Belief Functions

It is quite common in real world situations to form beliefs under Dempster-Shafer (DS) theory on various variables from a single source. This is true, in particular, in auditing. Also, the judgment about these beliefs is easily made in terms of simple support functions on individual variables. However, for propagating beliefs in a network of variables, one needs to convert these beliefs on individual variables to beliefs on the joint space of the variables pertaining to the single source of evidence. Although there are many possible solutions to the above problem that will yield beliefs on the joint space with the desired marginal beliefs, there is no method that will guarantee that the beliefs are derived from the same source, fully dependent evidence. In this article, we describe such a procedure based on a maximal order decomposition algorithm. The procedure is computationally efficient and is supported by objective chi-square and entropy criteria. While such assignments are not unique, alternative procedures that have been suggested, such as linear programming, are more computationally intensive and result in similar m-value determinations. It should be noted that our maximal order decomposition (i.e., minimum entropy) approach provides m-values on the joint space for fully dependent items of evidence.

We develop an information quality model based on a user-centric view adapted from Financial Accounting Standards Board1, Wang et al.2, and Wang and Strong3. The model consists of four essential attributes (or assertions): 'Accessibility,' 'Interpretability,' 'Relevance,' and 'Integrity.' Four sub-attributes lead to an evaluation of Integrity: 'Accuracy,' 'Completeness,' 'Consistency,' and 'Existence.' These sub-attributes relating to 'Integrity' are intrinsic in nature and relate to the process of how the information was created while the first three attributes: 'Accessibility,' 'Interpretability,' and 'Relevance' are extrinsic in nature. We present our model as an evidential network under the belief-function framework to permit user assessment of quality parameters. Two algorithms for combining assessments into an overall IQ measure are explored, and examples in the domain of medical information are used to illustrate key concepts. We discuss two scenarios, 'online-user' and 'assurance-provider,' which reflect two likely and important aspects of IQ evaluation currently facing information users -concerns about the impact of poor quality online information, and the need for information quality assurance.

This paper illustrates two formulas for assessing independence risk based on the Bayesian and belief‐functions frameworks. These formulas can be used to assess the role of threats to auditor independence as well as the role of threat‐mitigating safeguards. Also, these formulas provide a basis for evaluation of an audit firm's independence risk and a framework to educate stakeholders about the threats faced by the audit firm and the role of effective safeguards in mitigating these risks. The formulas also provide a means for regulators and lawmakers to evaluate whether they have effective safeguards in place given the existence of threats and for auditors to signal to various stakeholders that they have identified significant threats and have effective safeguards in place. To show the potential usefulness of these analytical models, several illustrations addressing increased transparency and the potential impact of regulations are presented.

In this study, we propose an unsupervised classification scheme based on the Dempster-Shafer Theory (TDS) and the Dezert-Smarandache Theory (DSmT) to characterize vegetated, aquatic and mineral surfaces. From pre-processed ASTER satellite images (georeferencing, geometric correction and 15 m re-sampling), neo-channels were produced by determining the spectral indices NDVI, MNDWI and NDBaI, considered as sources of information for classification of a given pixel. NDVI is a contrast function to highlight vegetation. By account, the MNDWI makes it possible to characterize the water and the NDBaI makes it possible to recognize the mineral resources. Then, we modeled respectively the formalisms of the DST and the DSmT, these formalisms are modeling tools close to advanced probabilities based on the notions of belief and fusion functions to take into account certain imperfections (uncertainty, ignorance, etc.) encountered in the acquisition of images. In addition, the DST manages a formalism of disjunction between the sources during the DSmT simultaneously manages a disjunction and a conjunction between the sources. Next we realized the algorithms and related codes that we implemented in the MATLAB environment. Our contribution lies in taking into account the imperfections (inaccuracies and uncertainties) linked to source information through the use of mass functions based on a simple Gaussian distribution support model in order to model each focal element independently of the others and to evaluate the belonging of a pixel to a class with respect to the majority of elements representing said class. The resulting results show that the DST approach is relatively satisfactory for the unsupervised classification of mineral surfaces and aquatic surfaces while it is not satisfactory for vegetated surfaces according to all proposed models. As for the DSmT, it presents satisfactory results for all the models proposed. The model with the exclusion integrity constraint E∩V ∩ M = φ was selected as the best model because having, in addition to an average rate of well-graded pixels of 93.34%, a compliance rate (96, 37%) with the terrain higher than those of the other models implemented.

Possibilistic networks are belief graphical models based on possibility theory. A possibilistic network either represents experts' epistemic uncertainty or models uncertain information from poor, scarce or imprecise data. Learning possibilistic networks from data in general and from imperfect or scarce datasets in particular, has not received enough attention. This work focuses on parameter learning of possibilistic networks. The main contributions of the paper are i) a study of an extension of the information affinity measure to assess the similarity of possibilistic networks and ii) a comparative empirical evaluation of two approaches for learning the parameters of a possibilistic network from empirical data.

This paper extends the decision tree technique to an uncertain environment where the uncertainty is represented by belief functions as interpreted in the Transferable Belief Model (TBM). This so-called belief decision tree is a new classification method adapted to uncertain data. We will be concerned with the construction of the belief decision tree from a training set where the knowledge about the instances' classes is represented by belief functions, and its use for the classification of new instances where the knowledge about the attributes' values is represented by belief functions.

Nowadays, the sustainability of human activities is a major worldwide concern. Indeed, the problem is no longer to evaluate only the efficiency of human activities, but also sustainability along many axes that can be of various kinds: economic, social, environmental, etc. Such assessments are a major challenge for today’s society. Because of the exponential development of means of data recording and storage (“big data” buzz word), and on the basis of Volume, Variety and Velocity properties of big data, scientists need to compute large amounts of data and so do not necessarily have time to clean them. In this context, they compute all available data whose types of imperfections are heterogeneous. Actors in several domains have to cope with such data, especially to assist humans in their decisions by merging them from many data sources (e.g. measurements, sensors, observations) to model behaviours of complex systems. Mathematical approaches to model imperfect data are well known and e...

Pressurized irrigation is one of the proposed plans to resolve the Urmia lake crisis. The effects of such plan can be assessed using the hydrological simulation. But different agricultural management approaches and uncertainty in the model inputs lead to complexity in the basin modeling which in turn increases the uncertainty of model outputs. The main purpose of this study is to determine the effect of the pressurized irrigation on Zarinehrud basin as the largest sub-basin of the Urmia Lake basin. For this purpose, by determining the probable scenarios of water demand, the impact of these scenarios on the basin hydrological components were simulated with SWAT model. Then by combining the results of the scenarios, the uncertainty bounds of the hydrological components were estimated using Bayesian model averaging (BMA). The results showed that the annual average of upper and lower bound of the basin outflow will be 1391 and 1316 MCM. Also irrigation efficiency in the field scale and ...

Machine learning is increasingly deployed in safety-critical domains where robustness against adversarial attacks is crucial and erroneous predictions could lead to potentially catastrophic consequences. This highlights the need for learning systems to be equipped with the means to determine a model's confidence in its prediction and the epistemic uncertainty associated with it, 'to know when a model does not know'. In this paper, we propose a novel Random-Set Convolutional Neural Network (RS-CNN) for classification which predicts belief functions rather than probability vectors over the set of classes, using the mathematics of random sets, i.e., distributions over the power set of the sample space. Based on the epistemic deep learning approach, random-set models are capable of representing the 'epistemic' uncertainty induced in machine learning by limited training sets. We estimate epistemic uncertainty by approximating the size of credal sets associated with the predicted belief functions, and experimentally demonstrate how our approach outperforms competing uncertainty-aware approaches in a classical evaluation setting. The performance of RS-CNN is best demonstrated on OOD samples where it manages to capture the true prediction while standard CNNs fail. Preprint. Under review.

Context: Several empirical studies investigated the benefits and drawbacks of acquiring a Software Reference Architecture (SRA) to construct a family of software systems with similar architectural needs. However, these empirical results have not been synthesized by any study yet. Such synthesized evidence is essential to make informed decisions whether or not to adopt an SRA in an organization. Goal: To aggregate existing empirically-grounded evidence about the benefits and drawbacks of SRAs, aiming at supporting organizations' decision making on their adoption. Method: To identify primary studies in the technical literature through a systematic literature review, and then, use the Structured Synthesis Method (SSM) to aggregate qualitative and quantitative evidence through the use of diagrammatic models. Results: From the five identified primary studies, five SRA benefits have considerably increased their belief value after aggregation: interoperability of software systems, reduced development costs, improved communication among stakeholders, reduced risk, and reduced time-to-market. Also, one drawback of SRAs has increased its belief value: the required learning curve for developers. Conclusions: The aggregated results consolidate knowledge and confidence on some of the studied SRA effects. The commonly reported effects showed a clear increment of their belief and pointed out to broader generalization. The effects that did not show any belief increment are important to detect areas requiring further evidence to reach a higher degree of consolidation. Practitioners might benefit from these results to support the decision of adopting an SRA in practice.

In diffusion social learning over weakly-connected graphs, it has been shown recently that influential agents shape the beliefs of non-influential agents. This paper analyzes this mechanism more closely and addresses two main questions. First, the article examines how much freedom influential agents have in controlling the beliefs of the receiving agents, namely, whether receiving agents can be driven to arbitrary beliefs and whether the network structure limits the scope of control by the influential agents. Second, even if there is a limit to what influential agents can accomplish, this article develops mechanisms by which they can lead receiving agents to adopt certain beliefs. These questions raise interesting possibilities about belief control over networked agents. Once addressed, one ends up with design procedures that allow influential agents to drive other agents to endorse particular beliefs regardless of their local observations or convictions. The theoretical findings are illustrated by means of examples.

In diffusion social learning over weakly-connected graphs, it has been shown recently that influential agents shape the beliefs of non-influential agents. This paper analyzes this mechanism more closely and addresses two main questions. First, the article examines how much freedom influential agents have in controlling the beliefs of the receiving agents, namely, whether receiving agents can be driven to arbitrary beliefs and whether the network structure limits the scope of control by the influential agents. Second, even if there is a limit to what influential agents can accomplish, this article develops mechanisms by which they can lead receiving agents to adopt certain beliefs. These questions raise interesting possibilities about belief control over networked agents. Once addressed, one ends up with design procedures that allow influential agents to drive other agents to endorse particular beliefs regardless of their local observations or convictions. The theoretical findings are illustrated by means of examples.

New semantics for numerical values given to possibil- ity measures are provided. For epistemic possibilities, the new approach is based on the semantics of the transferable belief model, itself based on betting odds interpreted in a less drastic way than what subjec- tive probabilities presupposes. It is shown that the least informative among the belief structures that are compatible with

Some data fusion problems seem to be naturally handled in the framework of possibility theory. As an example, the problem of modelling expert knowledge about numerical parameters in the field of reliability is reconsidered in that framework. Usually expert opinions about ...

The problem of assessing the value of a candidate is viewed here as a multiple combination problem. On the one hand, a candidate can be evaluated according to different criteria, and on the other hand, several experts are supposed to assess the value of candidates ...

Feature selection is a prolific research field, which has been widely studied in the last decades and has been successfully applied to numerous computer vision systems. It mainly aims to reduce the dimensionality and thus the system complexity. Features have not the same importance within the different classes. Some of them perform for class representation while others perform for class separation. In this paper, a new feature selection method based on discriminative power is proposed to select the relevant features under an uncertain framework, where the uncertainty is expressed through a possibility distribution. In an uncertain context, our method shows its ability to select features that can represent and discriminate between classes.

The most commonly used measures of accuracy of evidence in statistics are pre-experimental. A particular procedure is decided upon for use, and the accuracy of the evidence from an experiment is identified with the long run behavior of the procedure, were the experiment repeatedly performed. This long run behavior is evaluated by averaging the performance of the procedure over the sample space Z. In contrast, the LP states that post-experimental reasoning should be used, wherein only the actual observation x (and not the other observations in% that could have occured) is relevant. There are a variety of intermediate positions which call for partial conditioning on x and partial long run frequency interpretations. Partly for historical purposes, and partly to indicate that the case for at least some sort of conditioning is compelling, we discuss in this chapter various conditioning viewpoints. 2.1 SIMPLE EXAMPLES The following simple examples reveal the necessity of at least sometimes thinking conditionally, and will be important later. EXAMPLE 1. Suppose X, and X 2 are independent and P Θ (X Ί = θ-1) = P Q (X. = θ+1) = ±, i = 1,2. Here-«> < θ < °° is an unknown parameter to be estimated from X, and X 2 It is easy to see that a 75% confidence set of smallest size for θ is c(x v x 2) = the point yίXj+Xg) if X 1 f the point X^l if X 1 =

Machine learning is increasingly deployed in safety-critical domains where robustness against adversarial attacks is crucial and erroneous predictions could lead to potentially catastrophic consequences. This highlights the need for learning systems to be equipped with the means to determine a model's confidence in its prediction and the epistemic uncertainty associated with it, 'to know when a model does not know'. In this paper, we propose a novel Random-Set Convolutional Neural Network (RS-CNN) for classification which predicts belief functions rather than probability vectors over the set of classes, using the mathematics of random sets, i.e., distributions over the power set of the sample space. Based on the epistemic deep learning approach, random-set models are capable of representing the 'epistemic' uncertainty induced in machine learning by limited training sets. We estimate epistemic uncertainty by approximating the size of credal sets associated with the predicted belief functions, and experimentally demonstrate how our approach outperforms competing uncertainty-aware approaches in a classical evaluation setting. The performance of RS-CNN is best demonstrated on OOD samples where it manages to capture the true prediction while standard CNNs fail.

In this paper, we discuss a potential agenda for future work in the theory of random sets and belief functions, touching upon a number of focal issues: the development of a fully-fledged theory of statistical reasoning with random sets, including the generalisation of logistic regression and of the classical laws of probability; the further development of the geometric approach to uncertainty, to include general random sets, a wider range of uncertainty measures and alternative geometric representations; the application of this new theory to high-impact areas such as climate change, machine learning and statistical learning theory.

Information processing in modern pattern recognition systems is becoming increasingly complex due to the flood of data and the need to deal with different aspects of information imperfection. In this paper a simple and efficient possibilistic evidential method is defined, taking account of data heterogeneity, combined with proportional conflict redistribution to include information conflict, paradox, and scarcity, within a fusion framework. It ponders information constraints and updating for dynamic fusion, and appropriately considers training set elements imperfection, class set continuity, and system output information scalability, encompassing a significant range of issues encountered in current databases. One example of knowledge sources processing with those constraints is given to explain the main processing phases, followed by suitable application instances in satellite and medical image recognition.

This paper aims to provide a unified framework to deal with information imperfection and heterogeneity using possibility theory, in addition to information conflict and scarcity using Dempster-Shafer theory in order to classify imperfectly-described medical images. The proposed method is very robust and general. It can be applied without modification to any other database.

In this paper we introduce the pointfree version of rough sets. For this we consider a lattice L instead of the power set P (X) of a set X. We study the properties of lower and upper pointfree approximation, precise elements, and their relation with prime elements. Also, we study lower and upper pointfree approximation as a Galois connection, and discuss the relations between partitions and Galois connections.

We give an algebraic approach for defining rough sets on incomplete information systems. The constructed approximation sets are based on objects. Given several attributes, the value of each attribute can be known or unknown for each object. In the current paper, we introduce four different approaches, a real value, a binary, a ternary and a likelihood approach. Furthermore, we define operations on the elements of the introduced approximation sets. For all three cases we can show that the achieved structure is a quasi-Brouwer-Zadeh distributive lattice with the defined operations. We also show that the introduced lower and upper approximations build up commutative monoids with the introduced operations.

The rise of AI in human contexts places new demands on systems to be transparent and explainable. We examine some anthropomorphic ideas and principles relevant to such accountablity in order to develop a theoretical framework for thinking about digital systems in complex human contexts and the problem of explaining their behaviour. Structurally, complex systems are made of modular and hierachical components, which we model abstractly using a new notion of modes and mode transitions. A mode is an independent component of the system with its own objectives, monitoring data, and algorithms. The behaviour of a mode, including its transitions to other modes, is determined by belief functions that interpret the mode's monitoring data in the light of its objectives and algorithms. We show how these belief functions can help explain system behaviour by visualising their evaluation in higherdimensional geometric spaces. These ideas are formalised by abstract and concrete simplicial complexes.

Mathematical Theory of Evidence (MTE) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its foundation, many questions remain open. One of the most important open questions seems to be the relationship between frequencies and the Mathematical Theory of Evidence. The theory is blamed to leave frequencies outside (or aside of) its framework. The seriousness of this accusation is obvious: no experiment may be run to compare the performance of MTE-based models of real world processes against real world data. In this paper we develop a frequentist model of the MTE bringing to fall the above argument against MTE. We describe, how to interpret data in terms of MTE belief functions, how to reason from data about conditional belief functions, how to generate a random sample out of a MTE model, how to derive MTE model from data and how to compare results of reasoning in MTE model and reasoning from data. It is claimed in this paper that MTE is suitable to model some types of destructive processes

In this paper, it is proposed to apply the Dempster-Shafer Theory (DST) or the theory of evidence to map vegetation, aquatic and mineral surfaces with a view to detecting potential areas of observation of outcrops of geological formations (rocks, breastplates, regolith, etc.). The proposed approach consists in aggregating information by using the DST. From pretreated Aster satellite images (geo-referencing, geometric correction and resampling at 15 m), newchannels were produced by determining the spectral indices NDVI, MNDWI and NDBaI. Then, the DST formalism was modeled and generated under the MATLAB software, an image segmented into six classes including three absolute classes (E,V,M) and three classes of confusion ({E,V}, {M,V}, {E,M}). The control on the land, based on geographic coordinates of pixels of different classes on said image, has made it possible to make a concordant interpretation thereof. Our contribution lies in taking into account imperfections (inaccuracies and uncertainties) related to source information by using mass functions based on a simple support model (two focal elements: the discernment framework and the potential set of belonging of the pixel to be classified) with a normal law for the good management of these.

Récemment, une fondation axiomatique aété donnéeà la mesure du conflit entre fonctions de croyance. Dans ce contexte, il aété montré que le conflit peutêtreévalué par l'inconsistance résultant de leur combinaison conjonctive. Deux mesures de consistance entre fonctions de croyance ontété définies, donnant ainsi deux mesures de conflit. Dans ce papier, nous mettons en lumière que ces mesures de consistance correspondent aux normes infinies des fonctions de plausibilité et de contour, offrant ainsi une vue géométrique sur les mesures de conflit considérées. De plus, ce résultat nous permet de mettre eń evidence que la consistance d'une fonction de croyance n'est rien d'autre que sa distanceà l'état d'inconsistance totale. Comme une conséquence directe, le conflit entre fonctions de croyance estégalà un moins la distance entre leur combinaison conjonctive et l'inconsistance totale. Cela donne un nouveau regard sur l'utilisation de distances pour mesurer le conflit.

The importance of epistemic uncertainty in engineering is being recognized more and more. In this work, epistemic uncertainty is captured through the use of fuzzy variables, i.e. variables that are described in terms of possibility distributions. Taking into account epistemic uncertainty implies that one should also be able to propagate such uncertainty through increasingly complex models. In earlier work, we have developed a general tool, called Fuzzy Calculator, to propagate epistemic uncertainty regarding non-interactive fuzzy input variables. In reality, however, the fuzzy input variables of a model are often interactive. Taking into account this interactivity reduces the uncertainty on the fuzzy output variable and should therefore always be aimed for. However, the full determination of the joint possibility distribution of the fuzzy input variables is not an easy task. In literature, it is often claimed that triangular norms can be used to model interactivity between fuzzy variables. Making use of a generalization of Nguyen's alphacut approach, we have developed a general-purpose Fuzzy Calculator that is able to take into account interactivity modelled by a triangular norm. However, the absence of a general strategy to select an appropriate triangular norm often results in the use of other strategies to model interactivity in practice. Therefore, we have also applied our Fuzzy Calculator to a case study where the interactivity between the fuzzy input variables is identified through possibilistic clustering. The results illustrate that this Fuzzy Calculator is an efficient tool to propagate epistemic uncertainty regarding non-interactive as well as interactive fuzzy input variables.

It is quite common in real world situations to form beliefs under Dempster-Shafer (DS) theory on various variables from a single source. This is true, in particular, in auditing. Also, the judgment about these beliefs is easily made in terms of simple support functions on individual variables. However, for propagating beliefs in a network of variables, one needs to convert these beliefs on individual variables to beliefs on the joint space of the variables pertaining to the single source of evidence. Although there are many possible solutions to the above problem that will yield beliefs on the joint space with the desired marginal beliefs, there is no method that will guarantee that the beliefs are derived from the same source, fully dependent evidence. In this article, we describe such a procedure based on a maximal order decomposition algorithm. The procedure is computationally efficient and is supported by objective chi-square and entropy criteria. While such assignments are not unique, alternative procedures that have been suggested, such as linear programming, are more computationally intensive and result in similar m-value determinations. It should be noted that our maximal order decomposition (i.e., minimum entropy) approach provides m-values on the joint space for fully dependent items of evidence.

This paper presents an algorithm for developing models under Dempster-Shafer theory of belief functions for categorical and 'uncertain' logical relationships among binary variables. We illustrate the use of the algorithm by developing belief-function representations of the following categorical relationships: 'AND', 'OR', 'Exclusive OR (EOR)' and 'Not Exclusive OR (NEOR)', and 'AND-NEOR' and of the following uncertain relationships: 'Discounted AND', 'Conditional OR', and 'Weighted Average'. Such representations are needed to fully model and analyze a problem with a network of interrelated variables under Dempster-Shafer theory of belief functions. In addition, we compare our belief-function representation of the 'Weighted Average' relationship with the 'Weighted Average' representation developed and used by Shenoy and Shenoy 8. We find that Shenoy and Shenoy representation of the weighted average relationship is an approximation and yields significantly different values under certain conditions.

This article develops an alternative form of Dempster's rule of combination for binary variables. This alternative form does not only provide a closed form formulae for efficient computation but also enables researchers to develop closed form analytical formulae for assessing risks such as information security risk, fraud risk, audit risk, independence risk, etc., involved in assurance services. We demonstrate the usefulness of the alternative form in calculating the overall information security risk and also in developing an analytical model for assessing fraud risk.

G. Shafer views belief functions as the result of the fusion of elementary partially reliable testimonies from different sources. But any belief function cannot be seen as the combination of simple support functions representing such testimonies. Indeed the result of such a combination only yields a special kind of belief functions called separable. In 1995, Ph. Smets has indicated that any belief function can be seen as the combination of so-called generalized simple support functions. We propose a new interpretation of this result in terms of a pair of separable belief functions, one of them modelling testimonies while the other represents the idea of prejudice. The role of the latter is to weaken the weights of the focal sets of the former separable belief function. This bipolar view accounts for a form of resistance to accept the information supplied by the sources, which differs from the discounting of sources.

Capacities are monotonically increasing set functions that generalize probability and possibility measures. They are qualitative when they range on a finite linearly ordered scale. This paper pursues a parallel between qualitative capacities and the quantitative setting of belief functions. The qualitative setting appears to be as rich as the quantitative one, but qualitative counterparts of belief function notions do not always have the same meaning and/or behavior as in the quantitative case. The paper especially focuses on the comparison of qualitative capacities in terms of information content. Various information orderings are studied, including one based on a counterpart of Dempster rule of combination.

The objective of this paper is to describe the potential oered by the Dempster±Shafer theory (DST) of evidence as a promising improvement on``traditional'' approaches to decision analysis. Dempster±Shafer techniques originated in the work of Dempster on the use of probabilities with upper and lower bounds. They have subsequently been popularised in the literature on Arti®cial Intelligence (AI) and Expert Systems, with particular emphasis placed on combining evidence from dierent sources. In the paper we introduce the basic concepts of the DST of evidence, brie¯y mentioning its origins and comparisons with the more traditional Bayesian theory. Following this we discuss recent developments of this theory including analytical and application areas of interest. Finally we discuss developments via the use of an example incorporating DST with the Analytic Hierarchy Process (AHP).

In this paper we propose a generalised maximum-entropy classification framework, in which the empirical expectation of the feature functions is bounded by the lower and upper expectations associated with the lower and upper probabilities associated with a belief measure. This generalised setting permits a more cautious appreciation of the information content of a training set. We analytically derive the Karush-Kuhn-Tucker conditions for the generalised max-entropy classifier in the case in which a Shannon-like entropy is adopted.

The main purpose of this paper is to introduce the Dempster-Shafer theory ("DS" theory) of belief functions for managing uncertainties, specifically in the auditing and information systems domains. We illustrate the use of DS theory by deriving a fraud risk assessment formula for a simplified version of a model developed by Srivastava, Mock, and Turner (2007). In our formulation, fraud risk is the normalized product of four risks: risk that management has incentives to commit fraud, risk that management has opportunities to commit fraud, risk that management has an attitude to rationalize committing fraud, and the risk that auditor's special procedures will fail to detect fraud. We demonstrate how to use such a model to plan for a financial audit where management fraud risk is assessed to be high. In addition, we discuss whether audit planning is better served by an integrated audit/fraud risk assessment as now suggested in SAS 107 (AICPA 2006a, see also ASA 200 in AUASB 2007) or by the approach illustrated in this paper where a parallel, but separate, assessment is made of audit risk and fraud risk.

Different methods exist for estimating trips in public transportation systems. Some of the widely adopted estimation strategies are based on the traceability of passenger transfers. While these techniques have been effective in the case of some large cities, they fall short for trip estimation in smaller towns. This is because the underlying methodology leave aside single-route trips information, which are the most frequent in the latter case. In this paper we present a methodology based on combining probability distributions defined upon alternative partitions of the universe of possible trips. Our approach starts from intuitions similar to the Dempster-Shafer rule, but since in our application domain some of its basic assumptions fail to be satisfied, we estimate probability intervals by means of an aggregation procedure on the information of the different sources. Samples of those intervals yield the distributions to be used in simulation models of the behavior of the transportat...

The conditions under which a 2-monotone lower prevision can be uniquely updated (in the sense of focusing) to a conditional lower prevision are determined. Then a number of particular cases are investigated: completely monotone lower previsions, for which equivalent conditions in terms of the focal elements of the associated belief function are established; random sets, for which some conditions in terms of the measurable selections can be given; and minitive lower previsions, which are shown to correspond to the particular case of vacuous lower previsions.

In this paper, a proposition is made to learn the parameters of evidential contextual correction mechanisms from a learning set composed of soft labelled data, that is data where the true class of each object is only partially known. The method consists in optimizing a measure of discrepancy between the values of the corrected contour function and the ground truth also represented by a contour function. The advantages of this method are illustrated by tests on synthetic and real data.

In this paper, it is proposed to apply the Dempster-Shafer Theory (DST) or the theory of evidence to map vegetation, aquatic and mineral surfaces with a view to detecting potential areas of observation of outcrops of geological formations (rocks, breastplates, regolith, etc.). The proposed approach consists in aggregating information by using the DST. From pretreated Aster satellite images (geo-referencing, geometric correction and resampling at 15 m), newchannels were produced by determining the spectral indices NDVI, MNDWI and NDBaI. Then, the DST formalism was modeled and generated under the MATLAB software, an image segmented into six classes including three absolute classes (E,V,M) and three classes of confusion ({E,V}, {M,V}, {E,M}). The control on the land, based on geographic coordinates of pixels of different classes on said image, has made it possible to make a concordant interpretation thereof. Our contribution lies in taking into account imperfections (inaccuracies and uncertainties) related to source information by using mass functions based on a simple support model (two focal elements: the discernment framework and the potential set of belonging of the pixel to be classified) with a normal law for the good management of these.

Finite closure spaces with the Steinitz exchange property are characterized and the connection between the Steinitz and the MacLane exchange property and related exchange properties is discussed. A Kurosh-Ore theorem is proved for subadditive closure spaces with the Steinitz exchange property. Finally, closure spaces with monotone dimension functions are investigated. * Partially supported by Sonderforschungsbereich 303 (DFG). This paper is the expanded version of a talk presented at the joint US-German Seminar 'Applications of Combinatorial Methods in Mathematical Programming',

The need to meaningfully combine sets of rankings often comes up when one deals with ranked data. Although a number of heuristic and supervised learning approaches to rank aggregation exist, they generally require either domain knowledge or supervised ranked data, both of which are expensive to acquire. To address these limitations, we propose1 a mathematical and algorithmic framework for learning to aggregate (partial) rankings in an unsupervised setting, and instantiate it for the cases of combining ...

This article is concerned with the computational aspects of combining evidence within the theory of belief functions. It shows that by taking advantage of logical or categorical relations among the questions we consider, we can sometimes avoid the computational complexity associated with brute-force application of Dempster's rule. The mathematical setting for this article is the lattice of partitions of a fixed overall frame of discernment. Different questions are represented by different partitions of this frame, and the categorical relations among these questions are represented by relations of qualitative conditional independence or dependence among the partitions. Qualitative conditional independence is a categorical rather than a probabilistic concept, but it is analogous to conditional independence for random variables. We show that efficient implementation of Dempster's rule is possible if the questions or partitions for which we have evidence are arranged in a qualitative Markov tree-a tree in which separations indicate relations of qualitative conditional independence. In this case, Dempster's rule can be implemented by propagating belief functions through the tree.

We develop an information quality model based on a user-centric view adapted from Financial Accounting Standards Board 1 , Wang et al. 2 , and Wang and Strong 3. The model consists of four essential attributes (or assertions): 'Accessibility,' 'Interpretability,' 'Relevance,' and 'Integrity.' Four sub-attributes lead to an evaluation of Integrity: 'Accuracy,' 'Completeness,' 'Consistency,' and 'Existence.' These sub-attributes relating to 'Integrity' are intrinsic in nature and relate to the process of how the information was created while the first three attributes: 'Accessibility,' 'Interpretability,' and 'Relevance' are extrinsic in nature. We present our model as an evidential network under the belief-function framework to permit user assessment of quality parameters. Two algorithms for combining assessments into an overall IQ measure are explored, and examples in the domain of medical information are used to illustrate key concepts. We discuss two scenarios, 'online-user' and 'assurance-provider,' which reflect two likely and important aspects of IQ evaluation currently facing information users-concerns about the impact of poor quality online information, and the need for information quality assurance.

This paper illustrates two formulas for assessing independence risk based on the Bayesian and belief-functions frameworks. These formulas can be used to assess the role of threats to auditor independence as well as the role of threat-mitigating safeguards. Also, these formulas provide a basis for evaluation of an audit firm's independence risk and a framework to educate stakeholders about the threats faced by the audit firm and the role of effective safeguards in mitigating these risks. The formulas also provide a means for regulators and lawmakers to evaluate whether they have effective safeguards in place given the existence of threats and for auditors to signal to various stakeholders that they have identified significant threats and have effective safeguards in place. To show the potential usefulness of these analytical models, several illustrations addressing increased transparency and the potential impact of regulations are presented.

Several economic applications require to consider different data sources and to integrate the information coming from them. This paper focuses on statistical matching, in particular we deal with incoherences. In fact, when logical constraints among the variables are present incoherencies on the probability evaluations can arise. The aim of this paper is to remove such incoherences by using different methods based on distances minimization or least commitment imprecise probabilities extensions. An illustrative example shows peculiarities of the different correction methods. Finally, limited to pseudo distance minimization, we performed a systematic comparison through a simulation study.

Pour les exploitations du sous-sol, les données géologiques sont souvent peu nombreuses lorsque les projets sont à un stade précoce de développement, et le recours à l’avis d’experts est fréquent. Il est alors nécessaire de gérer les informations fournies par plusieurs experts, potentiellement conflictuelles. Sur un cas d’étude dédiée au stockage géologique du CO2, deux approches différentes ont été appliquées pour la gestion des incertitudes sur la valeur d’un paramètre estimée par 14 experts différents, une approche classique de type probabiliste ainsi qu’une approche basée sur la théorie de Dempster-Shafer. Les résultats sont discutés pour aider à la prise de décision.Handling potentially conflicting information coming from experts when other available data are scare or inexistent is an important issue for subsurface operations, especially for projects in the early stages of development. On a case study dedicated to the CO2 geological storage technology, two different approaches ...

Pour les exploitations du sous-sol, les données géologiques sont souvent peu nombreuses voire inexistantes notamment lorsque les projets sont à un stade précoce de développement. Dans cette situation le recours à l'avis d'experts est nécessaire. La gestion des données fournies par plusieurs experts, potentiellement conflictuelles, constitue donc une problématique importante dans le cadre des exploitations du sous-sol. Cette étude concerne la technologie du stockage géologique de CO 2 , et plus particulièrement la quantification, sur un site donné, de l'extension du panache de CO 2 dans le réservoir géologique. Des informations sur les valeurs minimales, médianes et maximales de la porosité du réservoir ont été collectées auprès de 14 experts pour mener à bien cette estimation. Une méthode classique d'analyse des incertitudes a été utilisée, en choisissant dans un premier temps un mode de représentation pour les informations collectées auprès des experts, en fusionnant les 14 jeux de données puis en propageant l'incertitude existante dans un modèle de migration de CO 2. Au sein de cette méthode, deux approches différentes ont été appliquées pour la gestion des incertitudes, une approche classique de type probabiliste ainsi qu'une approche basée sur la théorie de Dempster-Shafer. Les résultats de l'étude montrent que, dans un contexte de fort conflit entre experts, la fusion des jugements d'experts basée sur l'approche probabiliste ainsi que celle basée sur la règle disjonctive dans le cadre de Dempster-Shafer ne permettent pas réellement de discuter de la proportion de l'incertitude globale provenant du désaccord entre les experts. De plus, l'approche probabiliste fournit des résultats spécifiques mais non conservateurs et l'approche Dempster-Shafer disjonctive fournit des résultats conservateurs mais peu informatifs. Dans ce contexte, l'application d'une règle de fusion de type « compromis » a été nécessaire pour obtenir des informations supplémentaires pouvant être fournies aux décideurs. Pour cette étude, l'application d'une règle de fusion d'informations d'experts nouvellement publiée est proposée et son applicabilité est discutée pour aider à la prise de décision.

The crowdsourcing Tripadvisor platform do not offer a multi-criteria filtering functionality for their users. Thus, these users are obliged to choose only one criteria to filter a query’s results. In this paper, we introduce a new skyline operator, in the context of belief functions theory, to meet the multi-criteria filtering objective. The queried data, modeled with the theory of belief functions, takes into account all reviews and also reviewers’ reliabilities. Experiments show interesting results of the proposed skyline operator in terms of size and performance.