and key words This paper presents an historical overview of the evolution of the notion of probability . The different kinds of probability and the opposition between objectivists (or frequencists) and subjectivists are presented . Then we show how some works, following the wor k by Cox, aim at deducing what is called by others axioms of probabilities, from a given set of basic postulates which...

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...

Zadeh proposed and developed the theory of approximate reasoning in a long series of papers in the 1970’s (see e.g. [28, 29, 30, 31, 32, 34, 35]), at the same time when he introduced possibility theory [33] as a new approach to uncertainty modeling. His original approach is based on a fuzzy set-based representation of the contents of factual statements (expressing elastic restrictions on the po...

In this paper, some properties of Novel Weighted Averages that are related to the concepts of possibility theory are examined. It is shown that Novel Weighted Averages have certain interpretations in terms of addition of interactive interval or fuzzy constraints. To do this, alternative forms of Novel Weighted Averages are provided. In particular, an alternative form of Novel Weighted Averages ...

In this paper we present completeness results of several fuzzy logics trying to capture different notions of necessity (in the sense of Possibility theory) for Gödel logic formulas. In a first attempt, based on different characterizations of necessity measures on fuzzy sets, a group of logics, with Kripke style semantics, are built over a restricted language, indeed a two level language compose...

A method of instance-based learning is introduced which makes use of possibility theory and fuzzy sets. Particularly, a possibilistic version of the similarity-guided extrapolation principle underlying the instancebased learning paradigm is proposed. This version is compared to the commonly used probabilistic approach from a methodological point of view. Moreover, aspects of knowledge represent...

In this paper, we deal with the problem of modelling and recognizing composite objects. Recognition involves two stages: first, recognition of the components via their visual features and second recognition of correct positions of the components with respect to the composite object geometric model. The geometric model we use allows for deformable composite objects, as well as indefinite number ...

We consider lower probabilities on finite possibility spaces as models for the uncertainty about the state. These generalizations of classical probabilities can have some interesting properties; for example: k-monotonicity, avoiding sure loss, coherence, permutation invariance. The sets formed by all the lower probabilities satisfying zero or more of these properties are convex. We show how the...

In this paper we analyze two recent axiomatic approaches proposed by Dubois et al. [5] and by Giang and Shenoy [10] for qualita­ tive decision making where uncertainty is de­ scribed by possibility theory. Both axiom­ tizations are inspired by von Neumann and Morgenstern's system of axioms for the case of probability theory. We show that our ap­ proach naturally unifies two axiomatic sys­ tems ...