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International audience; This paper addresses the question of sequential collective decision making under qualitative uncertainty. It resumes the criteria introduced in previous works [4], [5], [6] by Ben Amor et al. and extends them to a more general context where every decision maker is free to have an optimistic or a pessimistic attitude w.r.t. uncertainty. These criteria are then considered for the optimization of possibilistic decision trees and an algorithmic study is performed for each of them. When the global utility does satisfy the monotonicity property, a classical possibilistic Dynamic Programming can be applied. Otherwise, two cases are possible: either the criterion is max oriented (the more is the satisfaction of any agent, the greater is the global satisfaction), and a dedicated algorithm can be proposed, that relies on as many calls to Dynamic Programming as the number of decision makers; or the criterion is min oriented (all the agents must like the common decision) and the optimal strategy can be provided by a Branch and Bound Algorithm. The paper concludes by an experimental study that shows the feasibility of the approaches, and details to what extent simple Dynamic programming algorithms can be used as approximation procedures for the non monotonic criteria.

The number of electronic applications using fuzzy logic-based solutions has increased considerably in the last few years. Concurrently, new CAD tools that explore different implementation technologies for this type of systems have been developed. In this paper we illustrate a fuzzy logic system design strategy based on a high level description. Employing this high level description, the knowledge base is translated to a format in appearance close to the natural language with the particularity that it uses a hardware description language (VHDL) directly synthesizable on an FPGA circuit. In addition, we analyze different approaches for FPGA implementations of fuzzy systems in order to characterize them in terms of area and speed. Among them, the use of specific processing architectures implemented on FPGAs presents as main advantages a good “cost-performance” ratio and an acceptably short development time. The different synthesis facilities provided by the Xfuzzy design environment for the implementation of programmable fuzzy systems, which take advantage of the available resources in the current FPGA families, are also analyzed in this paper., Partially funded by projects 58/02 of DGAECE (Junta de Andalucía) and TIC2001-1726 (CICYT).

International audience; Logic-based argumentation systems are developed for reasoning with inconsistent information. Starting from a knowledge base encoded in a logical language, they define arguments and attacks between them using the consequence operator associated with the language. Finally, a semantics is used for evaluating the arguments. In this paper, we focus on systems that are based on deductive logics and that use Dung's semantics. We investigate rationality postulates that such systems should satisfy. We define five intuitive postulates: consistency and closure under the consequence operator of the underlying logic of the set of conclusions of arguments of each extension, closure under sub-arguments and exhaustiveness of the extensions, and a free precedence postulate ensuring that the free formulas of the knowledge base (i.e., the ones that are not involved in inconsistency) are conclusions of arguments in every extension. We study the links between the postulates and explore conditions under which they are guaranteed or violated.

In a fuzzy classifier with ellipsoidal regions, a fuzzy rule, which is based on the Mahalanobis distance, is defined for each class. Then the fuzzy rules are tuned so that the recognition rate of the training data is maximized. In most cases, one fuzzy rule per one class is enough to obtain high generalization ability. But in some cases, we need to partition the class data to define more than one rule per class. In this paper, instead of partitioning the class data, we map the input space into the high dimensional feature space and then generate a fuzzy classifier with ellipsoidal regions in the feature space. We call this classifier kernel fuzzy classifier with ellipsoidal regions. To speed up training, first we select independent training data that span the subspace in the feature space and calculate the kernel principal components. By this method, we can avoid using singular value decomposition, which leads to training speedup. In the feature space, training data are usually degenerate. Namely, the space spanned by the mapped training data is a proper subspace. Thus, if the mapped test data are in the complementary subspace, the Mahalanobis distance may become erroneous and thus the probability of misclassification becomes high. To overcome this problem, we propose transductive training: in training, we add basis vectors of the input space as unlabelled data; and in classification, if mapped unknown data are not in the subspace we expand the subspace so that they are included. We demonstrate the effectiveness of our method by computer simulations.

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced.

International audience; When the information about uncertainty cannot be quantified in a simple, probabilistic way, the topic of possibilistic decision theory is often a natural one to consider. The development of possibilistic decision theory has lead to the proposition a series of possibilistic criteria, namely: optimistic and pessimistic possibilistic qualitative criteria [7], possibilistic likely dominance [2] and [9], binary possibilistic utility [11] and possibilistic Choquet integrals [24]. This paper focuses on sequential decision making in possibilistic decision trees. It proposes a theoretical study on the complexity of the problem of finding an optimal strategy depending on the monotonicity property of the optimization criteria – when the criterion is transitive, this property indeed allows a polytime solving of the problem by Dynamic Programming. We show that most possibilistic decision criteria, but possibilistic Choquet integrals, satisfy monotonicity and that the corresponding optimization problems can be solved in polynomial time by Dynamic Programming. Concerning the possibilistic likely dominance criteria which is quasi-transitive but not fully transitive, we propose an extended version of Dynamic Programming which remains polynomial in the size of the decision tree. We also show that for the particular case of possibilistic Choquet integrals, the problem of finding an optimal strategy is NP-hard. It can be solved by a Branch and Bound algorithm. Experiments show that even not necessarily optimal, the strategies built by Dynamic Programming are generally very good.

International audience; The semantics of modal logics for reasoning about belief or knowledge is often described in terms of accessibility relations, which is too expressive to account for mere epistemic states of an agent. This paper proposes a simple logic whose atoms express epistemic attitudes about formulae expressed in another basic propositional language, and that allows for conjunctions, disjunctions and negations of belief or knowledge statements. It allows an agent to reason about what is known about the beliefs held by another agent. This simple epistemic logic borrows its syntax and axioms from the modal logic KD. It uses only a fragment of the S5 language, which makes it a two-tiered propositional logic rather than as an extension thereof. Its semantics is given in terms of epistemic states understood as subsets of mutually exclusive propositional interpretations. Our approach offers a logical grounding to uncertainty theories like possibility theory and belief functions. In fact, we define the most basic logic for possibility theory as shown by a completeness proof that does not rely on accessibility relations.