Sampling-Based Possibility Theory for Engineering Analysis Under Uncertainty: Inference, Prediction and Optimization

Handling exceptions in a knowledge-based system is an important issue in many application domains, such as medical domain. Recently, there is an increasing interest in nonmonotonic extension of description logics to handle exceptions in ontologies. In this paper, we propose three preferential semantics for plausible subsumption to deal with exceptions in description logic-based knowledge bases. Our preferential semantics are defined in the framework of possibility theory, which is an uncertainty theory devoted to handling incomplete information. We consider the properties of these semantics and their relationships. We also discuss the relationship between two of our preferential semantics and two existing preferential semantics. We extend a description logic-based knowledge base by adding preferential subsumptions. Entailment of plausible subsumptions relative to an extended knowledge base is defined. Properties of the preferential subsumption relations relative to an extended description logic-based knowledge base are discussed. Finally, we show that our semantics for plausible subsumption can be reduced to standard semantics of an expressive description logic. Thus, the problem of plausible subsumption checking under our semantics can be reduced to the problem of subsumption checking under the classical semantics.

This paper discusses contemporary issues associated with the use of approximate reasoning techniques in knowledge-based systems relying on the theory of possibility. It aims at: providing lines along which comparison of existing systems can be done; pointing out directions toward which future systems should evolve.

Layers of protection analysis in the framework of possibility theory

Breast cancer early diagnosis is a major concern for reducing deadly cases. Automation of microcalcification detection is becoming increasingly important given their tiny scale. At this step, a high false negative rate is observed, leading to high ambiguity. In this context, conventional approaches are unable to handle such ambiguity. Possibility theory offers a powerful paradigm enabling to handle a high uncertainty level. Therefore, in this research,new possibilistic modeling strategy for microcalcification detection is proposed. The developed system is based on k-means clustering followed by a fusion of the corresponding possibility distributions, for decision making. For enhancing classification's accuracy, two aspects may be taken into consideration: scattering within classes and the class discrimination power. A high inter-class variance may be regarded as an evidence of good discrimination. Nevertheless, in case of existing highly scattered classes, miss-classifications of samples at the class margins are still encountered, even at high inter-class variance. Clustering solves this problem by redefining classes in a more compact way. Under this paradigm, the clustering optimization is performed using a criteria based on the Area Under Curve(AUC), where the confidence degree level is based on the consistency principle of Dubois and Prade. The above strategy has been applied for the detection of microcalcifications, based on a set of pyramidal and multi-resolution based features. Validation on the Digital Database for Screening Mammography (DDSM) public dataset has been undertaken. The proposed system, which gives 99.4 % detection accuracy, can be used to assist medical practitioners.

WEIGHTED FUZZY PATTERN MATCHING

Uncertainty quantification in LES of a turbulent bluff-body stabilized flame

This paper discusses fuzzy reasoning for approximately realizing nonlinear functions by a small number of fuzzy if-then rules with different specificity levels. Our fuzzy rule base is a mixture of general and specific rules, which overlap with each other in the input space. General rules work as default rules in our fuzzy rule base. First, we briefly describe existing approaches to the handling of default rules in the framework of possibility theory. Next, we show that standard interpolation-based fuzzy reasoning leads to counterintuitive results when general rules include specific rules with different consequents. Then, we demonstrate that intuitively acceptable results are obtained from a non-standard inclusion-based fuzzy reasoning method. Our approach is based on the preference for more specific rules, which is a commonly used idea in the field of default reasoning. When a general rule includes a specific rule and they are both compatible with an input vector, the weight of the general rule is discounted in fuzzy reasoning. We also discuss the case where general rules do not perfectly but partially include specific rules. Then we propose a genetics-based machine learning (GBML) algorithm for extracting a small number of fuzzy if-then rules with different specificity levels from numerical data using our inclusion-based fuzzy reasoning method. Finally, we describe how our approach can be applied to the approximate realization of fuzzy number-valued nonlinear functions

Possibilistic randomisation in strategic-form games

The paper survey recent AI-oriented works in qualitative decision developed by the authors in the framework of possibility theory. Lottery-based and act-based axiomatics underlying pessimistic and optimistic criteria for decision under uncertainty are first briefly restated, when uncertainty and preferences are encoded with an ordinal scale. A logical machinery capable of computing optimal decisions in the sense of these criteria is presented. Then an approach to qualitative decision under uncertainty which does not require a commensurateness hypothesis between the uncertainty and the preference scales is proposed; this approach is closely related to nonmonotonic reasoning, but turns our to be ineffective for practical decision. Lastly, the modeling of preference as prioritized sets of goals, as sets of solutions reaching some given level of satisfaction, or in terms of possibilistic constraints is discussed briefly.

In this paper we present an extension of the ATMS, called "possibilistic ATMS", where the management of uncertainty is integrated inside the basic capabilities of the ATMS. Uncertainty pervading justifications or grading assumptions is represented in the framework of possibility theory using necessity measures. The main interest of a possibilistic ATMS is to take advantage of the uncertainty pervading the available knowledge and rank-order environments in which a given proposition is true. Possibilistic ATMS offer a solution to the revision of uncertain knowledge bases by deleting the least certain piece(s) of knowledge that cause(s) the inconsistency. Moreover the functionalities of the possibilistic ATMS provide a simple procedure for computing the most "acceptable" maximal consistent sub-bases of a partially inconsistent knowledge base. The implementation of a possibilistic ATMS using a specially tailored typed-resolution is briefly discussed.

Autonomous search is an ongoing cycle of sensing, statistical estimation, and motion control with the objective to find and localise targets in a designated search area. Traditionally, the theoretical framework for autonomous search combines sequential Bayesian estimation with information theoretic motion control. This paper formulates autonomous search in the framework of possibility theory. Although the possibilistic formulation is slightly more involved than the traditional method, it provides a means for quantitative modelling and reasoning in the presence of epistemic uncertainty. This feature is demonstrated in the paper in the context of partially known probability of detection, expressed as an interval value. The paper presents an elegant Bayes-like solution to sequential estimation, with the reward function for motion control defined to take into account the epistemic uncertainty. The advantages of the proposed search algorithm are demonstrated by numerical simulations.

Aortic dissection is a cardiovascular disease with a disconcertingly high mortality. When it comes to diagnosis, medical imaging techniques such as Computed Tomography, Magnetic Resonance Tomography or Ultrasound certainly do the job, but also have their shortcomings. Impedance cardiography is a standard method to monitor a patients heart function and circulatory system by injecting electric currents and measuring voltage drops between electrode pairs attached to the human body. If such measurements distinguished healthy from dissected aortas, one could improve clinical procedures. Experiments are quite difficult, and thus we investigate the feasibility with finite element simulations beforehand. In these simulations, we find uncertain input parameters, e.g., the electrical conductivity of blood. Inference on the state of the aorta from impedance measurements defines an inverse problem in which forward uncertainty propagation through the simulation with vanilla Monte Carlo demands a prohibitively large computational effort. To overcome this limitation, we combine two simulations: one simulation with a high fidelity and another simulation with a low fidelity, and low and high computational costs accordingly. We use the inexpensive low-fidelity simulation to learn about the expensive high-fidelity simulation. It all boils down to a regression problem—and reduces total computational cost after all.

Independence relations play an important role in uncertain reasoning based on Bayesian networks. In particular, they are useful in decomposing joint distributions into more elementary local ones. Recently, in a possibility theory framework, several qualitative independence relations have been proposed, where uncertainty is encoded by means of a complete pre-order between states of the world. This paper studies the well-known graphoid properties of these qualitative independences. Contrary to the probabilistic independence, several qualitative independence relations are not necessarily symmetric. Therefore, we also analyze the symmetric counterparts of graphoid properties (called reverse graphoid properties).

This paper presents some imprecise and uncertain information retrieval methods available in the fuzzy set and possibility theory framework and implemented in the SIMCAIR software [ANDRES 89]. The main application of those methods concerns fuzzy querying in fuzzy databases [CAYROL 82], [TESTEMALE 84]. The example used in this paper will concern cars. The methods described are however nearly directly applicable for another major application field: efficient rules firing in expert systems. The specific feature of this work is that in contradiction with systems which allow either the data or the requests to be fuzzy [BOSC 86], [SALTON 83], the SIMCAIR software allows both data and requests to be described in a fuzzy way.

Towards robust quantification and reduction of uncertainty in hydrologic predictions: Integration of particle Markov chain Monte Carlo and factorial polynomial chaos expansion