2026-04-29T22:57:48Zhttps://repisalud.isciii.es/rest/oai/requestoai:repisalud.isciii.es:20.500.12105/227022024-11-29T07:12:20Zcom_20.500.12105_15322com_20.500.12105_2051col_20.500.12105_16967
Repisalud
author
Massanet, Sebastia
author
Recasens, Jordi
author
Torrens, Joan
2024-09-10T13:08:53Z
2024-09-10T13:08:53Z
2019-03-15
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
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.
eng
Fuzzy implication function
T-power based implications
Invariance property
Continuous t-norm
Powers of t-norms
Some characterizations of T-power based implications
research article