Extensions of (weakly) null-additive, monotone set functions from rings of subsets to generated algebras

  • Authors:

  • Toshiaki Murofushi

  • Affiliations:

  • Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2007

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Abstract

This paper shows that the greatest and least monotone extensions of a null-additive (resp. weakly null-additive), monotone set function from a ring of subsets to the algebra generated by the ring are null-additive (resp. weakly null-additive). In addition, the paper characterizes all the (weakly) null-additive, monotone extensions.