The legacy of 50 years of fuzzy sets: A discussion

International audienceThis note provides a brief overview of the main ideas and notions underlying fifty years of research in fuzzy set and possibility theory, two important settings introduced by L.A. Zadeh for representing sets with unsharp boundaries and uncertainty induced by granules of information expressed with words. The discussion is organized on the basis of three potential understanding of the grades of membership to a fuzzy set, depending on what the fuzzy set intends to represent: a group of elements with borderline members, a plausibility distribution, or a preference profile. It also questions the motivations for some existing generalized fuzzy sets. This note clearly reflects the shared personal views of its authors

Coalitions of Arguments: An Approach with Constraint Programming

The aggregation of generic items into coalitions leads to the creation of sets of homogenous entities. In this paper we accomplish this for an input set of arguments, and the result is a partition according to distinct lines of thought, i.e., groups of "coherent" ideas. We extend Dung\u27s Argumentation Framework (AF) in order to deal with coalitions of arguments. The initial set of arguments is partitioned into not-intersected subsets. All the found coalitions show the same property inherited by Dung, e.g., all the coalitions in the partition are admissible (or conflict-free, complete, stable): they are generated according to Dung\u27s principles. Each of these coalitions can be assigned to a different agent. We use Soft Constraint Programming as a formal approach to model and solve such partitions in weighted AFs: semiring algebraic structures can be used to model different optimization criteria for the obtained coalitions. Moreover, we implement and solve the presented problem with JaCoP, a Java constraint solver, and we test the code over a small-world network

Ordering based decision making: a survey

Decision making is the crucial step in many real applications such as organization management, financial planning, products evaluation and recommendation. Rational decision making is to select an alternative from a set of different ones which has the best utility (i.e., maximally satisfies given criteria, objectives, or preferences). In many cases, decision making is to order alternatives and select one or a few among the top of the ranking. Orderings provide a natural and effective way for representing indeterminate situations which are pervasive in commonsense reasoning. Ordering based decision making is then to find the suitable method for evaluating candidates or ranking alternatives based on provided ordinal information and criteria, and this in many cases is to rank alternatives based on qualitative ordering information. In this paper, we discuss the importance and research aspects of ordering based decision making, and review the existing ordering based decision making theories and methods along with some future research directions

A map of dependencies among three-valued logics

International audienceThree-valued logics arise in several fields of computer science, both inspired by concrete problems (such as in the management of the null value in databases) and theoretical considerations. Several three-valued logics have been defined. They differ by their choice of basic connectives, hence also from a syntactic and proof-theoretic point of view. Different interpretations of the third truth value have also been suggested. They often carry an epistemic flavor. In this work, relationships between logical connectives on three-valued functions are explored. Existing theorems of functional completeness have laid bare some of these links, based on specific connectives. However we try to draw a map of such relationships between conjunctions, negations and implications that extend Boolean ones. It turns out that all reasonable connectives can be defined from a few of them and so all known three-valued logics appear as a fragment of only one logic. These results can be instrumental when choosing, for each application context, the appropriate fragment where the basic connectives make full sense, based on the appropriate meaning of the third truth-value

Enabling local computation for partially ordered preferences

Many computational problems linked to uncertainty and preference management can be expressed in terms of computing the marginal(s) of a combination of a collection of valuation functions. Shenoy and Shafer showed how such a computation can be performed using a local computation scheme. A major strength of this work is that it is based on an algebraic description: what is proved is the correctness of the local computation algorithm under a few axioms on the algebraic structure. The instantiations of the framework in practice make use of totally ordered scales. The present paper focuses on the use of partially ordered scales and examines how such scales can be cast in the Shafer-Shenoy framework and thus benefit from local computation algorithms. It also provides several examples of such scales, thus showing that each of the algebraic structures explored here is of interest

04271 Abstracts Collection -- Preferences: Specification, Inference, Applications

From 27.06.04 to 02.07.04, the Dagstuhl Seminar 04271 ``Preferences: Specification, Inference, Applications\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available