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

作者：John Terry Rickard, Janet Aisbett, Greg G. Gibbon · 发表于：IEEE Transactions on Fuzzy Systems · 年份：2008 · DOI：10.1109/tfuzz.2008.2006369 · 被引用次数：107 · 研究领域：Fuzzy Logic and Control Systems、Rough Sets and Fuzzy Logic、Multi-Criteria Decision Making

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.