POSSIBILITY THEORY

Computer vision is an ever growing discipline whose ambitious goal is to enable machines with the intelligent
visual skills humans and animals are provided by Nature, allowing them to interact effortlessly
with complex, dynamic environments. Designing automated visual recognition and sensing systems
typically involves tackling a number of challenging tasks, and requires an impressive variety of sophisticated
mathematical tools. In most cases, the knowledge a machine has of its surroundings is at best
incomplete – missing data is a common problem, and visual cues are affected by imprecision. The need
for a coherent mathematical ‘language’ for the description of uncertain models and measurements then
naturally arises from the solution of computer vision problems.

The theory of evidence (sometimes referred to as ‘evidential reasoning’, ‘belief theory’ or ‘Dempster-
Shafer theory’) is, perhaps, one of the most successful approaches to uncertainty modelling, as arguably
the most straightforward and intuitive approaches to a generalized probability theory. Emerging in the
last Sixties from a profound criticism of the more classical Bayesian theory of inference and modelling
of uncertainty, it stimulated in the last decades an extensive discussion of the epistemic nature of both
subjective ‘degrees of beliefs’ and frequentist ‘chances’ or relative frequencies. More recently, a renewed
interest in belief functions, the mathematical generalization of probabilities which are the object of study
of the theory of evidence, has seen a blossoming of applications to a variety of fields of applied science.

In this Book we are going to show how, indeed, the fruitful interaction of computer vision and evidential
reasoning is able stimulate a number of advances in both fields. From a methodological point of
view, novel theoretical advances concerning the geometric and algebraic properties of belief functions as
mathematical objects will be illustrated in some detail in Part II, with a focus on a perspective ‘geometric
approach’ to uncertainty and an algebraic solution of the issue of conflicting evidence. In Part III we will
illustrate how these new perspectives on the theory of belief functions arise from important computer vision
problems, such as articulated object tracking, data association and object pose estimation, to which
in turn the evidential formalism can give interesting new solutions. Finally, some initial steps towards
a generalization of the notion of total probability to belief functions will be taken, in the perspective of
endowing the theory of evidence with a complete battery of estimation and inference tools to the benefit
of scientists and practitioners.

The belief that Aristotle opposes potency (dunamis) to actuality (energeia or entelecheia) has gone mostly untested. This essay defines and distinguishes forms of the Opposition Hypothesis—the Actualization, Privation, and Modal—examining the texts and arguments adduced to support them. Using Aristotle's own account of opposition, the texts appear instead to show that potency and actuality are compatible, while arguments for their opposition produce intractable problems. Notably, Aristotle's refutation of the Megarian Identity Hypothesis applies with equal or greater force to the Opposition Hypothesis. For Aristotle, then, potency and actuality are compatible.

Fuzzy numerical technique for FMEA has been proposed to deal with the drawbacks of crisp FMEA and fuzzy rule based FMEA approaches. Fuzzy numerical approaches based on de-fuzzification also suffer from the drawback of providing arbitrary priority ranks of failure modes even when their membership functions overlap. To overcome this drawback we developed a new methodology integrating the concepts of similarity value measure of fuzzy numbers and possibility theory. Similarity value measure has been applied to group together failure modes having similar amount of risk value. The possibility theory has been used for checking for conformance guidelines. Two case studies have been shown to demonstrate the methodology thus developed. The proposed methodology is more robust in nature as it does not require arbitrary precise operations like de-fuzzification to prioritise the failure modes. Application of possibility theory is new to the domain of risk analysing using FMEA.

Bipolar argument graphs represent the structure of complex pro and
contra arguments for one or more standpoints. In this article, ampliative and exclusionary principles of evaluating argument strength in bipolar acyclic argumentation graphs are laid out and compared to each other. Argument chains, linked arguments, link attackers and supporters, and convergent arguments are discussed. The strength of conductive arguments is also addressed but it is argued that more work on this type of argument is needed to properly distinguish argument strength from more general value-based components of such arguments. The overall conclusion of the article is that there is no justifiably unique solution to the problem of argument strength outside of a particular epistemological framework.

A possibility measure can encode a family of probability measures. This fact is the basis for a transformation of a probability distribution into a possibility distribution that generalises the notion of best interval substitute to a probability distribution with prescribed confidence. This paper describes new properties of this transformation, by relating it with the well-known probability inequalities of Bienaymé-Chebychev and Camp-Meidel. The paper also provides a justification of symmetric triangular fuzzy numbers in the spirit of such inequalities. It shows that the cuts of such a triangular fuzzy number contains the "confidence intervals" of any symmetric probability distribution with the same mode and support. This result is also the basis of a fuzzy approach to the representation of uncertainty in measurement. It consists in representing measurements by a family of nested intervals with various confidence levels. From the operational point of view, the proposed representation is compatible with the recommendations of the ISO Guide for the expression of uncertainty in physical measurement.

We propose in this paper a method based, on the one hand, on possibility theory to calculate the similarity among the objects of any casebase, taking into account the imperfection and the heterogeneity of data, and based, on the other hand, on the geometric models like the linear and the circular unidimensional scaling and on the graphic models like the ultrametric trees in order to represent and to visualize this similarity in such a way that we can explore and discover the potential structures and patterns that exist in the data. This approach will be applied to an endoscopic casebase in order to recognize the lesions and the pathologies of this base, and several concrete examples will be given along the paper in order to clarify the mathematical concepts of the method.

introduced the concept of possibilistic mean, variance and covariance of fuzzy numbers. In this paper, we extend some of these results to a nonlinear type of fuzzy numbers called adaptive fuzzy numbers (see Bodjanova (2005, Information Science, 172, 73-89) for detail). We then discuss the application of these results to decision making problems in which the parameters may involve uncertainty and vagueness. As an application, we develop expression for fuzzy net present value (FNPV) of future cash flows involving adaptive fuzzy numbers by using their possibilistic moments. An illustrative numerical example is given to illustrate the results.

In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint produces unrealistic typicality values for large data sets. In this paper, we propose a new model called possibilistic-fuzzy c-means (PFCM) model. PFCM produces memberships and possibilities simultaneously, along with the usual point prototypes or cluster centers for each cluster. PFCM is a hybridization of possibilistic c-means (PCM) and fuzzy c-means (FCM) that often avoids various problems of PCM, FCM and FPCM. PFCM solves the noise sensitivity defect of FCM, overcomes the coincident clusters problem of PCM and eliminates the row sum constraints of FPCM. We derive the first-order necessary conditions for extrema of the PFCM objective function, and use them as the basis for a standard alternating optimization approach to finding local minima of the PFCM objective functional. Several numerical examples are given that compare FCM and PCM to PFCM. Our examples show that PFCM compares favorably to both of the previous models. Since PFCM prototypes are less sensitive to outliers and can avoid coincident clusters, PFCM is a strong candidate for fuzzy rule-based system identification.

Anxiety disorders and sensory over-responsivity (SOR) are common in children with autism spectrum disorders (ASD), and there is evidence for an association between these two conditions. Currently, it is unclear what causal mechanisms may exist between SOR and anxiety. We propose three possible theories to explain the association between anxiety and SOR: (a) SOR is caused by anxiety; (b) Anxiety is caused by SOR; or (c) SOR and anxiety are causally unrelated but are associated through a common risk factor or diagnostic overlap. In this paper, we examine support for each theory in the existing anxiety, autism, and neuroscience literature, and discuss how each theory informs choice of interventions and implications for future studies.

The aim of this paper is to present a fusion approach of multi-granularity linguistic information for managing information assessed in di erent linguistic term sets (multi-granularity linguistic term sets) together with its application in a decision making problem with multiple information sources, assuming that the linguistic performance values given to the alternatives by the di erent sources are represented in linguistic term sets with di erent granularity and=or semantic. In this context, a decision process based on two steps is proposed with a view to obtaining the solution set of alternatives. First, the fusion of the multi-granularity linguistic performance values is carried out in order to obtain collective performance evaluations. In this step, on the one hand, the multi-granularity linguistic information is made uniform using a linguistic term set as the uniform representation base, the basic linguistic term set. On the other hand, the collective performance evaluations of the alternatives are obtained by means of an aggregation operator, being fuzzy sets on the basic linguistic term set. Second, the choice of the best alternative(s) from the collective performance evaluations is performed. To do that, a fuzzy preference relation is computed from the collective performance evaluations using a ranking method of pairs of fuzzy sets in the setting of Possibility Theory, applied to fuzzy sets on the basic linguistic term set. Then, a choice degree may be applied on the preference relation in order to rank the alternatives. ?

1] Climate change impact assessment on water resources with downscaled General Circulation Model (GCM) simulation output is characterized by uncertainty due to incomplete knowledge about the underlying geophysical processes of global change (GCM uncertainties) and due to uncertain future scenarios (scenario uncertainties). Disagreement between different GCMs and scenarios in regional climate change impact studies indicates that overreliance on a single GCM with a scenario could lead to inappropriate planning and adaptation responses. This paper focuses on modeling GCM and scenario uncertainty using possibility theory in projecting streamflow of Mahanadi river, at Hirakud, India. A downscaling method based on fuzzy clustering and Relevance Vector Machine (RVM) is applied to project monsoon streamflow from three GCMs with two green house emission scenarios. Possibilities are assigned to all the GCMs with scenarios based on their performance in modeling the streamflow of the recent past (1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005), when there are signals of climate forcing. The possibilities associated with different GCMs and scenarios are used as weights in computing the possibilistic mean of the CDFs projected for three standard time slices 2020s, 2050s, and 2080s. The result shows that the value of streamflow at which the CDF reaches 1 reduces with time, which shows the reduction in probability of occurrence of extreme high flow events in future. Historic record of monsoon streamflow of Mahanadi river also shows similar decreasing trend, which may be due to the effect of high surface warming. Reduction in Mahandai streamflow is likely to pose a major challenge for water resources engineers in meeting water demands in future.

This paper presents a discrete choice model for evaluating parking users' behaviour. In order, to explicitly take into account imprecision and uncertainty lying in user's choice process, the proposed model has been developed within the framework of Possibility Theory. This approach is an alternative way to represent imperfect knowledge (uncertainty) of users about both parking and transportation system status, as well the natural approximate reasoning of the human decision maker (imprecision). The resulting model is a quantitative soft computing tool that could support traffic analysts in planning parking policies and Advanced Travellers Information System (ATIS). In fact, effects of information on user choice can be incorporated in the model itself. Thus, we consider the parking user be a decision-maker that assumes a certain choice set (set of perceived parking alternatives); the user has some information about parking supply system and he/she associates to each parking alternatives an approximate perceived cost/utility that is represented by a possibility distribution; finally, user chooses the alternative which minimise/maximise his/her perceived parking cost/utility. The results have shown how the model is able to represent the effect of various parking policies on users behaviour and how the single component of the parking policy affects the decision-process.

Rendón, The fuzzy classifier system: motivations and first results, Proc. First Intl. Conf. on Parallel Problem Solving from Nature-PPSN I, Springer, Berlin, 1991, pp. 330-334 (scatter Mamdani fuzzy rules for control/modeling problems) M. Valenzuela-Rendón, Reinforcement learning in the fuzzy classifier system, Expert Systems with Applications 14 (1998) 237-247 (scatter Mamdani fuzzy rules for control/modeling problems) J.R. Velasco, Genetic-based on-line learning for fuzzy process control, IJIS 13 (10-11) (1998) 891-903 (scatter Mamdani fuzzy rules for control problems)

In this paper, we present a modeling approach, based on Fuzzy Data Fusion, to reproduce drivers' dynamic choice behavior under an Advanced Traveler Information System (ATIS). The proposed model uses the Possibility Theory to model Uncertainty embedded in human perception of information. We have introduced a time-dependent Possibility Distribution of Information to model the users' changing perception of travel time also based on current network conditions. Drivers' choice models are often developed and calibrated by using Stated Preference (SP) surveys, amongst others. In this work, we present an experiment to set up an SP-tool based on a driving simulator developed at the Polytechnic University of Bari. The results obtained by the proposed model are analyzed and compared with the driver dynamic behavior observed in the experiment.

En los discursos actuales, el futuro oscila entre la omnipresencia un poco banal y la clausura del tiempo. A partir de la noción de futuridad, es posible pensar en una estrategia de pensamiento que permita no solo proyectar futuros, sino también mapear posibilidades, inventar, improvisar y descubrir. Para ello, articulando inquietudesfilosóficas, políticas y etnográficas, es necesario volver sobre algunos sentidos y límites de la palabra «futuro» y ensayar una propuesta para pensar la potencia política de la posibilidad.

In the twenty-first century, a company has to organize around the customers in order to be a successful and viable firm. Customers expect to get what they would like, with a side order of customization. This approach raises several questions that have to be answered, one of which is that despite nowadays customers are knowledgeable in general, they are still far from being experts that can really co-create a product or a service. Therefore, the fundamental challenge is to avoid the abortion of the configuration process by the customer. Based on problem analysis regarding customers' involvement in the configuration process, the main areas of investigation to be considered are the minimization of the complexity experienced by the customers and the reduction of the cognitive overhead, considering not only the extent of choice, but also the lack of understanding about which solution meets their needs and also the uncertainties about the behavior of the supplier and the purchasing process. The paper presents one approach towards defining the appropriate customer profile that enables the adaptation of the process of co-creation to different customers that suits each individual customer's needs and limitations.

The compact representation of incomplete probabilistic knowledge which can be encountered in risk evaluation problems, for instance in environmental studies is considered. Various kinds of knowledge are considered such as expert opinions about characteristics of distributions or poor statistical information. The approach is based on probability families encoded by possibility distributions and belief functions. In each case, a technique for representing the available imprecise probabilistic information faithfully is proposed, using different uncertainty frameworks, such as possibility theory, probability theory, and belief functions, etc. Moreover the use of probability-possibility transformations enables confidence intervals to be encompassed by cuts of possibility distributions, thus making the representation stronger. The respective appropriateness of pairs of cumulative distributions, continuous possibility distributions or discrete random sets for representing information about the mean value, the mode, the median and other fractiles of ill-known probability distributions is discussed in detail.

Risk assessment is an important and significant aid in the decision making process. Risk assessment is performed using 'model' and a model is a function of parameters which are usually affected by uncertainty. Some model parameters are affected by aleatory uncertainty and some others are affected by epistemic uncertainty. In this paper we propose a hybrid method to deal with propagation of both kinds of uncertainty within the same computation of risk.

Nous présentons dans cet article, en premier lieu, une étude comparative de trois théories mathématiques permettant de
réaliser la fusion des sources d’information. Cette étude vise à dégager les caractéristiques inhérentes aux théories des
possibilités, des fonctions de croyance (TFC) et du raisonnement plausible et paradoxal (DSmT) afin d’établir une stratégie
de choix qui nous permet d’adopter la théorie la plus adéquate pour résoudre un problème de fusion en tenant compte
des informations acquises et des imperfections qui les accompagnent. En deuxième lieu, nous présentons également une
nouvelle méthode pour déterminer les éléments focaux paradoxaux pertinents à l’aide des histogrammes de niveaux de gris
et qui permet aussi de réduire la cardinalité de l’hyper-puissance. Ainsi, nous avons élaboré une nouvelle technique pour
ordonner et coder les éléments focaux généralisés. Cette méthode est exploitée, en particulier, pour calculer la cardinalité
de Dezert et Smarandache.

The probabilistic and the possibilistic methods of safety evaluation of structure under uncertain parameters have been developed independently. When the structural system is defined with some of the input parameters as possibilistic and others are sufficient enough to model as probabilistic, available literatures normally start with either probabilistic or possibilistic description of all the variables. This may pose restriction on necessary flexibility to the designer at early stage of modelling of the structural system. The primary objective of the present work is to critically examine various emerging methods of transformation of the possibilistic variables to equivalent probabilistic variables so that probabilistic safety evaluation approach becomes compatible with the nature and quality of the input data. Relying on the fundamental concept of equivalent transformations, i.e. the entropy based transformation and the scaling of fuzzy membership function, the reliability analysis is proposed in the framework of second moment format. In doing so, the bounds on the reliability indices based on the evidence theory are also obtained encompassing the first-order reliability analysis for consistent comparison among alternative transformations. Finally, the reliability computation under hybrid uncertainty is elucidated numerically with examples for comparative study on the suitability of the transformation alternatives.

Component-based software engineering has been projected off-late as an appropriate paradigm for embedded systems development. However this becomes feasible only if the dependability attributes, such as reliability, of embedded systems can be properly estimated and guaranteed using appropriate models. Another recent trend is the prevalence of architectural modelling of software systems due to the advantages such as composability reasoning and analysis of system behaviour as well as the flexibility and reusability of models. However, a major issue is that there exist uncertainty in the reliability parameters associated with the traditional testing-based approaches for particular architectural entities (e.g. components and/or connectors). In this context, we propose a new approach for the reliability estimation of component-based software systems, which steps on an architectural model of the system using Generalized Nets. This notation is a generalization of Petri nets and is an all-purpose formal modelling technique for the description of parallel phenomena. For the reliability description, we apply possibility theory, which has the potential to solve the uncertainty aspect. This is based on fuzzy sets and describes reliability properties of software components in systems architecture with fuzzy measures.

In several works, Deleuze carefully differentiated the virtual from the possible. In her article « Actuel / virtuel » (Vocabulaire de Gilles Deleuze), Anne Sauvagnargues insists on this distinction. Their assimilation is indeed frequent, and symptomatic of a theoretical loosening. Yet, if one should not assimilate them, one should not maintain either, as she does, that the actual and the virtual are "categories that replace other couples such as intelligible vs. sensitive, essence vs. existence, possible vs. real" (22). What Deleuze asserts is remarkably and importantly different: « The virtuality of the Idea has nothing in common with a possibility. » (Différence et répétition 247). The complete absence of the notion of possibility in Deleuze's last text on the virtual (" L'actuel et le virtuel ") could indeed make one think that the concept of virtuality gained the philosopher's preference; and that one should stop conceiving of the virtual in terms of possibility. But many other portions of works prove that the category of possibility is far from being overrun, and support the pertinence of the relationship between virtuality and possibility; among which, one that defines chaos: "It is a void that is not a nothingness, but a virtual, containing all the possible particles and drawing all the possible forms that loom to disappear straight away, without consistency or reference, without consequences." (Qu'est-ce que la philosophie? 111) We will argue that, instead of replacing possibility by virtuality, Deleuze worked at complicating and refining both concepts through an insistent study of their relationship.

Providing cognitive assistance to Alzheimer’s patients in smart homes is a field of research that receives a lot of attention lately. The recognition of the patient’s behavior when he carries out some activities in a smart home is primordial in order to give adequate assistance at the opportune moment. To address this challenging issue, we present a formal activity recognition framework based on possibility theory and description logics. We present initial results from an implementation of this recognition approach in a smart home laboratory.

In this paper we solve the problem of approximating a belief measure with a necessity measure or “consonant belief function” in a geometric framework. Consonant belief functions form a simplicial complex in both the space of all belief functions and the space of all mass vectors: partial approximations are first sought in each component of the complex, while global solutions are selected among them. As a first step in this line of study, we seek here approximations which minimize Lp norms. Approximations in the mass space can be interpreted in terms of mass redistribution, while approximations in the belief space generalize the maximal outer consonant approximation. We compare them with each other and with other classical approximations, and illustrate them with the help of a running example.

At the application level, it is important to be able to define the measurement result as an interval that will contain an important part of the distribution of the measured values, that is, a coverage interval. This practice acknowledged by the International Organization for Standardization (ISO) Guide is a major shift from the probabilistic representation. It can be viewed as a probability/possibility transformation by viewing possibility distributions as encoding coverage intervals. In this paper, we extend previous works on unimodal distributions by proposing a possibility representation of bimodal probability distributions. Indeed, U-shaped distributions or Gaussian mixture distribution are not very rare in the context of physical measurements. Some elements to further propagate such bimodal possibility distributions are also exposed. The proposed method is applied to the case of three independent or positively correlated C-grade resistors in series and compared with the Guide to the Expression of Uncertainty in Measurement (GUM) and Monte Carlo methods.

This study considers a model of road congestion with average cost pricing. Subjects must choose between two routes -Road and Metro. Travel cost on the road is increasing in the number of commuters who choose this route, while travel cost on the metro is decreasing in the number of its users. We examine how changes to road capacity, number of commuters, and metro pricing scheme influence the commuters' route-choice behavior.

In this paper, we extend the domains of armation and negation operators, and more important, of triangular (semi)norms and (semi)conorms from the unit interval to bounded partially ordered sets. The fundamental properties of the original operators are proven to be conserved under this extension. This clearly shows that they are essentially based upon order-theoretic notions. Consequently, a rather general order-

The study evaluates social acceptability of three alternative forest management regimes: state-controlled management; community-based management; and collaborative management involving multiple stakeholders. Villagers, foresters, park employees, entrepreneurs and environmentalists were surveyed. A fuzzylogic based possibility schema for evaluation of forest stakeholder attitudes is developed, and empirically used to investigate stakeholder attitudes towards these alternative forest regimes in Mount Kilimanjaro, Tanzania. Non-parametric statistical analysis is used to draw statistical inferences. The three regimes are ranked based on efficiency, justice, and (un)certainty criteria. The results indicate that the conventional bureaucratic forest regime is falling out of favor in the interests of multi-stakeholders forest management. Due to strategic significance of Mount Kilimanjaro forest resources, and diverse interests of multi-stakeholders (local to global), complete devolution of power to local communities did not gunner an overall favorable social acceptability, either, among the surveyed stakeholders. The findings, however, support a strong desire for increased societal participation in the form of collaborative multi-stakeholder forest management. This outcome calls for significant policy changes to increase participation, as well as harmonization of values and institutions of different stakeholders as a pre-requisite for negotiation among the stakeholders in Mount Kilimanjaro who seek to co-ordinate their activities for sustainable forest management.

Classical approaches of Information Retrieval treat documents and queries as "bags of words" with no syntax and no semantic. This representation is based on the co-occurrence of words in a text and does not take into account the semantic relations that exist between them. With the advent of ontologies, at the end of the 1990s, new approaches of Information Retrieval have appeared. These approaches attempt to capture the semantics of documents and queries by representing them with ontology concepts. A classical ontology does not avoid the vagueness and uncertainty that characterize human reasoning, in modeling the real world. Using the theory of possibility seems to be a solution.

This paper addresses the problem of edge restoration in digital images. Taking advantage of an ensemble approach, multiple type-1 fuzzy filters are combined to reach a decision. The fuzzy logic concept for linguistic variables and possibility theory is discussed with regard to knowledge representation and inference procedures. To improve conventional deinterlacing issues, we adopt type-1 fuzzy set concepts to design a weight measuring approach. We demonstrate that the fuzzy ensemble approach model is well-suited to image processing, and provide case studies in the video deinterlacing field. In our proposed method, five fuzzy membership functions (MFs) of linguistic variable-based fuzzy logic filters are derived from the type-1 (a.k.a. ordinary or primary) fuzzy MF. The weight measuring process of our proposed model is used to assign weights to six candidate deinterlaced pixels that are interpolated according to edge direction. The use of a different MF for each direction allows the filter to characterize each pixel variation influence independently, according to its direction. The weights from all MFs are multiplied with the candidate deinterlaced pixels. The results of the empirical trials clearly show that the proposed system can successfully deal with several image types containing motion or detail elements.

Intelligent agents require methods to revise their epistemic state as they acquire new information. Jeffrey's rule, which extends conditioning to probabilistic inputs, is appropriate for revising probabilistic epistemic states when new information comes in the form of a partition of events with new probabilities and has priority over prior beliefs. This paper analyses the expressive power of two possibilistic counterparts to Jeffrey's rule for modeling belief revision in intelligent agents. We show that this rule can be used to recover several existing approaches proposed in knowledge base revision, such as adjustment, natural belief revision, drastic belief revision, and the revision of an epistemic state by another epistemic state. In addition, we also show that some recent forms of revision, called improvement operators, can also be recovered in our framework.

In the setting of possibility theory, a tool named 'fuzzy pattern matching' (FPM) has been proposed in the eighties, and then successfully used in flexible querying of fuzzy databases and in classification. Given a pattern representing a request expressed in terms of fuzzy sets, and a database containing imprecise or fuzzy attribute values, the FPM returns two matching degrees. Namely, for each item in the base, the possibility and the certainty that it matches the requirements of the pattern are computed. In multiple-source information systems, attribute values are often assessed in linguistic terms belonging to different vocabularies. The request itself, which may include preferences, may be expressed using terms of another vocabulary. The paper proposes a counterpart of FPM, called 'Qualitative Pattern Matching' (QPM), for estimating levels of matching between a request and data expressed with words; words can be related together through a qualitative thesaurus or ontology, where approximate synonymy and specialization relations are encoded. Given a request, QPM rank-orders the items which possibly, or which certainly match the requirements, according to the preferences of the user. The proposed approach is based on a qualitative assessment of matching degrees which does not necessarily require the use of numerical scales. Its merits for dealing with information querying in face of heterogeneous sources of information are advocated. Application to the handling of textual data in information retrieval is also outlined.

In this paper we argue that early warning systems for engineering facilities can be developed by combining and integrating existing technologies and theories. As example, we present an efficient integration of fuzzy expert systems, fault tree analysis and World Wide Web technologies to their application in the development of the Landfill Operation Management Advisor (LOMA), a novel early warning and emergency response system for solid waste landfill operations. The aim of LOMA is to provide assistance to landfill managers on their efforts in preventing accidents and operational problems and to help them to develop emergency response plans if these operational problems shall occur. Additional aim is to disseminate information and knowledge to the public on landfill Environmental Modelling & Software 24 (2009) 8-25 2 operational problems and their adverse effects. This aim is related to solid waste organizations that have to accord with legislations similar to the European Union's EC Directive (2003/4/EC) on Public Access to Environmental Information.

This paper presents a new approach to the problem of designing Radial Basis Function Neural Networks (RBFNNs) to approximate a given function. The presented algorithm focuses in the first stage of the design where the centers of the RBFs have to be placed. This task has been commonly solved by applying generic clustering algorithms although in other cases, some specific clustering algorithms were considered. These specific algorithms improved the performance by adding some elements that allow them to use the information provided by the output of the function to be approximated but they did not add problem specific knowledge. The novelty of the new developed algorithm is the combination of a fuzzy-possibilistic approach with a supervising parameter and the addition of a new migration step that, through the generation of RBFNNs, is able to take proper decisions on where to move the centers. The algorithm also introduces a fuzzy logic element by setting a fuzzy rule that determines the input vectors that influence each center position, this fuzzy rule considers the output of the function to be approximated and the fuzzy-possibilistic partition of the data.

ecises Abstract: The problem of expert opinions representation and ag- gregation has long been adressed in the only framework of probability theory. Nevertheless, recent years have wit- nessed many proposals in other uncertainty theories (pos- sibility theory, evidence theory, imprecise probabilities). This paper casts the problem of aggregating expert opi- nions in a common underlying framework and shows how uncertainty

AbstraetmBoth certainty factors and possibility theory have been successfully used to represent uncertainty in expert systems. Both of these methods were investigated during the development of a rule-based expert system for selecting tillage alternatives for corn and soybean production in Ontario. The expert system was used to test uncertainty management methods and to determine the appropriateness of possibility theory and certainty factors for representing and combining uncertainty in the knowledge base. Several techniques for representing uncertainty with these two methods are reviewed and the strengths and weaknesses of the two approaches, in terms of this project, are discussed. For expert systems in which evidence from many sources is accumulated toward a hypothesis, certainty factors appear to be more responsive than possibility theory methods. The system was validated against human experts and found to peororm extremely well.

Conditioning is crucial in applied science when inference involving time series is involved. Belief
calculus is an effective way of handling such inference in the presence of uncertainty, but different approaches
to conditioning in that framework have been proposed in the past, leaving the matter unsettled.
We propose here an approach to the conditioning of belief functions based on geometrically projecting
them onto the simplex associated with the conditioning event in the space of all belief functions. We show
here that such a geometric approach to conditioning often produces simple results with straightforward
interpretations in terms of degrees of belief. The question of whether classical approaches, such as for
instance Dempster’s conditioning, can also be reduced to some form of distance minimization remains
open: the study of families of combination rules generated by (geometric) conditioning rules appears to
be the natural prosecution of the presented research.

Risk theory is usually developed within probability theory. The aim of this paper is to propose an approach of the risk aversion by possibility theory, initiated by Zadeh in 1978. The main notion studied in this paper is the possibilistic risk premium associated with a fuzzy number A and a utility function u. Under the hypothesis that the utility function u verifies certain hypotheses, one proves a formula to evaluate the possibilistic risk premium in terms of u and of some possibilistic indicators.

Purpose -Research on the use/disclosure of intellectual capital (IC) information by sell-side analysts, using content analysis of their reports, is growing. The objectives of this paper are to establish the importance of this perspective in understanding the role of IC in communicating firm value, to introduce possible theoretical frameworks to interpret the findings of such studies, and to propose methodological developments. Methodology/approach -The paper argues for the need to look at IC from the perspective of sell-side analysts, and then advocates the use of several theoretical frameworks to enrich current understanding of the role of IC as it is used/disclosed by sell-side analysts. Current methodologies used in this type of research are critiqued with a view to proposing multiple research methods. Findings -Looking at IC from the sell-side analyst perspective helps us to understand how the capital market appreciates this information. However, IC information that analysts disclose cannot be taken at its face value. Issues of signalling, analysts' incentives/influences, political economy view, and globalisation are introduced as providing theoretical frameworks for explaining IC disclosure in sell-side analysts' reports. To obtain a richer picture of the role of IC information in analysts' decision processes, multiple research methods are proposed. Practical implications -The proposals in this paper may inform and guide future research on IC information use/disclosure by sell-side analysts with theoretical underpinnings and methodological rigour. Originality/ value -This paper is the first attempt to propose possible theories for interpreting findings of studies on IC use/discsloure by sell-side analysts and suggest multiple research methodologies in this type of research.

In order to design effective advanced traffic information systems (ATIS) suitable mathematical models have to be defined to simulate the effects of information on users route choice behaviour and then to incorporate it into traffic assignment models to estimate how traffic demand loads the roads network.

This paper is a first step in laying down a theoretical foundation for asset allocation under uncertainty, based on possibility theory. First, fuzzy financial knowledge representation is treated. Then, some issues relevant to financial decision making are approached from the standpoint of possibility theory.

When clustering produces more than one candidate to partition a finite set of objects O, there are two approaches to validation (i.e., selection of a "best" partition, and implicitly, a best value for c, which is the number of clusters in O). First, we may use an internal index, which evaluates each partition separately. Second, we may compare pairs of candidates with each other, or with a reference partition that purports to represent the "true" cluster structure in the objects. This paper generalizes many of the classical indices that have been used with outputs of crisp clustering algorithms so that they are applicable for candidate partitions of any type (i.e., crisp or soft, with soft comprising the fuzzy, probabilistic, and possibilistic cases). Space prevents inclusion of all of the possible generalizations that can be realized this way. Here, we concentrate on the Rand index and its modifications. We compare our fuzzy-Rand index with those of Campello, Hullermeier and . Numerical examples are given to illustrate various facets of the new indices. In particular, we show that our indices can be used, even when the partitions are probabilistic or possibilistic, and that our method of generalization is valid for any index that depends only on the entries of the classical (i.e., four-pair types) contingency table for this problem.

A fuzzy morphological approach is here presented to retrieve structural properties of images considered as fuzzy sets. The basic concepts of the possibility theory and of the mathematical morphology are brie y illustrated, together with their suggested integration. Some applications to astronomical images are also shown.

Naïve Bayesian network classifiers have proved their effectiveness to accomplish the classification task, even if they work under the strong assumption of independence of attributes in the context of the class node. However, as all of them are based on probability theory, they run into problems when they are faced with imperfection. This paper proposes a new approach of classification

This study attempts to apply a management science technique to improve the efficiency of Hospital Administration. We aim to design the performance of the surgical services at a Public Hospital that allows the Decision-Maker to plan surgical scheduling over one year in order to reduce waiting lists.