DocumentCode :
873398
Title :
Fuzzy Subsethood for Fuzzy Sets of Type-2 and Generalized Type- 
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 $n$
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 :
