean logic in terms of source behavior assumptions with respect to relevance and truthfulness. We are led to generalize the unnormalized Dempster’s rule to all Boolean connectives, while taking into account the uncertainties pertaining to assumptions concerning the behavior of sources. Eventually, we further extend this approach to an even more general setting, where source behavior assumptions do not have to be restricted to relevance and truthfulness. We also establish the commutativity property between correction and fusion processes, when the behaviors of the sources are independent.     

Corrigendum to “Belief functions contextual discounting and canonical decompositions” [International Journal of Approximate Reasoning 53 (2012) 146–158]

Proposition 4 and Theorem 1 of the article “Belief functions contextual discounting and canonical decompositions” [International Journal of Approximate Reasoning 53 (2012) 146–158] provide an erroneous result. We give here the true result with a correct proof.     

Belief functions contextual discounting and canonical decompositions

In this article, the contextual discounting of a belief function, a classical discounting generalization, is extended and its particular link with the canonical disjunctive decomposition is highlighted. A general family of correction mechanisms allowing one to weaken the information provided by a source is then introduced, as well as the dual of this family allowing one to strengthen a belief function.     

Joint distributions of random sets and their relation to copulas

Random sets are set-valued random variables. They have been applied in various fields like stochastic geometry, statistics, economics, engineering or computer science, and are often used for modeling uncertainty. In an earlier paper the author has defined joint capacity and joint containment functionals which are multivariate set functions describing the joint distribution of random sets. This paper is concerned with the question how copulas can be used to describe or model the dependence of random sets. It is demonstrated that a joint containment functional can be related to its margins by a family of copulas. Furthermore, the paper provides a first insight how copulas can be used to define joint containment functionals.     

Constructing and evaluating alternative frames of discernment

We construct alternative frames of discernment from input belief functions. We assume that the core of each belief function is a subset of a so far unconstructed frame of discernment. The alternative frames are constructed as different cross products of unions of different cores. With the frames constructed the belief functions are combined for each alternative frame. The appropriateness of each frame is evaluated in two ways: (i) we measure the aggregated uncertainty (an entropy measure) of the combined belief functions for that frame to find if the belief functions are interacting in interesting ways, (ii) we measure the conflict in Dempster’s rule when combining the belief functions to make sure they do not exhibit too much internal conflict. A small frame typically yields a small aggregated uncertainty but a large conflict, and vice versa. The most appropriate frame of discernment is that which minimizes a probabilistic sum of the conflict and a normalized aggregated uncertainty of all combined belief functions for that frame of discernment.     

民间信仰的历史传承与申遗策略——以温州宁村“汤和信仰”为例

浙江温州龙湾区“汤和信仰”是地方民间信仰中最具特殊性、典型性的个案之一。通过文献资料和田野材料，叙述了从“汤和信仰”到“汤和信俗”的产生、演变过程，分析了汤和信仰在历史上曾属于国家和民间两个层面的特点，阐释了汤和信仰申遗成功的背景、策略和意义。     

An evidential approach to SLAM,path planning,and active exploration

Probability theory has become the standard framework in the field of mobile robotics because of the inherent uncertainty associated with sensing and acting. In this paper, we show that the theory of belief functions with its ability to distinguish between different types of uncertainty is able to provide significant advantages over probabilistic approaches in the context of robotics. We do so by presenting solutions to the essential problems of simultaneous localization and mapping (SLAM) and planning based on belief functions. For SLAM, we show how the joint belief function over the map and the robot's poses can be factored and efficiently approximated using a Rao-Blackwellized particle filter, resulting in a generalization of the popular probabilistic FastSLAM algorithm. Our SLAM algorithm produces occupancy grid maps where belief functions explicitly represent additional information about missing and conflicting measurements compared to probabilistic grid maps. The basis for this SLAM algorithm are forward and inverse sensor models, and we present general evidential models for range sensors like sonar and laser scanners. Using the generated evidential grid maps, we show how optimal decisions can be made for path planning and active exploration. To demonstrate the effectiveness of our evidential approach, we apply it to two real-world datasets where a mobile robot has to explore unknown environments and solve different planning problems. Finally, we provide a quantitative evaluation and show that the evidential approach outperforms a probabilistic one both in terms of map quality and navigation performance.     

新发现的南明天妃封号

介绍从明人管绍宁文集中新发现南明朝天妃加封安定慈惠之号。指出褒封缘由为崇祯十七年（1644）七月，皇太后张氏自河南由水路平安抵达南京，弘光政权认为此皆沿途众水神佑护之果，故而对一路大小河神俱加封赐。     

论信念在认识活动中的双重作用

信念在人们的认识活动中发挥着双重作用。一方面，信念起到纽带、选择、动力、预测和定向的积极作用；另一方面，它起到僵化、误导和抑制的消极作用。