This paper is a reply to Laviolette and Seaman’s critical discussion of fuzzy set theory. Rather than questioning the interest of the Bayesian approach to uncertainty, some reasons why Bayesian find the idea of a fuzzy set not palatable are laid bare. Some links between fuzzy sets and probability that Laviolette and Seaman seem not to be aware of are pointed out. These links suggest that, contr...

This paper presents further work on a 3D visualisation system for the reconstruction of historical structures which takes into account archaeological uncertainty. The uncertainty associated with an archaeologist’s interpretation is represented using possibility theory and visualised by shader-based information visualisation schemes. An increase or decrease in uncertainty is influenced by any re...

This paper explores the existing relationship between Possibility Theory and Theory of Evidence, when they are both applied to fuzzy arithmetic. Possibility Theory arithmetic is based on the extension principle (projection of the joint possibility distribution), while in Theory of Evidence, the consonant bodies of evidence obtained from each operand are combined into a new joint body of evidenc...

QCD sheds considerable light on several of the most basic features of the natural world including the origin of mass, the feebleness of gravity, the extent to which the properties of matter can be determined conceptually, the possible utility of the anthropic principle, and the metatheoretic notions of effectiveness and computability. I discuss these applications here. Contemporary academic or ...

In comparison to possibility theory, the Transferable Belief Model (TBM) – a nonproba-bilistic interpretation of Dempster-Shafer theory – enjoys little choice in terms of aggre-gation operators for the fusion of information. In this thesis, the problem of introducingsome flexibility for the combination of belief functions – the mathematical tool allowingthe representation of...

1. Preliminaries In general, for languages which allow a flexible order of major constituents, the grammatical variations of simple sentences are truth-conditionally equivalent regardless of the constituent sequences and of the intonational patterns. In Spanish, for instance, the six logically possible variations of sentences containing three constituents, namely, subject, verb, and object are ...

In this paper, we investigate the extraction of fuzzy rules from data tables based on possibility theory. A possibilistic decision language is used to represent the extracted fuzzy rules. The algorithm for rule extraction is presented and the complexity analysis is carried out. Since the results of the rule induction process strongly depend on the representation language, we also discuss some a...

Possibility theory offers a qualitative framework for modeling decision under uncertainty. In this setting, pessimistic and optimistic decision criteria have been formally justified. The computation by means of possibilistic logic inference of optimal decisions according to such criteria has been proposed. This paper presents an Answer Set Programming (ASP)-based methodology for modeling decisi...

DL-Lite is a powerful and tractable family of description logics specifically tailored for applications that use huge volumes of data. In many real world applications, data are often provided by several and potentially conflicting sources of information having different levels of priority. Possibility theory offers a very natural framework to deal with ordinal and qualitative uncertain beliefs ...

Formal implemented models of analogy face two opposing challenges. On the one hand, they must be powerful and flexible enough to handle gradient and probabilistic data. This requires an ability to notice statistical regularities at many different levels of generality, and in many cases, to adjudicate between multiple conflicting patterns by assessing the relative strength of each, and to genera...