POSSIBILITY THEORY

13th International Conference of Artificial Intelligence and Fuzzy Logic (AI & FL 2025) provides a forum for researchers who address this issue and to present their work in a peer-reviewed forum. Authors are solicited to contribute to the conference by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the following areas, but are not limited to these topics only.

Preface vii 1 Pattern Recognition 1 1.1 Fuzzy models for pattern recognition 1 1.2 Why fuzzy pattern recognition? 1.3 Overview of the volume 8 1.4 Comments and bibliography 2 Cluster Analysis for Object Data 2.1 Cluster analysis 2.2 Batch point-prototype clustering models A. The c-means models B. Semi-supervised clustering models 23 C. Probabilistic Clustering D. Remarks on HCM/FCM/PCM E. The Reformulation Theorem 2.3 Non point-prototype clustering models A. The Gustafson-Kessel (GK) Model B. Linear manifolds as prototypes C. Spherical Prototypes D. Elliptical Prototypes E. Quadric Prototypes F. Norm induced shell prototypes G. Regression models as prototypes H. Clustering for robust parametric estimation 2.4 Cluster Validity A. Direct Measures B. Davies-Bouldin Index C. Dunn's index D. Indirect measures for fuzzy clusters E. Standardizing and normalizing indirect indices F. Indirect measures for non-point prototype models G. Fuzzification of statistical indices 2.5 Feature Analysis 2.6 Comments and bibliography vi FUZZY PATTERN RECOGNITION 3 Cluster Analysis for Relational Data 3.1 Relational Data A. Crisp Relations B. Fuzzy Relations 3.2 Object Data to Relational Data 3.3 Hierarchical Methods 3.4 Clustering by decomposition of fuzzy relations 3.5 Relational clustering with objective functions A. The Fuzzy Non Metric (FNM) model B. The Assignment-Prototype (AP) Model C. The relational fuzzy c-means (RFCM) model D. The non-Euclidean RFCM (NERFCM) model 3.6 Cluster validity for relational models 3.7 Comments and bibliography 4 Classifier Design 4.1 Classifier design for object data 4.2 Prototype classifiers A. The nearest prototype classifier B. Multiple prototype designs 4.3 Methods of prototype generation A. Competitive learning networks B. Prototype relabeling C. Sequential hard c-means (SHCM) D. Learning vector quantization (LVQ) E. Some soft versions of LVQ F. Case Study : LVQ and GLVQ-F 1-nmp designs G. The soft competition scheme (SCS) H. Fuzzy learning vector quantization (FLVQ) 1. The relationship between c-Means and CL schemes J. The mountain "clustering" method (MCM) 4.4 Nearest neighbor classifiers 4.5 The Fuzzy Integral 4.6 Fuzzy Rule-Based Classifiers A. Crisp decision trees B. Rules from crisp decision trees C. Crisp decision tree design D. Fuzzy system models and function approximation E. The Chang -Pavlidis fuzzy decision tree F. Fuzzy relatives of 1D3 G. Rule-based approximation based on clustering H. Heuristic rule extraction I. Generation of fuzzy labels for training data 4.7 Neural-like architectures for classification A. Biological and mathematical neuron models B. Neural network models C. Fuzzy Neurons D. Fuzzy aggregation networks E. Rule extraction with fuzzy aggregation networks Contents vii 4.8 Adaptive resonance models A. The ARTl algorithm B. Fuzzy relatives of ART C. Radial basis function networks 4.9 Fusion techniques A. Data level fusion B. Feature level fusion C. Classifier fusion 4.10 Syntactic pattern recognition A. Language-based methods B. Relation-based methods 4.11 Comments and bibliography 5 Image Processing and Computer 'Vision 5.

A continuous predicate on a domain, or more generally a topological space, can be concretely described as an open or closed set, or less obviously, as the set of all predicates consistent with it. Generalizing this scenario to quantitative predicates, we obtain under certain wellunderstood hypotheses an isomorphism between continuous functions on points and supremum preserving functions on open sets, both with values in a fixed lattice. The functions on open sets provide a topological foundation for possibility theories in Artificial Intelligence, revealing formal analogies of quantitative predicates with continuous valuations. Three applications of this duality demonstrate its usefulness: we prove a universa] property for the space of quantitative predicates, we characterize its inf-irreducible elements, and we show that bicontinuous lattices and Scott-continuous maps form a cartesian closed category.

Composite plans created from different image sets are generated through Deformable Image Registration (DIR) and present a challenge in accurately presenting uncertainties, which vary with anatomy. Our effort focuses on the application of Fuzzy Set theory to provide an accurate dose representation of such a composite treatment plan. The accuracy of the DIR is generally verified through geometrical visual checks, including the confirmation of the corresponding anatomies with edge features, such as bone or organ boundaries. However, the remaining volume of the image (mostly soft tissues) has few significant image features and therefore greater uncertainty. We fuzzified the deformation vector and derived a Fuzzy composite dose. The fuzzification was implemented using Gaussian functions based on the varying uncertainties in the DIR. After establishing the theoretical basis for this new approach, we present two-and three-dimensional examples as proof-of-concept. Using Fuzzy Set theory, composite dose plans displaying localitybased uncertainties were successfully created, providing information previously unavailable to clinicians. Previous to Fuzzy Set dose presentations, clinicians had no measure of confidence in the accuracy of a composite dose plan. Using fuzzified composite dose presentations, clinicians can determine a safe additional dose to previously treated anatomy. This will possibly increase the treatment success rate and reduce the rate of complications.

In order to understand the source and extent of the greater-than-classical information processing power of quantum systems, one wants to characterize both classical and quantum mechanics as points in a broader space of possible theories. One approach to doing this, pioneered by Abramsky and Coecke, is to abstract the essential categorical features of classical and quantum mechanics that support various information-theoretic constraints and possibilities, e.g., the impossibility of cloning in the latter, and the possibility of teleportation in both. Another approach, pursued by the authors and various collaborators, is to begin with a very conservative, and in a sense very concrete, generalization of classical probability theory-which is still sufficient to encompass quantum theory-and to ask which "quantum" informational phenomena can be reproduced in this much looser setting. In this paper, we review the progress to date in this second programme, and offer some suggestions as to how to link it with the categorical semantics for quantum processes developed by Abramsky and Coecke.

This paper presents the results and the main lessons learnt from Phase V of BEMUSE, an international programme promoted by the Working Group on Accident Management and Analysis (GAMA) of OECD to address the issue of the capabilities of best-estimate computational tools and uncertainty analysis. The scope of Phase V is the uncertainty analysis of a Large Break Loss-Of-Coolant-Accident (LBLOCA) in a Pressurized Water Reactor. Fourteen participants from twelve organizations and ten countries participated in the Phase V of BEMUSE. The paper starts with a general description of the BEMUSE programme including the objectives, structure, and the outline of the Phase V specification. Then it summarizes some general aspects on the uncertain model parameters and the results for the uncertainty analysis and for the sensitivity evaluation. To end with, general recommendations and conclusions are presented as practical guidance for uncertainty analysis performance.

Fuzzy sets theory has successfully accommodated the lack of clear-cut boundaries of poverty and its gradual nature. On the other hand, uncertainties related to lack of knowledge and imprecision in poverty data need also to be accounted for. The accuracy of poverty analysis is highly subject to how well these features are adequately addressed. We argue that possibility theory is an appropriate framework to deal with incomplete knowledge in poverty. Indeed, considering "the possibility of poverty" instead of the "probability of poverty" allows us to achieve a more realistic handling of this phenomenon. Empirical possibility distributions of monetary poverty states are derived based on our previous works and alpha-cut analysis is used to explore their features. Also, collective possibilistic poverty measures for each state are computed along with an aggregate possibilistic poverty ratio. This possibilistic modeling is applied to the analysis of poverty in Tunisia in 2005 and 2010.

In possibility theory, there are two kinds of possibilistic causal networks depending if possibilistic conditioning is based on the minimum or on the product operator. Similarly there are also two kinds of possibilistic logic: standard (min-based) possibilistic logic and quantitative (product-based) possibilistic logic. Recently, several equivalent transformations between standard possibilistic logic and min-based causal networks have been proposed. This paper goes one step further and shows that product-based causal networks can be encoded in product-based knowledge bases. The converse transformation is also provided.

Possibilistic networks are important and efficient tools for reasoning under uncertainty. This paper proposes a new graphical model for decision making under uncertainty based on possibilistic networks. In possibilistic decision problems under uncertainty, available knowledge is expressed by means of possibility distribution and preferences are encoded by means another possibility distribution representing the qualitative utility. The first part of the paper proposes a new graphical way to represent such problem, where agent's knowledge and preferences are encoded separately by two distinct possibilistic networks. The first one encodes agent's beliefs and the second one represents the qualitative utility. The second part of the paper proposes a new algorithm for computing optimistic optimal decisions based on merging these two possibilistic networks. In fact, the qualitative possibilistic decision is viewed as a data fusion problem of these two particular possibilistic networks. We show that the computation of optimal decisions comes down to compute a normalization degree of the junction tree associated with the graph representing the fusion of agent's beliefs and preferences.

In multiple-agent logic, a formula is in the form of (a, A) where a is a propositional formula and A is a subset of agents. It states that at least all agents in A believe that a is true. This paper presents a method of refutation for this logic, based on a general resolution principle and using a linear strategy, which is sound and complete. This strategy is then extended so as to deal with certainty levels. It manipulates formulas in the form (a, α/A) expressing that all agents in set A believe at least at some level α that a is true. Finally, an experimental study is provided with the aim to estimate the performance of the proposed algorithms.

This paper first proposes a new graphical model for decision making under uncertainty based on min-based possibilistic networks. A decision problem under uncertainty is described by means of two distinct min-based possibilistic networks: the first one expresses agent's knowledge while the second one encodes agent's preferences representing a qualitative utility. We then propose an efficient algorithm for computing optimistic optimal decisions using our new model for representing possibilistic decision making under uncertainty. We show that the computation of optimal decisions comes down to compute a normalization degree of the junction tree associated with the graph resulting from the fusion of agent's beliefs and preferences. This paper also proposes an alternative way for computing optimal optimistic decisions. The idea is to transform the two possibilistic networks into two equivalent possibilistic logic knowledge bases, one representing agent's knowledge and the ...

In multiple-agent logic, a formula is in the form of (a, A) where a is a propositional formula and A is a subset of agents. It states that at least all agents in A believe that a is true. This paper presents a method of refutation for this logic, based on a general resolution principle and using a linear strategy, which is sound and complete. This strategy is then extended so as to deal with certainty levels. It manipulates formulas in the form (a, α/A) expressing that all agents in set A believe at least at some level α that a is true. Finally, an experimental study is provided with the aim to estimate the performance of the proposed algorithms.

The paper presents a 'multiple agent' logic where formulas are pairs of the form (a, A), made of a proposition a and a subset of agents A. The formula (a, A) is intended to mean '(at least) all agents in A believe that a is true'. The formal similarity of such formulas with those of possibilistic logic, where propositions are associated with certainty levels, is emphasised. However, the subsets of agents are organised in a Boolean lattice, while certainty levels belong to a totally ordered scale. The semantics of a set of 'multiple agent' logic formulas is expressed by a mapping which associates a subset of agents with each interpretation (intuitively, the maximal subset of agents for whom this interpretation is possibly true). Soundness and completeness results are established. Then a joint extension of the multiple agent logic and possibilistic logic is outlined. In this extended logic, propositions are then associated with both sets of agents and certainty levels. A formula then expresses that 'all agents in set A believe that a is true at least at some level'. The semantics is then given in terms of fuzzy sets of agents that find an interpretation more or less possible. A specific feature of possibilistic logic is that the inconsistency of a knowledge base is a matter of degree. The proposed setting enables us to distinguish between the global consistency of a set of agents and their individual consistency (where both can be a matter of degree). In particular, given a set of multiple agent possibilistic formulas, one can compute the subset of agents that are individually consistent to some degree.

In possibility theory, there are two kinds of possibilistic causal networks depending if possibilistic conditioning is based on the minimum or on the product operator. Similarly there are also two kinds of possibilistic logic: standard (min-based) possibilistic logic and quantitative (product-based) possibilistic logic. Recently, several equivalent transformations between standard possibilistic logic and min-based causal networks have been proposed. This paper goes one step further and shows that product-based causal networks can be encoded into product-based knowledge bases. The converse transformation is also provided.

Cuevas 2 I Aristotle's "De Anima" discusses several different aspects of what type of thing the soul is, as well as the things that it can and cannot do and the attributes that it does and does not have. Aristotle outlines that the purpose of this treatise is "to study and know the nature of essence of the soul, and then all of its coincidental properties; [of which some] seem to be distinctive attributes of the soul, while others also seem to belong to animals because they have souls." 1 In this paper I will defend the claim that based on Aristotle's philosophy of the soul and subsequent commentary the soul is the primary substance and form of the living body (in short, the essence), and that the soul is the agent by which humans exercise action. For this paper, I shall use as references two articles: first, "Soul as Subject in Aristotle's De Anima" by Christopher Shields; and second, "The Priority of Soul as Actuality in Aristotle's De Anima" by Ignacio De Ribera-Martin. I have chosen these two articles as they both focus on the implications of Aristotle's claims in "De Anima," Book 2. More specifically, Shields argues against the notion that, based on Aristotle's claims in this text, the soul cannot be a subject by referring to the context in which Aristotle appears to deny subjecthood of the soul and claiming that the passage does not in fact refer to the soul as subject but, rather, that it is primarily concerned with the soul as substance. De Ribera-Martin, on the other hand, discusses the foundations upon which it can be claimed that the soul is the first actuality of the body, and argues to defend that the soul as actuality takes priority over other actualities in the definition of the actuality that is the cause of the living being and its powers. Importantly in the justification for pairing both sources, I must note that De Ribera-Martin's treatment of 1 Aristotle, "De Anima" I. 1, 402a5-10

Clustering techniques have always been oriented to solve classification and pattern recognition problems. This clustering techniques have been used also to initialize the centers of the Radial Basis Function (RBF) when designing an RBF Neural Network (RBFNN) that approximates a function. Since classification and function approximation problems are quite different, it is necessary to design a new clustering technique specialized in the problem of function approximation. In this paper, a new clustering technique it is proposed to make the right initialization of the centers of the RBFs. The novelty of the algorithm is the employment of a possibilistic partition of the data, rather than a hard or fuzzy partition as it is commonly used in clustering algorithms. The use of this kind of partition with the addition of several components to use the information provided by the output, allow the new algorithm to provide better results and be more robust than the other clustering algorithms even if noise exits in the input data.

Acute urinary retention (AUR) in women is not uncommon. Many reports have been published discussing the possible theories and pathogeneses of this condition. AUR induced by uterine fibroid is a rare entity that has been mentioned only in case reports. All the reported cases focused mainly on the different approaches for fibroid management. In this study, we present a 52-year-old female with recurrent episodes of urinary retention that was related to periods of menstruation. Pelvic magnetic resonance imaging revealed a markedly enlarged uterus with multiple fibroids. The patient had laparoscopic hysterectomy with postoperative resolution of patient's symptoms and improved uroflow studies. This is the first article that proves the cure of AUR following hysterectomy using an objective tool.

Emotions classification of text documents is applied to reveal if the document expresses a determined emotion from its writer. As different supervised methods are previously used for emotion documents' classification, in this research we present a novel model that supports the classification algorithms for more accurate results by the support of TF-IDF measure. Different experiments have been applied to reveal the applicability of the proposed model, the model succeeds in raising the accuracy percentage according to the determined metrics (precision, recall, and f-measure) based on applying the refinement of the lexicon, integration of lexicons using different perspectives, and applying the TF-IDF weighting measure over the classifying features. The proposed model has also been compared with other research to prove its competence in raising the results' accuracy.

A client steps into your office to discuss an immigration matter. The client, Geovanni, appears to be an effeminate gay man, but Geovanni tells you that she is transgender and considers herself to be female. 1 * The author is the legal director of Immigration Equality, formerly known as the Lesbian and Gay Immigration Rights Task Force. Immigration Equality advocates for equal rights for lesbian, gay, bisexual, transgender, and HIV-positive individuals under U.S. immigration law. The author would like to thank legal intern Aaron Morris (anticipated juris doctorate at American University, 2005) for his invaluable assistance with this Article. The author would also like to thank Dean Spade, founder of the Sylvia Rivera Law Project, for reading and commenting on portions of the Article. NEILSONCHRISTENSEN[2] 2/3/2011 10:00 PM 102 FORDHAM URBAN LAW JOURNAL [Vol. XXXII remote location, and raped her. Based on the years of abuse she has suffered on account of her transgender identity, Geovanni wants to apply for asylum. 2

A client steps into your office to discuss an immigration matter. The client, Geovanni, appears to be an effeminate gay man, but Geovanni tells you that she is transgender and considers herself to be female. 1 * The author is the legal director of Immigration Equality, formerly known as the Lesbian and Gay Immigration Rights Task Force. Immigration Equality advocates for equal rights for lesbian, gay, bisexual, transgender, and HIV-positive individuals under U.S. immigration law. The author would like to thank legal intern Aaron Morris (anticipated juris doctorate at American University, 2005) for his invaluable assistance with this Article. The author would also like to thank Dean Spade, founder of the Sylvia Rivera Law Project, for reading and commenting on portions of the Article. NEILSONCHRISTENSEN[2] 2/3/2011 10:00 PM 102 FORDHAM URBAN LAW JOURNAL [Vol. XXXII remote location, and raped her. Based on the years of abuse she has suffered on account of her transgender identity, Geovanni wants to apply for asylum. 2

This paper describes a logical machinery for computing decisions, where the available knowledge on the state of the world is described by a possibilistic propositional logic base i.e., a collection of logical statements associated with qualitative certainty levels, and where the preferences of the user are also described by another possibilistic logic base whose formula weights are interpreted in terms of priorities. Two attitudes are allowed for the decision maker: a pessimistic risk-averse one and an optimistic one. The computed decisions are in agreement with a qualitative counterpart to the classical theory of expected utility, recently developed by three of the authors. A link is established between this logical view of qualitative decision making and an ATMSbased computation procedure. E cient algorithms for computing pessimistic and optimistic optimal decisions are nally given in this logical setting using some previous work of the fourth author.

A database represents part of reality by containing data representing properties of real objects or concepts. To many real-world concepts or objects, time is an essential aspect and thus it should often be (implicitly) represented by databases, making these temporal databases. However, like other data, the time-related data in such databases may also contain imperfections such as uncertainties. One of the main purposes of a database is to allow the retrieval of information or knowledge deduced from its data, which is often done by querying the database. Because users may have both positive and negative preferences, they may want to query a database in a bipolar way. Moreover, their demands may have some temporal aspects. In this paper, a novel technique is presented, to query a valid-time relation containing uncertain valid-time data in a heterogeneously bipolar way, allowing every elementary query constraint a specific temporal constraint.

Databases model parts of reality by containing data representing properties of real-world objects or concepts. Often, some of these properties are time-related. Thus, databases often contain data representing time-related information. However, as they may be produced by humans, such data or information may contain imperfections like uncertainties. An important purpose of databases is to allow their data to be queried, to allow access to the information these data represent. Users may do this using queries, in which they describe their preferences concerning the data they are (not) interested in. Because users may have both positive and negative such preferences, they may want to query databases in a bipolar way. Such preferences may also have a temporal nature, but, traditionally, temporal query conditions are handled specifically. In this paper, a novel technique is presented to query a valid-time relation containing uncertain valid-time data in a bipolar way, which allows the query to have a single bipolar temporal query condition.

Clustering techniques have always been oriented to solve classification and pattern recognition problems. This clustering techniques have been used also to initialize the centers of the Radial Basis Function (RBF) when designing an RBF Neural Network (RBFNN) that approximates a function. Since classification and function approximation problems are quite different, it is necessary to design a new clustering technique specialized in the problem of function approximation. In this paper, a new clustering technique it is proposed to make the right initialization of the centers of the RBFs. The novelty of the algorithm is the employment of a possibilistic partition of the data, rather than a hard or fuzzy partition as it is commonly used in clustering algorithms. The use of this kind of partition with the addition of several components to use the information provided by the output, allow the new algorithm to provide better results and be more robust than the other clustering algorithms even if noise exits in the input data.

Author's Declaration I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public.

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.

Data mining classification plays an important role in the prediction of outcomes. One of the outstanding classifications methods in data mining is Naive Bayes Classification (NBC). It is capable of envisaging results and mostly effective than other classification methods. Many Naive Bayes classification method provide low performance in classification and regression problems  Ones of the facts behinds the performances of the NBC is dues to the assumptions of contingent on independence amidst predictors and the initials hyper parameters. However, this strong assumption leads to loss of accuracy. In this study, a new method for boosting the accuracy of NBC was proposed. The proposed new technique uses a grid search to give better accuracy Naive Bayes classification.

Data mining classification plays an important role in the prediction of outcomes. One of the outstanding classifications methods in data mining is Naive Bayes Classification (NBC). It is capable of envisaging results and mostly effective than other classification methods. Many Naive Bayes classification method provide low performance in classification and regression problems  Ones of the facts behinds the performances of the NBC is dues to the assumptions of contingent on independence amidst predictors and the initials hyper parameters. However, this strong assumption leads to loss of accuracy. In this study, a new method for boosting the accuracy of NBC was proposed. The proposed new technique uses a grid search to give better accuracy Naive Bayes classification.

This work joins the assets of two different classification procedures for National Oceanic and Atmospheric Administration Advanced Very High Resolution Radiometer (NOAA AVHRR) data. The first procedure presented by Rodríguez Yi et al. (2000) was based on image segmentation following supervised classification by regions. Eight vegetation classes were identified using this procedure. A Kappa coefficient of 0.4 indicated that image segmentation associated to supervised classification by regions is a procedure that is useful for mapping vegetation classes on a regional scale. SPRING software was used to perform image segmentation and supervised classification using AVHRR channel 1 and 2 mosaics. Prior to image segmentation (region growing algorithm), the histograms of these channels were equalized to avoid a preference for a channel with large variance. The best segmentation treshold values for area and similarity were 2 and 25, respectively. Supervised classification by regions was based on the Bhattacharrya distance with a threshold of 95% for correct classification. Twelve Landsat images together with field information were used as ancillary data to support the training sample selection in the supervised classification procedure. The second procedure presented by Durieux et al. (2000) was based on fuzzy logic classification of multisource data and NOAA-AVHRR images. This methodology used jointly overlay operations, multiple criteria analysis methods and fuzzy procedure. Vegetation classification was based on the biogeographical analysis of relationships between geographical data and vegetation distribution associated to remote sensing information given by the spectral response of each vegetation type. Multi-source data were associated to expert knowledge using a fuzzy ponderation. Resulting maps described the potentiality of each vegetation class to be present in a pixel in relation with the considered criterion. Fusions of possibility distribution for each vegetation class were done using a new individualized method. Finally a maximum operator was used to discriminate vegetation class potentialities in the final integration. The main characteristics of this method were the use of possibility theory to handle imprecision due to pixel classification, and the ability to merge numerical sources (satellite image spectral bands, climatic map, DEM, soil map) and symbolic sources (expert knowledge about best localization of classes).

In real-world problems, input data may be pervaded with uncertainty. In this paper, we investigate the behavior of naive possibilistic classifiers, as a counterpart to naive Bayesian ones, for dealing with classification tasks in presence of uncertainty. For this purpose, we extend possibilistic classifiers, which have been recently adapted to numerical data, in order to cope with uncertainty in data representation. Here the possibility distributions that are used are supposed to encode the family of Gaussian probabilistic distributions that are compatible with the considered data set. We consider two types of uncertainty: i) the uncertainty associated with the class in the training set, which is modeled by a possibility distribution over class labels, and ii) the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data. Moreover, the approach takes into account the uncertainty about the estimation of the Gaussian distribution parameters due to the limited amount of data available. We first adapt the possibilistic classification model, previously proposed for the certain case, in order to accommodate the uncertainty about class labels. Then, we propose an algorithm based on the extension principle to deal with imprecise attribute values. The experiments reported show the interest of possibilistic classifiers for handling uncertainty in data. In particular, the probability-to-possibility transform-based classifier shows a robust behavior when dealing with imperfect data.

In this paper, we address the problem of possibilistic network-based classification with uncertain inputs. Possibilistic networks are powerful tools for representing and reasoning with uncertain and incomplete information in the framework of possibility theory. We first consider the direct use of Jeffrey's rule in the framework of possibility theory in order to perform classification with uncertain inputs. Then we study the property of Markov-blanket in our context. Lastly, we propose an efficient algorithm for possibilistic classifiers with uncertain inputs ensuring the same classification results as using the possibilistic counterpart of Jeffrey's rule. Our algorithm performs this task in a polynomial time without assuming strong independence relations between observations.

Graphical belief models are compact and powerful tools for representing and reasoning under uncertainty. Possibilistic networks are graphical belief models based on possibility theory. In this paper, we address reasoning under uncertain inputs in both quantitative and qualitative possibilistic networks. More precisely, we first provide possibilistic counterparts of Pearl's methods of virtual evidence then compare them with the possibilistic counterparts of Jeffrey's rule of conditioning. As in the probabilistic setting, the two methods are shown to be equivalent in the quantitative setting regarding the existence and uniqueness of the solution. However in the qualitative setting, Pearl's method of virtual evidence which applies directly on graphical models disagrees with Jeffrey's rule and the virtual evidence method. The paper provides the precise situations where the methods are not equivalent. Finally, the paper addresses related issues like transformations from one method to another and commutativity.

Interval-based possibilistic logic is a flexible setting extending standard possibilistic logic such that each logical expression is associated with a sub-interval of [0, 1]. This paper focuses on the fundamental issue of conditioning in the interval-based possibilistic setting. The first part of the paper first proposes a set of natural properties that an interval-based conditioning operator should satisfy. We then give a natural and safe definition for conditioning an interval-based possibility distribution. This definition is based on applying standard min-based or product-based conditioning on the set of all associated compatible possibility distributions. We analyze the obtained posterior distributions and provide a precise characterization of lower and upper endpoints of the intervals associated with interpretations. The second part of the paper provides an equivalent syntactic computation of interval-based conditioning when interval-based distributions are compactly encoded by means of interval-based possibilistic knowledge bases. We show that intervalbased conditioning is achieved without extra computational cost comparing to conditioning standard possibilistic knowledge bases.

Possibility theory and possibilistic logic are well-known uncertainty frameworks particularly suited for representing and reasoning with uncertain, partial and qualitative information. Belief update plays a crucial role when updating beliefs and uncertain pieces of information in the light of new evidence. This paper deals with conditioning uncertain information in a qualitative interval-valued possibilistic setting. The first important contribution concerns a set of three natural postulates for conditioning intervalbased possibility distributions. We show that any interval-based conditioning satisfying these three postulates is necessarily based on the set of compatible standard possibility distributions. The second contribution consists in a proposal of efficient procedures to compute the lower and upper endpoints of the conditional interval-based possibility distribution while the third important contribution provides a syntactic counterpart of conditioning interval-based possibility distributions in case where these latter are compactly encoded in the form of possibilistic knowledge bases.

Possibilistic networks are graphical models particularly suitable for representing and reasoning with uncertain and incomplete information. According to the underlying interpretation of possibilistic scales, possibilistic networks are either quantitative (using product-based conditioning) or qualitative (using min-based conditioning). Among the multiple tasks, possibilitic models can be used for, classification is a very important one. In this paper, we address the problem of handling uncertain inputs in binary possibilistic-based classification. More precisely, we propose an efficient algorithm for revising possibility distributions encoded by a naive possibilistic network. This algorithm is suitable for binary classification with uncertain inputs since it allows classification in polynomial time using several efficient transformations of initial naive possibilistic networks.

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.

Possibility theory and possibilistic logic are well-known uncertainty frameworks particularly suited for representing and reasoning with uncertain, partial and qualitative information. Belief update plays a crucial role when updating beliefs and uncertain pieces of information in the light of new evidence. This paper deals with conditioning uncertain information in a qualitative interval-valued possibilistic setting. The first important contribution concerns a set of three natural postulates for conditioning intervalbased possibility distributions. We show that any interval-based conditioning satisfying these three postulates is necessarily based on the set of compatible standard possibility distributions. The second contribution consists in a proposal of efficient procedures to compute the lower and upper endpoints of the conditional interval-based possibility distribution while the third important contribution provides a syntactic counterpart of conditioning interval-based possibility distributions in case where these latter are compactly encoded in the form of possibilistic knowledge bases.

Conditioning is an important task for designing intelligent systems in artificial intelligence. This paper addresses an issue related to the possibilistic counterparts of Jeffrey's rule of conditioning. More precisely, it addresses the existence and unicity of solutions computed using the possibilistic counterparts of the socalled kinematics properties underlying Jeffrey's rule of conditioning. We first point out that like the probabilistic framework, in the quantitative possibilistic setting, there exists a unique solution for revising a possibility distribution given uncertainty bearing on a set of exhaustive and mutually exclusive events. However, in the qualitative possibilistic framework, the situation is different. In particular, the application of the kinematics principle does not guarantee the existence of a solution. We provide precise conditions where the unicity of the revised possibility distribution exists.

Possibilistic networks are belief graphical models based on possibility theory. This paper deals with a special kind of possibilistic networks called three-valued possibilistic networks where only three possibility levels are used to encode uncertain information. The paper analyzes different semantics of three-valued networks and provides precise relationships relating the different semantics. More precisely, the paper analyzes two categories of methods for deriving a three-valued joint possibility distribution from a three-valued possibilistic network. The first category of methods is based on viewing the three-valued possibilistic network as a family of compatible networks and defining combination rules for deriving the threevalued joint distribution. The second category is based on three-valued chain rules using three-valued operators inspired from some three-valued logics. Finally, the paper shows that the inference using the well-known Junction tree algorithm cannot be extended to all the three-valued chain rules.

In this paper, we address the problem of possibilistic network-based classification with uncertain inputs. Possibilistic networks are powerful tools for representing and reasoning with uncertain and incomplete information in the framework of possibility theory. We first consider the direct use of Jeffrey's rule in the framework of possibility theory in order to perform classification with uncertain inputs. Then we study the property of Markov-blanket in our context. Lastly, we propose an efficient algorithm for possibilistic classifiers with uncertain inputs ensuring the same classification results as using the possibilistic counterpart of Jeffrey's rule. Our algorithm performs this task in a polynomial time without assuming strong independence relations between observations.

Possibilistic networks are graphical models particularly suitable for representing and reasoning with uncertain and incomplete information. According to the underlying interpretation of possibilistic scales, possibilistic networks are either quantitative (using product-based conditioning) or qualitative (using min-based conditioning). Among the multiple tasks, possibilitic models can be used for, classification is a very important one. In this paper, we address the problem of handling uncertain inputs in binary possibilistic-based classification. More precisely, we propose an efficient algorithm for revising possibility distributions encoded by a naive possibilistic network. This algorithm is suitable for binary classification with uncertain inputs since it allows classification in polynomial time using several efficient transformations of initial naive possibilistic networks.

When do probability distribution functions (PDFs) about future climate misrepresent uncertainty? How can we recognise when such misrepresentation occurs and thus avoid it in reasoning about or communicating our uncertainty? And when we should not use a PDF, what should we do instead? In this paper we address these three questions. We start by providing a classification of types of uncertainty and using this classification to illustrate when PDFs misrepresent our uncertainty in a way that may adversely affect decisions. We then discuss when it is reasonable and appropriate to use a PDF to reason about or communicate uncertainty about climate. We consider two perspectives on this issue. On one, which we argue is preferable, available theory and evidence in climate science basically excludes using PDFs to represent our uncertainty. On the other, PDFs can legitimately be provided when resting on appropriate expert judgement and recognition of associated risks. Once we have specified the border between appropriate and inappropriate uses of PDFs, we explore alternatives to their use. We briefly describe two formal alternatives, namely imprecise probabilities and possibilistic distribution functions, as well as informal possibilistic alternatives. We suggest that the possibilistic alternatives are preferable.

Web information is too heterogeneous that users have difficulties to retrieve their needed information: text, image orvideo. In this context, the collaborative work presents one solution proposed to solve this problem. Collaborative retrieval enables the retrieval histories' sharing between users having the same profile across multiple tools such as annotations. We propose in this paper to improve collaborative retrieval performance, considering the annotations as a new source of information describing documents. In our contribution, we propose to apply the relevance feedback to extend the user's query. So we use a possibilistic approach to extract the relevant terms from annotations given in semi-structured documents returned by collaborative retrieval systems.

Over the last decade, the production and use of digital spatial data has increased rapidly. This strong growth has caused duplication of data collection efforts and a suboptimal uses of resources (Warnecke et al. 1998; Wehn de Montalvo 2003; Omran et al. 2006). Spatial Data Infrastructures (SDIs) play an important role in optimizing the organization and use of spatial data. SDIs are supposed to facilitate Spatial Data Sharing (SDS) among organizations, which is a basic condition for data access and multiple use at all levels (Crompvoets et al. 2004; Harvey and Tulloch 2006). While technical aspects in spatial data sharing receive much attention (Bishr 1998; Stoimenov et al. 2005), it cannot be expected that all spatial data sharing obstacles can be solved by technical solutions. The technical aspect has been addressed to solve problems of data integration (interoperability) (Harvey 2002; Goodchild et al. 1998). For SDS not only technical interoperability, but also "soft interoperability" is important for successful SDIs. Nedovic-Budic and Pinto (2001) introduce the term "soft interoperability" to draw attention to the human and behavior aspects of SDS, which is an inherently social phenomenon. The challenge of improving SDS is in a better understanding of the human (individual and organization) behavior. There are many examples of SDS failure. A short introduction to these cases may help the reader to get an impression of the importance and nature of the problem and set the stage for the remainder of this dissertation. The first example is from the Egyptian Survey Authority (ESA). ESA is executing the Egyptian Cadastral Information Management (ECIM) Project, which involves the management of spatial data. The ECIM project started in March 2002 to support the computerization of the cadastral system in Egypt. This project aims to improve the links between the land information system for cadastral services and the systems for land registration and taxation. In order to achieve this goal, ESA collaborates with the Real Estate Publicity Department (REPD) of the Ministry of Justice (responsible for the land registry) and the Real Estate Taxation Department (RETD) of the Ministry of Finance. The system that is managed within the ECIM Project consists of ESA's own cadastral data and workflows, and the information exchange links with REPD's land registration system and RETD's land taxation system (Elrouby et al. 2005). Many of the challenges to the ECIM Project have been caused by the lack of cooperation between these organizations. The relationship between ESA and REPD deteriorated in the course of the project, 2002 and 2005 (Elrouby et al. 2005). The second example is from National Authority for Remote Sensing and Space Sciences (NARSS) in Egypt. NARSS has a core of eight different divisions: 1) geology and mineral resources; 2) agriculture applications, soils, and marine; 3) engineering studies and water resources; 4) environmental studies and land use; 5) space sciences and strategic studies; 6) image processing, computer and ground receiving station; 7) aerial photography, aviation and surveying; and 8) scientific training and continuous studies. Spatial data are fragmented across multiple systems and databases, and linkages are lacking (Omran 2005; Omran et al. 2006). This lack of linkages also precludes effective updating of the data, to maintain a high-level of accuracy, or to do any serious reporting. The main problem is the lack of cooperation between the eight divisions. C Ch ha ap pt te er r 1 1 4 Ch ha ap pt te er r 1 1 6 S SD DS S: : B Br ri id dg gi in ng g t th he e G Ga ap p 13 S SD DS S: : B Br ri id dg gi in ng g t th he e G Ga ap p S SD DS S: : B Br ri id dg gi in ng g t th he e G Ga ap p S SD DS S: : A A C Cr ro os ss s C Cu ul lt tu ur ra al l M Mo od de el l S SD DS S: : A A C Cr ro os ss s C Cu ul lt tu ur ra al l M Mo od de el l Chapter 7 Conclusions and Eye to the Future C Co on nc cl lu us si io on ns s a an nd d E Ey ye e t to o t th he e F Fu ut tu ur re e