Thick Sets, Multiple-Valued Mappings, and Possibility Theory

  • Didier Dubois
  • Luc JaulinEmail author
  • Henri Prade
Part of the Studies in Computational Intelligence book series (SCI, volume 892)


Carrying uncertain information via a multivalued function can be found in different settings, ranging from the computation of the image of a set by an inverse function to the Dempsterian transfer of a probabilistic space by a multivalued function. We then get upper and lower images. In each case one handles so-called thick sets in the sense of Jaulin, i.e., lower and upper bounded ill-known sets. Such ill-known sets can be found under different names in the literature, e.g., interval sets after Y. Y. Yao, twofold fuzzy sets in the sense of Dubois and Prade, or interval-valued fuzzy sets, ... Various operations can then be defined on these sets, then understood in a disjunctive manner (epistemic uncertainty), rather than conjunctively. The intended purpose of this note is to propose a unified view of these formalisms in the setting of possibility theory, which should enable us to provide graded extensions to some of the considered calculi.


Thick set Interval analysis Possibility theory Inverse image Uncertainty 


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© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.IRIT - CNRSToulouse Cedex 09France
  2. 2.Lab-STICC, ENSTA-BretagneBrestFrance

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