Entailment for measure based belief structures

We discuss the Dempster–Shafer belief structure on finite universes and note its use for modeling variables that have both probabilistic uncertainty as well as imprecision. We note for these structures the probability that the variable lies in a subset cannot be precisely known but only be known to an interval value. We discuss methods for deducing this uncertainty interval. We next discuss the issue of entailment of belief structures, inferring the validity of additional belief model of a variable from an already established belief model of the variable. We next discuss a more general belief structure were the underling uncertainty rather tha0n being based on a probability distribution is based on a general measure type of uncertainty. We then extend the concept of entailment to the case where the belief structures are these more general measure based belief structures. In order to accomplish this we must extend the idea of containment from classic Dempster–Shafer belief structures to measure based belief structures.     

Hierarchical aggregation functions generated from belief structures

We deal with the development of tools useful for the construction of multicriteria decision functions that allow for the modeling of the types of complexity that is the hallmark of human intelligence. We first discuss the fuzzy measure, describe its potential for characterizing relationships between multiple criteria, and introduce the class of ordered aggregation functions that can be based on a fuzzy measure. We then focus on the two fuzzy measures associated with the Dempster-Shafer belief structure, plausibility, and belief, and describe the types of ordered aggregation functions obtained using these measures. This leads us to introduce a new class of aggregation functions obtained by allowing a decision maker to provide his decision imperative in terms of components (concepts) that contribute to his overall satisfaction. Each component consists of a value, a subset of criteria and an agenda for combining the criteria in the component. Finally, it is shown how these components can be combined to allow for the representation of hierarchical decision functions     

On the aggregation of prioritized belief structures

The focus of this work is to provide a procedure for aggregating prioritized belief structures. Motivated by the ideas of nonmonotonic logics an alternative to the normalization step used in Dempster's rule when faced with conflicting belief structures is suggested. We show how this procedure allows us to make inferences in inheritance networks where the knowledge is in the form of a belief structure     

Cumulative distribution functions from Dempster-Shafer belief structures

We discuss the Dempster-Shafer belief structure. We introduce the idea of a cumulative distribution induced by a Dempster-Shafer belief structure. We call these belief-cumulative distribution (B-CDs) functions. We study the properties of these distribution functions and show that they are interval functions. We investigate the possibility of using these distribution functions as a tool for knowledge representation.     

Constructing efficient belief network structures with expertprovided information

Presents a technique to construct efficient belief network structures for application areas where large amounts of data are available and information on the ordering of the variables can be obtained from domain experts. We identify classes of networks that are efficient for propagating beliefs. We formulate the problem as one of determining the belief network representation from a given class that best represents the data. We use the I-Divergence measure which is known to have certain desirable properties for evaluating different approximations. We present some theoretical findings that characterize the nature of solutions that are obtained. These theoretical results lead to an efficient solution procedure for finding the best network representation. We also discuss other information that may be reasonably obtained from experts, and show how such information leads to improving the efficiency of the technique to find the best network structure     

Generalized probabilities of fuzzy events from fuzzy belief structures

We extend Shafer's theory of evidence to include the ability to have belief structures involving fuzzy sets. We then obtain under the condition of Bayesian belief structure a whole family of possible definitions for the probability of fuzzy sets. We also suggest a procedure for including belief qualification in pruf.     

On the combination and normalization of interval-valued belief structures

This paper investigates the issues of combination and normalization of interval-valued belief structures within the framework of Dempster-Shafer theory (DST) of evidence. Existing approaches are reviewed, examined and critically analysed. They either ignore the normalization or separate it from the combination process, leading to irrational or suboptimal interval-valued belief structures. A new logically correct optimality approach is developed, where the combination and the normalization are optimised together rather than separately. Numerical examples are provided throughout the paper.     

Shape optimization of buckling sensitive structures

The optimal design of structures with distinct geometrically non-linear behavior has attracted a great deal of interest in the last years mainly with respect to sizing for prescribed external loads. In the present contribution a method is proposed to maximize the critical load under certain constraints, e.g. for a given volume, allowing varying shape as well as cross-sections. The combination of direct computation of the critical load and path-following methods is integrated into a general optimization procedure consisting of mathematical programming techniques, sensitivity analysis and computer aided geometric design methods. The formulation includes imperfection sensitivity as an important part within the optimization process.     

On the fusion of imprecise uncertainty measures using belief structures

Our interest is in the fusion of information from multiple sources when the information provided by the individual sources is expressed in terms of an imprecise uncertainty measure. We observe that the Dempster-Shafer belief structure provides a framework for the representation of a wide class of imprecise uncertainty measures. We then discuss the fusion of multiple Dempster-Shafer belief structures using the Dempster rule and note the problems that can arise when using this fusion method because of the required normalization in the face of conflicting focal elements. We then suggest some alternative approaches fusing multiple belief structures that avoid the need for normalization.     

Entailment for intuitionistic fuzzy sets based on generalized belief structures

Entailment for measure-based belief structures can extend the possible probability value range of variables on a space and obtain more information from variables. However, if the variable space comes from intuitionistic fuzzy sets, the classical entailment for measure-based belief structures will not work in this issue. To deal with this situation, we propose the entailment for intuitionistic fuzzy sets based on generalized belief structures in this paper to apply the entailment for measure based belief structures on space, which is made up of non-membership degree, membership degree and hesitancy degree of a given intuitionistic fuzzy sets. Numerical examples are mentioned to prove the effectively and flexibility of this proposed entailment model. The experimental results indicate that the proposed algorithm can extend the possible probability value range of variables of space efficiently and obtain more information from intuitionistic fuzzy sets.     

On the Dempster-Shafer evidence theory and non-hierarchicalaggregation of belief structures

The Dempster's rule of combination is a widely used technique to integrate evidence collected from different sources. In this paper, it is shown that the values of certain functions defined on a family of belief structures decrease (by scale factors depending on the degree of conflict) when the belief structures are combined according to the Dempster's rule. Similar results also hold when an arbitrary belief structure is prioritized while computing the combination. Furthermore, the length of the belief-plausibility interval is decreased during a nonhierarchical aggregation of belief structures. Several types of inheritance networks are also proposed each of which allows considerable flexibility in the choice of prioritization     

复杂惯性敏感结构的矩阵解析建模方法

微惯性器件的性能首先取决于其挠性支承结构的力学性能.高精度微惯性器件的需求与微加工的普及,使得微惯性器件的挠性支承结构趋向复杂,但主要体现为组合复杂性,提出了矩阵解析建模方法,论述了该方法的基本概念、刚度矩阵与弹性矩阵的坐标系变换和集总计算等问题,并结合实例简要说明了应用矩阵解析建模方法的基本步骤.     

An improved soft likelihood function for Dempster–Shafer belief structures

Information fusion is an important research direction. In the field of information fusion, there are many methods for evidence combination. Recently, Yager proposed a method of soft likelihood function to combine probabilistic evidence effectively. Considering that basic probability assignment (BPA) can deal with uncertainty information more effectively, in this paper, we extend Yager's soft likelihood function to combine BPA. First, according to the BPA evaluations of evidence sources, belief function and plausibility function on each alternative are calculated. Then, interval numbers are constructed by the obtained belief function and plausibility function to indicate the belief interval on each alternative. Next, the descending sorting of interval numbers is aggregated by the ordered weighted averaging operator. Finally, by sorting the result of the aggregation, the ordering of alternatives is obtained. A numerical example and an example of application in Iris data set classification illustrate the effectiveness of the improved method.     

Theory-relational belief revision

Annals of Mathematics and Artificial Intelligence - The prominent formal framework for belief change established by Alchourrón, Gärdenfors and Makinson circumscribes the territory of all...     

TOPSIS with belief structure for group belief multiple criteria decision making

The technique for order performance by similarity to ideal solution(TOPSIS)is one of the major techniques in dealing with multiple criteria decision making(MCDM)problems, and the belief structure(BS)model has been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with BS model is proposed to solve group belief MCDM problems. Firstly, the group belief MCDM problem is structured as a belief decision matrix in which the judgments of each decision maker are described as BS models, and then the evidential reasoning approach is used for aggregating the multiple decision makers' judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. To measure the separation from ideal solutions, the concept and algorithm of belief distance measure are defined, which can be used for comparing the difference between BS models. Finally, the relative closeness and ranking index are calculated for ranking the alternatives. A numerical example is given to illustrate the proposed method.     

Dynamic belief revision operators

The AGM approach to belief change is not geared to provide a decent account of iterated belief change. Darwiche and Pearl have sought to extend the AGM proposal in an interesting way to deal with this problem. We show that the original Darwiche-Pearl approach is, on the one hand excessively strong and, on the other rather limited in scope. The later Darwiche-Pearl approach, we argue, although it addresses the first problem, still remains rather permissive. We address both these issues by (1) assuming a dynamic revision operator that changes to a new revision operator after each instance of belief change, and (2) strengthening the Darwiche-Pearl proposal. Moreover, we provide constructions of this dynamic revision operator via entrenchment kinematics as well as a simple form of lexicographic revision, and prove representation results connecting these accounts.     

基于证据距离和矛盾因子的加权证据合成法

针对Dempster-shafer (DS)理论直接对高冲突证据合成时会有融合结果不合理的问题,本文提出了一种加权证据合成法.在多个证据融合时,该方法综合利用证据距离和矛盾因子表示证据冲突.并根据各证据与其它证据的冲突程度确定其权重系数,基于此又分别采用两种适用于不同情况的方法对证据基本置信指派函数修正,然后用DS规则合成.算例实验表明了本文方法对高冲突证据融合的有效性,并且其融合结果还具有良好的收敛性.     

TOPSIS with fuzzy belief structure for group belief multiple criteria decision making

TOPSIS is one of the major techniques in dealing with multiple criteria decision making (MCDM) problems, and Belief Structure (BS) model and Fuzzy BS model have been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with Fuzzy BS model is proposed to solve Group Belief MCDM problems. Firstly, the Group Belief MCDM problem is structured as a fuzzy belief decision matrix in which the judgments of each decision maker are described as Fuzzy BS models, and then the Evidential Reasoning approach is used for aggregating the multiple decision makers’ judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. In order to measure the separation from the ideal belief solutions, the concept and algorithm of Belief Distance Measure are introduced to compare the difference between Fuzzy BS models. Using the Belief Distance Measure, the relative closeness and ranking index can be calculated for ranking the alternatives. A numerical example is finally given to illustrate the proposed method.     

Analyzing the monotonicity of belief interval based uncertainty measures in belief function theory

Measuring the uncertainty of pieces of evidence is an open issue in belief function theory. A rational uncertainty measure for belief functions should meet some desirable properties, where monotonicity is a very important property. Recently, measuring the total uncertainty of a belief function based on its associated belief intervals becomes a new research idea and has attracted increasing interest. Several belief interval based uncertainty measures have been proposed for belief functions. In this paper, we summarize the properties of these uncertainty measures and especially investigate whether the monotonicity is satisfied by the measures. This study provide a comprehensive comparison to these belief interval based uncertainty measures and is very useful for choosing the appropriate uncertainty measure in the practical applications.