Article thumbnail

Extended gradual interval (EGI) arithmetic and its application to gradual weighted averages

By Reda Boukezzoula, Sylvie Galichet, Laurent Foulloy and Mohed Elmasry


International audienceWe combine the concepts of gradual numbers and Kaucher arithmetic on extended intervals to define extended gradual interval (EGI) arithmetic in which subtraction and division operators are the inverse operators of addition and multiplication, respectively. Use of the proposed EGI operators can lead to non-monotonic gradual intervals that are not fuzzy subsets and cannot be represented by fuzzy intervals. In this context and when fuzzy representation results are desired, an approximation strategy is proposed to determine the nearest fuzzy interval of the non-monotonic gradual interval obtained. This approximation is viewed as an interval regression problem according to an optimization procedure. The EGI operators are applied to the common fuzzy weighted average (FWA) leading to a gradual weighted average (GWA)

Topics: [INFO]Computer Science [cs], [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA]
Publisher: 'Elsevier BV'
Year: 2014
DOI identifier: 10.1016/j.fss.2013.08.003
OAI identifier: oai:HAL:hal-00855106v1
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • https://hal.archives-ouvertes.... (external link)
  • https://hal.archives-ouvertes.... (external link)
  • https://hal.archives-ouvertes.... (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.