Centroid of a type-2 fuzzy set
Information Sciences: an International Journal
IEEE Transactions on Fuzzy Systems
Interval type-2 fuzzy logic systems: theory and design
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
On type-2 fuzzy sets and their t-norm operations
Information Sciences: an International Journal
On type-2 fuzzy relations and interval-valued type-2 fuzzy sets
Fuzzy Sets and Systems
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Computing the centroid of a type-2 fuzzy set (T2 FS) is an important operation for such sets. For an interval T2 FS, the centroid can be computed by using two iterative procedures that were developed by Karnik and Mendel [2]. In this paper, we prove that if the footprint of uncertainty for an interval T2 FS is symmetrical about the primary variable y at y=m, then the centroid is also symmetrical about y=m and its defuzzified value equals m. As a consequence of this, computation of the centroid for such a T2 FS is reduced by 50%, and the importance of obtaining a non-symmetrical interval T2 FS prior to defuzzification is demonstrated.