Embedded interval valued type-2 fuzzy sets

Type-2 fuzzy sets are growing in popularity as, for certain applications they model uncertainty and imprecision better than type-1 fuzzy sets. However, type-2 fuzzy sets can be difficult to understand and explain. Recent work has introduced embedded type-2 fuzzy sets and the representation theorem which enable us to discuss type-2 fuzzy sets in a different way. In particular they allow for alternative proofs of theoretical results which are often easier to follow. Interval valued type-2 fuzzy sets are found to be useful in many application. This paper presents embedded interval valued type-2 fuzzy sets to aid the discussion of interval valued type-2 fuzzy sets and to prove the join and meet of interval valued type-2 fuzzy sets.

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