Abstract
This paper addresses a flaw in the application of the Nguyen type theorem recently published in Fuzzy Sets and Systems by Urbanski et al. (2021). A counterexample is given to prove wrong the suggested application. Appropriate applications to product t-norm arithmetic of fuzzy intervals are provided. It is observed that the Nguyen type theorem introduces equivalent level of complexity in fuzzy arithmetic compared with the direct use of the generalized extension principle.
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