This work proposes to consider Xu-Xia-partial order for the antitonicity property of Typical Hesitant Fuzzy Negations (THFN) which is coherent with the usual negation notion in L-fuzzy logic in the sense of Goguen. In addition, we will study the class of strong THFN generalizing some important properties of fuzzy negation, such as Trillas' characterization of strong fuzzy negations.
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Santos et al. (2014) studied this question.
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