A note on convergence properties of interval-valued capacity functionals and Choquet integrals

  • Authors:
  • Lee-Chae Jang

  • Affiliations:
  • Department of Computer Engineering, Kon-Kuk University, Chungju 138-701, Republic of Korea

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2012

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Abstract

Based on the classical theory of random sets, Feng and Nguyen (2007) [5] studied the convergence of capacity functionals of random sets in terms of Choquet integrals. In this paper, we consider an interval-valued capacity functional which is motivated by the goal to generalize a capacity functional and the Choquet integral with respect to an interval-valued capacity. In particular, we discuss some convergence theorems for interval-valued capacity functionals and interval-valued probability measures in the Hausdorff metric and Choquet weak sense.