Fuzzy n-cell numbers and the differential of fuzzy n-cell number value mappings

  • Authors:

  • Guixiang Wang;Congxin Wu

  • Affiliations:

  • Department of Mathematics, Harbin Institute of Technology, Heilongjiang, Harbin 150001, People's Republic of China;Department of Mathematics, Harbin Institute of Technology, Heilongjiang, Harbin 150001, People's Republic of China

  • Venue:
  • Fuzzy Sets and Systems - Fuzzy intervals
  • Year:
  • 2002

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Abstract

In this paper, we give the definition of a special kind of n-dimension fuzzy numbers, fuzzy n-cell numbers, discuss their operations and representation theorems, define a complete metric on the fuzzy n-cell number space and prove that the metric is equivalent to the supremum metric derived by the Hausdorff metric between the level sets of the n-dimension fuzzy numbers, and obtain an embedding theorem of the fuzzy n-cell number space (isometrically embeds it into a concrete Banach space). We also consider the differential of the fuzzy mappings from an interval into the fuzzy n-cell number Space by using the embedding theorem.