• DocumentCode
    873398
  • Title

    Fuzzy Subsethood for Fuzzy Sets of Type-2 and Generalized Type- {n}

  • Author

    Rickard, J.T. ; Aisbett, J. ; Gibbon, G.

  • Author_Institution
    Distrib. Infinity, Inc., Larkspur, CO
  • Volume
    17
  • Issue
    1
  • fYear
    2009
  • Firstpage
    50
  • Lastpage
    60
  • Abstract
    In this paper, we use Zadeh´s extension principle to extend Kosko´s definition of the fuzzy subsethood measure S(G, H) to type-2 fuzzy sets defined on any set X equipped with a measure. Subsethood is itself a fuzzy set that is a crisp interval when G and H are interval type-2 sets. We show how to compute this interval and then use the result to compute subsethood for general type-2 fuzzy sets. A definition of subsethood for arbitrary fuzzy sets of type-n > 2 is then developed. This subsethood is a type-(n - 1) fuzzy set, and we provide a procedure to compute subsethood of interval type-3 fuzzy sets.
  • Keywords
    fuzzy set theory; extension principle; fuzzy subsethood measure; generalized type-n fuzzy sets; type-2 fuzzy sets; Australia; Color; Fuzzy sets; Gray-scale; H infinity control; Image converters; Medical diagnosis; Stock markets; Uncertainty; Weather forecasting; Fuzzy inference; fuzzy measures; fuzzy sets; fuzzy subsethood; type $n$ fuzzy sets; type-2 fuzzy sets;
  • fLanguage
    English
  • Journal_Title
    Fuzzy Systems, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    1063-6706
  • Type

    jour

  • DOI
    10.1109/TFUZZ.2008.2006369
  • Filename
    4633632
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=873398