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We design, implement and assess in this paper a new architecture of a possibilistic mono- and cross-language information retrieval (IR/CLIR) system. The latter is useful to experiment query disambiguation, expansion and translation processes in both IR and CLIR frameworks. We take advantage of possibility theory to overcome the problems of query disambiguation and expansion in an uncertain and imprecise IR/CLIR context. We investigate the impact of combining possibilistic query disambiguation with expansion on IR/CLIR efficiency. A co-occurrence graph representation is exploited to quantify the similarity between query terms and their semantically close words (expansion task) or between query terms and their possible meanings (disambiguation task). We extend the possibilistic mono-language query disambiguation approach to a cross-language framework. We conduct a set of experiments using ROMANSEVAL data collection, the French–English parallel text corpus Europarl and the CLEF-2003 French–English IR/CLIR test collection. Results highlight some statistically significant improvements of our possibilistic approaches when compared to some state-of-the-art IR/CLIR works.

In this research paper, we propose an automatic segmentation method of multispectral magnetic resonance image (MRI) of the human brain using an information fusion approach through the framework of the possibility theory. The fusion process is summarized into three essential steps. First, a data is extracted from the various images and modeled in a common mathematical framework, in this step the fuzzy C-means (FCM) algorithm is chosen. The combination rule is used to combine this information in the second step. A final segmented image is the result of the last phase. Our experimental results using simulated brain MRI datasets show that the proposed approach overcome the impact of the noise and substantially improve the accuracy of image segmentation.

A DataSpace Support Platform (DSSP) is a self-sustained and self-managed system which needs to support uncertainty among its mediated schemas and its schema mappings. Some approaches for managing such uncertainty by assigning probabilities and reliability degrees to schema mappings have been proposed. Unfortunately, the number of mappings self-generated by a DSSP is usually too large and among those possible mappings, some might be totally correct and others partially correct. Therefore, providing probabilities or reliability degrees to the mappings is necessary but not sufficient to resolve uncertainty among them. This paper proposes a stepper-based approach called pos-mapping to managing reliable mappings using possibility theory. Instead of choosing a threshold for managing the reliable mappings, pos-mapping approach orders and divides the set of reliable mappings into subsets of possibility distributions and assigns to each of these subsets a recursive possibility degree function. The recursiveness of the possibility degree function leads to an incremental management of the possibility distributions. Experimental results show that our system is more efficient than the existing systems and the accuracy of the results increases with the number of reliable schemas in the DSSP.

Representational issues of preferences in the framework of a possibilistic ordinal decision model under uncertainty were introduced by Dubois and Prade a few years ago. In this framework, finite, linear, commensurate uncertainty and preference scales are assumed and decisions are ranked according to their expected utility in terms of Sugeno integrals. In this paper we generalise the model by allowing (i) to measure uncertainty and preferences on finite, distributive lattices with involution, and (ii) to formulate the utility expectations in terms of generalized Sugeno integrals where t-norms and t-conorms play a role. For these generalized utility functions we provide axiomatic characterisations. Finally, we also briefly comment the case of working with belief states that may be partially inconsistent, which is usual in case-based decision making problems or when several inconsistent sources of information are available.

We first survey the basic results in recent paper on fuzzy queueing theory based on possibility theory. Then we apply this to two application problems: (1) machine servicing problem (optimal size of service crews); and (2) then a queueing decision problem where we find the optimal number of servers.

This paper presents a new method for approximating an unrestricted belief measure assuring that the "order" defined by the compatibility degree between evidence and the singletons set is preserved. Our approach, based on the concept of fuzzy T-preorder, also allows us to define several equivalence criteria over the set of all basic probability assignment functions on a given domain. Some others related aspects as uniqueness of the approximations are also addressed.

We re-take the possibilistic model for information sources recently put forward by the first author, as opposed to the standard probabilistic models of information theory. Based on an interpretation of possibilistic source coding inspired by utility functions, we define a notion of possibilistic entropy for a suitable class of interactive possibilistic sources, and compare it with the possibilistic entropy of stationary non-interactive sources. Both entropies have a coding-theoretic nature, being obtained as limit values for the rates of optimal compression codes. We list properties of the two entropies, which might support their use as measures of "possibilistic ignorance".

In this contribution a fuzzy object-based data model for imperfect spatial information is proposed within the formal framework of fuzzy set theory and possibility theory. The proposal integrates the two opposite views of geographic entities seen as either exact objects or continuous fields in current Geographic Information Systems. By assuming a Fuzzy Object-Oriented Data modelling approach new data types for representing geographic entities characterized by either unsharp boundaries or indeterminate boundaries and relationships are defined.

Linguistic qualifiers are adopted both to express the extent by which an element of the spatial domain satisfies a gradual property, and to identify regions with indeterminate boundaries.

This paper deals with the extraction of default rules from a database of examples. The proposed approach is based on a special kind of probability distributions, called "big-stepped probabilities", which are known to provide a semantics for non-monotonic reasoning. The rules which are learnt are genuine default rules, which could be used (under some conditions) in a non-monotonic reasoning system and can be encoded in possibilistic logic.

We re-take the possibilistic (as opposed to probabilistic) approach to information coding put forward in ^1,2. To enhance the possibilistic approach also outside the realm of "subjective" uncertainties, in this paper we adopt an "objective" interpretation of possibilistic source coding based on utility functions and an "objective" interpretation of possibilistic channel coding based on distortion measures and similarity indices. We stress the relationship between possibilistic coding as based on distortions between sequences and algebraic coding as based on minimum distances between codewords. We compute the operational (coding-theoretic) entropy for a new class of possibilistic sources.

In this note we provide a proof for the existence theorem of possibility space for uncountable case and verify Cai's conjecture in 1996 [1]. The proof paves the way to link possibility space or possibilistic variable to the fuzzy set theory.

In this paper a general formulation of a fuzzy single machine scheduling problem is proposed. Such notions as schedule, precedence relation and cost function in the fuzzy case are defined. The concept of f-regular function, being a generalization of a regular function, known from the classical theory of scheduling is introduced. A wide class of problems with f-regular cost functions is analyzed and some general properties of such problems are shown.

This paper focuses on the role that social norms play in the selection of equilibrium points seen as social conventions under unforeseen contingencies — that is, their role in the emergence of regularities of behavior which are self-enforcing and effectively adhered to by bounded rational agents due to their self-policing incentives. Differently stated, given a set of game situations imperfectly described, we want to understand how general and abstract norms provide at least the starting point for a norm-based equilibrium selection reasoning procedure which in the end will be able to determine which equilibrium point, belonging to perfectly described games, will be played as the unique solution of each imperfectly described game. In order to solve such a problem we introduce a selection process based on the reformulation of default logic in terms of possibility theory.

The belief structure resulting from the combination of consonant and independent marginal random sets is not, in general, consonant. Also, the complexity of such a structure grows exponentially with the number of combined random sets, making it quickly intractable for computations. In this paper, we propose a simple guaranteed consonant outer approximation of this structure. The complexity of this outer approximation does not increase with the number of marginal random sets (i.e., of dimensions), making it easier to handle in uncertainty propagation. Features and advantages of this outer approximation are then discussed, with the help of some illustrative examples.

In the past decades, the theory of possibility has been developed as a theory of uncertainty that is compatible with the theory of probability. Whereas probability theory tries to quantify uncertainty that is caused by variability (or equivalently randomness), possibility theory tries to quantify uncertainty that is caused by incomplete information. A specific case of incomplete information is that of ill-known sets, which is of particular interest in the study of temporal databases. However, the construction of possibility distributions in the case of ill-known sets is known to be overly complex. This paper contributes to the study of ill-known sets by investigating the inference of uncertainty when constraints are specified over ill-known values. More specific, in this paper it is investigated how the knowledge about constraint satisfaction can be inferred if the constraints themselves are defined by means of ill-known values. It is shown how such reasoning can contribute to the study of (fuzzy) temporal databases.

The connection between probability and possibility has been studied for decades. Several studies have intended to provide a unified interpretation for these concepts; other studies attempt to discover their transformation relationship. This paper addresses these problems using a unified perspective. By extending the viewpoint of interpreting the grade of membership as a conditional probability, we introduce the conditional probability mass function and likelihood mass function to describe randomness and fuzziness, respectively. We draw the conclusion that conditional probability is undetermined itself and can be used for describing either randomness or fuzziness, depending on how it is interpreted. A fuzzy Bayesian theorem is presented based on the fuzziness interpretation of conditional probability. Additionally, a probability-possibility conversion is derived by assigning different interpretations for conditional probability of the Bayesian theorem, which is notably similar to Klir's normalized transformation. An example of target recognition demonstrates that the fuzzy Bayesian classifier outperforms the usual Bayesian classifier.

Uncertainty and inconsistency pervade human knowledge. Possibilistic logic, where propositional logic formulas are associated with lower bounds of a necessity measure, handles uncertainty in the setting of possibility theory. Moreover, central in standard possibilistic logic is the notion of inconsistency level of a possibilistic logic base, closely related to the notion of consistency degree of two fuzzy sets introduced by L. A. Zadeh. Formulas whose weight is strictly above this inconsistency level constitute a sub-base free of any inconsistency. However, several extensions, allowing for a paraconsistent form of reasoning, or associating possibilistic logic formulas with information sources or subsets of agents, or extensions involving other possibility theory measures, provide other forms of inconsistency, while enlarging the representation capabilities of possibilistic logic. The paper offers a structured overview of the various forms of inconsistency that can be accommodated in possibilistic logic. This overview echoes the rich representation power of the possibility theory framework.

In decision problems involving two dimensions (like several agents in uncertainty) the properties of expected utility ensure that the result of a two-stepped procedure evaluation does not depend on the order with which the aggregations of local evaluations are performed (e.g., agents first, uncertainty next, or the converse). We say that the aggregations on each dimension commute. In a previous conference paper, Ben Amor, Essghaier and Fargier have shown that this property holds when using pessimistic possibilistic integrals on each dimension, or optimistic ones, while it fails when using a pessimistic possibilistic integral on one dimension and an optimistic one on the other. This paper studies and completely solves this problem when more general Sugeno integrals are used in place of possibilistic integrals, leading to double Sugeno integrals. The results show that there are capacities other than possibility and necessity measures that ensure commutation of Sugeno integrals. Moreover, the relationship between two-dimensional capacities and the commutation property for their projections is investigated.

The problem of belief change is considered as a major issue in managing the dynamics of an information system. It consists in modifying an uncertainty distribution, representing agents’ beliefs, in the light of a new information. In this paper, we focus on the so-called multiple iterated belief revision or C-revision, proposed for conditioning or revising uncertain distributions under uncertain inputs. Uncertainty distributions are represented in terms of ordinal conditional functions. We will use prioritized or weighted knowledge bases as a compact representation of uncertainty distributions. The input information leading to a revision of an uncertainty distribution is also represented by a set of consistent weighted formulas. This paper shows that C-revision, defined at a semantic level using ordinal conditional functions, has a very natural representation using weighted knowledge bases. We propose simple syntactic methods for revising weighted knowledge bases, that are semantically meaningful in the frameworks of possibility theory and ordinal conditional functions. In particular, we show that the space complexity of the proposed syntactic C-revision is linear with respect to the size of initial weighted knowledge bases.

An extension of Shannon entropy to the theory or belief and evidence is analyzed. Expressed as the weighed sum of logarithms of beliefs, it is termed an index of confusion. It is shown to exhibit a pathological behavior when reaching its maximum. The alternative, linear version of this index is shown to behave properly, reaching its extremum for a natural extension of the uniform distribution. Lastly, the consonant case of nested supports of evidence, is studied thoroughly, both in the finite setting, and when the frame of discernment is a real line.