Abstract
The α-cut (i.e., α-plane) of type-2 fuzzy sets is a very useful tool for computation. However, there are some theoretical mistakes in type-2 fuzzy sets literature discussing the topic of α-cuts. This paper will illustrate these mistakes through examples and specifically address the two new questions induced by them: (1) Taking the α-cut (resp. α-strong cut) of the result obtained by performing a T-extension operation of ⁎ (i.e., t-norm extension operation of a general binary operation) on two type-2 fuzzy sets is equal to what? (2) What conditions are required for taking the α-cut (resp. α-strong cut) of the result obtained by performing a T-extension operation of ⁎ on two type-2 fuzzy sets to be equal to performing the ⁎ operation on the α-cuts (resp. α-strong cuts) of these two type-2 fuzzy sets? Finally, we will get a comprehensive answer to these two questions.
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