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Introduction

  • Inés CousoEmail author
  • Didier Dubois
  • Luciano Sánchez
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

Random sets originate in works published in the mid-sixties by well-known economists, Aumann [1] and Debreu [3] on the integration of set-valued functions. They have been given a full-fledged mathematical development by Kendall [10] and Matheron [16]. Random sets seem to have been originally used to handle uncertainty in spatial information, namely to tackle uncertainty in the definitions of geographical areas, in mathematical morphology, and in connection to geostatistics (to which Matheron is a major pioneering contributor, as seen by his work on kriging). Under this view, a precise realisation of a random set process is a precisely located set or region in an area of interest. This approach, especially applied to continuous spaces, raises subtle mathematical issues concerning the correct topology for handling set-valued realisations, that perhaps hide the intrinsic simplicity and intuitions behind random sets (e.g., casting them in a finite setting). The reason is that continuous random sets, like in geostatistics, were perhaps more easily found in applications than finite ones at that time. In any case this peculiarity has confined random sets to very specialised areas of mathematics.

Keywords

Belief Function Evidence Theory Fuzzy Random Variable Possibility Theory Fuzzy Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Departamento de Estadística e I. O. y D. M.Universidad de OviedoOviedoSpain
  2. 2.IRIT, CNRSUniversité Paul SabatierToulouse Cedex 09France
  3. 3.Departamento de InformáticaUniversidad de OviedoOviedoSpain

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