Identifier to cite or link to this item: http://hdl.handle.net/20.500.13003/17588
Some characterizations of T-power based implications
WOS ID: 000457563400004
Scopus EID: 2-s2.0-85051405526
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CitationMassanet Sebastia, Recasens Jordi, Torrens Joan. Some characterizations of T-power based implications. Fuzzy Sets Syst. 2019 Mar 15;359:42-62.
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.
KeywordsFuzzy implication function
T-power based implications
Powers of t-norms