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00925njm 22002777a 4500 dc Massanet, Sebastia author Recasens, Jordi author Torrens, Joan author 2019-03-15 Recently, the so-called family of T-power based implications was introduced. These operators involve the use of Zadeh's quantifiers modelled by powers of t-norms in its definition. Due to the fact that Zadeh's quantifiers constitute the usual method to modify fuzzy propositions, most of the members of this family of fuzzy implication functions satisfy an important property in approximate reasoning such as the invariance of the truth value of the fuzzy conditional when both the antecedent and the consequent are modified using the same quantifier. In this paper, an in-depth analysis of this property is performed by characterizing all binary functions satisfying it. From this general result, a fully characterization of the subfamily of T-power based implications which satisfy the invariance property is presented. Furthermore, a characterization of the whole family of T-power based implications is proved in which a novel property which slightly resembles the hypothetical syllogism plays a key role. Massanet Sebastia, Recasens Jordi, Torrens Joan. Some characterizations of T-power based implications. Fuzzy Sets Syst. 2019 Mar 15;359:42-62. 10.1016/j.fss.2018.08.007 1872-6801 0165-0114 Fuzzy Sets and Systems http://hdl.handle.net/20.500.13003/17588 2-s2.0-85051405526 https://hdl.handle.net/20.500.12105/22702 457563400004 Fuzzy implication function T-power based implications Invariance property Continuous t-norm Powers of t-norms Some characterizations of T-power based implications