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In classical Constraint Satisfaction Problems (CSPs) knowledge is embedded in a set of hard constraints, each one restricting the possible values of a set of variables. However constraints in real world problems are seldom hard, and CSP's are often idealizations that do not account for the preference among feasible solutions. Moreover some constraints may have priority over others. Lastly, constraints may involve uncertain parameters. This paper advocates the use of fuzzy sets and possibility theory as a realistic approach for the representation of these three aspects. Fuzzy constraints encompass both preference relations among possible instanciations and priorities among constraints. In a Fuzzy Constraint Satisfaction Problem (FCSP), a constraint is satisfied to a degree (rather than satisfied or not satisfied) and the acceptability of a potential solution becomes a gradual notion. Even if the FCSP is partially inconsistent, best instanciations are provided owing to the relaxation of ...

: This paper proposes an extension of the constraint-based approach to job-shop scheduling, that accounts for the flexibility of temporal constraints and the uncertainty of operation durations. The set of solutions to a problem is viewed as a fuzzy set whose membership function reflects preference. This membership function is obtained by an egalitarist aggregation of local constraint-satisfaction levels. Uncertainty is qualitatively described is terms of possibility distributions. The paper formulates a simple mathematical model of jobshop scheduling under preference and uncertainty, relating it to the formal framework of constraint-satisfaction problems in Artificial Intelligence. A combinatorial search method that solves the problem is outlined, including fuzzy extensions of well-known look-ahead schemes. 1. Introduction There are traditionally three kinds of approaches to jobshop scheduling problems: priority rules, combinatorial optimization and constraint analysis. The first kind ...

We present a new approach to deal with default information based on the theory of belief functions. Our semantic structures, inspired by Adams' epsilon semantics, are epsilon-belief assignments, where mass values are either close to 0 or close to 1. In the first part of this paper, we show that these structures can be used to give a uniform semantics to several popular non-monotonic systems, including Kraus, Lehmann and Magidor's system P, Pearl's system Z, Brewka's preferred sub-theories, Geffner's conditional entailment, Pinkas' penalty logic, possibilistic logic and the lexicographic approach. In the second part, we use epsilon-belief assignments to build a new system, called LCD, and show that this system correctly addresses the well-known problems of specificity, irrelevance, blocking of inheritance, ambiguity, and redundancy.

In this paper, it is shown that fuzzy sets and possibility theory provide an homogeneous framework for the representation of both imprecise/uncertain information and soft queries with a flexible interpretation. Incompletely known information as well as flexible query handling capabilities are expected to extend the range of applications for future database management systems. The term fuzzy databases which is extensively used in the specialized literature covers several different meanings which are reviewed. A special emphasis is put on flexible queries addressed to regular databases. Such queries enables the user to easily express preferences among more or less admissible attribute values. Several approaches for introducing flexibility, including fuzzy sets, are compared. A query language based on SQL is outlined and some issues related to query processing are discussed. In addition, possibility theory proves to be useful for representing imperfectly known data and soft constraints. P...

. This paper is an attempt to cast both uncertainty and time in a logical framework. It generalizes possibilistic logic, previously developed by the authors, where each classical formula is associated with a weight which obeys the laws of possibility theory. In the possibilistic temporal logic we present here, each formula is associated with a time set (a fuzzy set in the more general case) which represents the set of instants where the formula is certainly true (more or less certainly true in the general case). When a particular instant is fixed we recover possibilistic logic. Timed possibilistic logic generalizes possibilistic logic also in the sense that we substitute the lattice structure of the set of the (fuzzy) subsets of the temporal scale to the lattice structure underlying the certainty weights in possibilistic logic. Thus many results from possibilistic logic can be straightforwardly generalized to timed possibilistic logic. Illustrative examples are given. 1. Introduction ...

This paper clarifies our understanding of the construction and use of arguments as a paradigm for practical reasoning. We understand practical reasoning as being contrasted to formal (mathematical) reasoning. The latter involves reasoning within a well defined and consistent theory using a specific, well-understood consequence relation. The former involves, as we see it, reasoning from databases, that are collections of facts. These facts need not necessarily comprise a coherent and consistent `picture' and they do not necessarily stand in relationship to any specific model or theory. As a consequence they can be inconsistent, with respect to a classical consequence relation. Reasoning with inconsistencies is one of the types of practical reasoning that is considered by the AI community. Other types of practical reasoning involve induction, abduction etc. A system of argumentation formalizes the notions of construction and use of arguments as a formal system, and makes explicit the difference between formal and practical reasoning. Formal reasoning is a special case of practical reasoning, where all arguments are equally acceptable. In this paper we focus (only) on practical reasoning involving inconsistencies, but we believe that the argumentation-paradigm

Allowing for flexible queries enables database users to express preferences inside minimal requirements, and, if necessary, priorities inside compound queries. In other words, clear-cut properties can be refined by ordering the interpretations compatible with them, according to user's preferences. Often the representation of these preferences can be viewed as modelling linguistic-like terms in requests. In this paper, the theoretical issues raised by the introduction of flexible queries are studied in the case of the division operator, in the framework of fuzzy sets and possibility theory. The notion of division is well-known in the context of regular relations and the extension of this operation to fuzzy relations (induced by the flexible queries) is investigated. Several types of extended divisions can be envisaged, depending on the meaning of the grades attached to the tuples of the fuzzy relations (degree of fulfillment of gradual properties, level of importance of components in a ...

this paper, we present a multi-sources information-fusion method for satellite image classification. Main characteristics of this method are the use of possibility theory to handle the uncertainty connected with pixel classification, and the ability to mix numeric sources (satellite image spectral bands) and symbolic sources (expert knowledge about best localisation of classes and out-image data for example). Moreover, this information-fusion method is low time consuming and with a linear complexity. First we introduce briefly the possibility theory and the conjunctive fusion method used. Then we apply this fusion method to a satellite image classification problem. Classes are defined by their spectral response on the one hand, and by the description of their best geographical context on the other hand. We compute the possibility distribution for numeric sources on the one hand, and for symbolic sources on the other hand. Finally the fusion handles possibility measures coming from numeric sources and from symbolic sources.

This paper discusses recent approaches to the representation of imperfect information, as they have appeared in the last twenty years. The stress is on ideas rather than mathematics. Especially, it is pointed out that beside old questions such as the numerical representation of partial belief, new aspects of information imperfection are the topic of active research, such as vagueness and granularity. Moreover, while the problem of devising procedures for decision- making in the face of imperfect information is still an important area, much research in Artificial Intelligence focuses on reasoning and methods for automating reasoning processes on the computer. The latter aims at devising intelligent information systems, as opposed to decisionsupport systems. Clearly issues pertaining to vagueness and granularity are present in information system research as much as issues related to uncertainty and incompleteness of available knowledge. Moreover, this trend has put forward a strong emphasis on logic, in nonstandard forms, a concern that was not so common in past schools of uncertainty modelling, such as in statistics or decision theory. The thrust of the paper is as follows : in the first part, traditional views of uncertainty based on probability are briefly recalled and taken as a starting point. Then several trends are reviewed that depart from these traditional views : they reflect concerns about other aspects of imperfect information such as imprecision, belief viewed as an ordering relation, lexical vagueness, and granularity. An analysis of how these aspects may interfere is provided ; it is also pointed out that these notions can often be considered from two points of view which can be called objective and subjective, respectively. In the second part the questio...