Abstract
Xie recently extended nullnorms and uninorms to fuzzy truth values and investigated whether the extended nullnorms and extended uninorms form respectively type-2 nullnorms and type-2 uninorms on the algebra of fuzzy truth values. In this note, we show by counterexamples that there exist some flaws in a previous paper by Xie [Fuzzy Sets Syst. 352 (2018) 92-118], such as Corollaries 2.1, 3.1, 4.1 and 4.2, Lemmas 3.3, 3.4, 3.5, 3.6, 3.7 and 3.8, Propositions 3.4, 3.5, 3.10, 3.11, 4.1 and 4.4, Theorems 3.1, 3.3, 4.1 and 4.3, and then we provide the correct versions. In addition, Proposition 3.7 in that paper is correct, but its proof contains a flaw. We point out the flaw and give a more general result than Proposition 3.7 in that paper.
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