Characterizing isometries on the order polytope with an application to the theory of fuzzy measures

  • Authors:
  • E. F. Combarro;P. Miranda

  • Affiliations:
  • University of Oviedo, Campus de Viesques s/n, 33204 Gijón, Spain;Complutense University of Madrid, Plaza de Ciencias, 3, 28040 Madrid, Spain

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

In this paper we study the group of isometries over the order polytope of a poset. We provide a result that characterizes any isometry based on the order structure in the original poset. From this result we provide upper bounds for the number of isometries over the order polytope in terms of its number of connected components. Finally, as an example of application, we recover the set of isometries for the polytope of fuzzy measures and the polytope of p-symmetric measures when the indifference partition is fixed.