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

@article{Rickard2009FuzzySF,
  title={Fuzzy Subsethood for Fuzzy Sets of Type-2 and Generalized Type- \$\{n\}\$},
  author={John T. Rickard and Janet Aisbett and Greg Gibbon},
  journal={IEEE Transactions on Fuzzy Systems},
  year={2009},
  volume={17},
  pages={50-60}
}
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… CONTINUE READING
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