Uncertainty in Ontologies: Dempster-Shafer Theory for Data Fusion Applications

Nowadays ontologies present a growing interest in Data Fusion applications. As a matter of fact, the ontologies are seen as a semantic tool for describing and reasoning about sensor data, objects, relations and general domain theories. In addition, uncertainty is perhaps one of the most important characteristics of the data and information handled by Data Fusion. However, the fundamental nature of ontologies implies that ontologies describe only asserted and veracious facts of the world. Different probabilistic, fuzzy and evidential approaches already exist to fill this gap; this paper recaps the most popular tools. However none of the tools meets exactly our purposes. Therefore, we constructed a Dempster-Shafer ontology that can be imported into any specific domain ontology and that enables us to instantiate it in an uncertain manner. We also developed a Java application that enables reasoning about these uncertain ontological instances.Comment: Workshop on Theory of Belief Functions, Brest: France (2010

Loss Distribution Approach for Operational Risk Capital Modelling under Basel II: Combining Different Data Sources for Risk Estimation

The management of operational risk in the banking industry has undergone significant changes over the last decade due to substantial changes in operational risk environment. Globalization, deregulation, the use of complex financial products and changes in information technology have resulted in exposure to new risks very different from market and credit risks. In response, Basel Committee for banking Supervision has developed a regulatory framework, referred to as Basel II, that introduced operational risk category and corresponding capital requirements. Over the past five years, major banks in most parts of the world have received accreditation under the Basel II Advanced Measurement Approach (AMA) by adopting the loss distribution approach (LDA) despite there being a number of unresolved methodological challenges in its implementation. Different approaches and methods are still under hot debate. In this paper, we review methods proposed in the literature for combining different data sources (internal data, external data and scenario analysis) which is one of the regulatory requirement for AMA

A logic-based analysis of Dempster-Shafer theory

AbstractDempster-Shafer (DS) theory is formulated in terms of propositional logic, using the implicit notion of provability underlying DS theory. Dempster-Shafer theory can be modeled in terms of propositional logic by the tuple (Σ, ϱ), where Σ is a set of propositional clauses and ϱ is an assignment of mass to each clause Σi ϵ Σ. It is shown that the disjunction of minimal support clauses for a clause Σi with respect to a set Σ of propositional clauses, ξ(Σi, Σ), when represented in terms of symbols for the ϱi 's, corresponds to a symbolic representation of the Dempster-Shafer belief function for δi. The combination of Belief functions using Dempster's rule of combination corresponds to a combination of the corresponding support clauses. The disjointness of the Boolean formulas representing DS Belief functions is shown to be necessary. Methods of computing disjoint formulas using network reliability techniques are discussed.In addition, the computational complexity of deriving DS Belief functions, including that of the logic-based methods which are the focus of this paper, is explored. Because of intractability even for moderately sized problem instances, efficient approximation methods are proposed for such computations. Finally, implementations of DS theory based on domain restrictions of DS theory, hypertree embeddings, and the ATMS, are examined

Miniature mobile sensor platforms for condition monitoring of structures

In this paper, a wireless, multisensor inspection system for nondestructive evaluation (NDE) of materials is described. The sensor configuration enables two inspection modes-magnetic (flux leakage and eddy current) and noncontact ultrasound. Each is designed to function in a complementary manner, maximizing the potential for detection of both surface and internal defects. Particular emphasis is placed on the generic architecture of a novel, intelligent sensor platform, and its positioning on the structure under test. The sensor units are capable of wireless communication with a remote host computer, which controls manipulation and data interpretation. Results are presented in the form of automatic scans with different NDE sensors in a series of experiments on thin plate structures. To highlight the advantage of utilizing multiple inspection modalities, data fusion approaches are employed to combine data collected by complementary sensor systems. Fusion of data is shown to demonstrate the potential for improved inspection reliability

Software quality and reliability prediction using Dempster -Shafer theory

As software systems are increasingly deployed in mission critical applications, accurate quality and reliability predictions are becoming a necessity. Most accurate prediction models require extensive testing effort, implying increased cost and slowing down the development life cycle. We developed two novel statistical models based on Dempster-Shafer theory, which provide accurate predictions from relatively small data sets of direct and indirect software reliability and quality predictors. The models are flexible enough to incorporate information generated throughout the development life-cycle to improve the prediction accuracy.;Our first contribution is an original algorithm for building Dempster-Shafer Belief Networks using prediction logic. This model has been applied to software quality prediction. We demonstrated that the prediction accuracy of Dempster-Shafer Belief Networks is higher than that achieved by logistic regression, discriminant analysis, random forests, as well as the algorithms in two machine learning software packages, See5 and WEKA. The difference in the performance of the Dempster-Shafer Belief Networks over the other methods is statistically significant.;Our second contribution is also based on a practical extension of Dempster-Shafer theory. The major limitation of the Dempsters rule and other known rules of evidence combination is the inability to handle information coming from correlated sources. Motivated by inherently high correlations between early life-cycle predictors of software reliability, we extended Murphy\u27s rule of combination to account for these correlations. When used as a part of the methodology that fuses various software reliability prediction systems, this rule provided more accurate predictions than previously reported methods. In addition, we proposed an algorithm, which defines the upper and lower bounds of the belief function of the combination results. To demonstrate its generality, we successfully applied it in the design of the Online Safety Monitor, which fuses multiple correlated time varying estimations of convergence of neural network learning in an intelligent flight control system