New results on α -cuts of type-2 fuzzy sets
Fuzzy Sets and Systems, ISSN: 0165-0114, Vol: 498, Page: 109152
2025
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Article Description
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.
Bibliographic Details
Elsevier BV
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