Advances in type-2 fuzzy sets and systems

A Survey of Interval‐Valued Fuzzy Sets

“…A particular case of a type 2 fuzzy set is an interval type 2 fuzzy set (see [17,). An interval type 2 fuzzy set = A in U is defined by…”

“…In [17,[31][32][33], it turns out that an interval type 2 fuzzy set is the same as an IVFS if we take a = 1. Handbook of Granular Computing…”

“…Starting from the work of Mitchell (see [94]), Mendel presented in [17] a new expression for IV similarities. In the same paper, Mendel posed the following open question: finding the possible connection (if there is one) between the similarity measure (3) and the expression that he proposes.…”

“…The IV similarities defined in [17,60] have in common the fact that they give an interval as a result, that is, an element of L ([0, 1]). However, the IV similarities proposed in [70,[95][96][97][98] are an adaptation of the well-known measures of similarity between fuzzy sets, so that they give an element of [0, 1] as a result.…”

“…In [17] Mendel writes, 'it turns out that an interval type 2 fuzzy set is the same as an interval-valued fuzzy set for which there is a very extensive literature. These two seemingly different kinds of fuzzy sets were historically approached from very different starting points, which as we shall explain next has turned out to be a very good thing'.…”