On the distributivity of T-power based implications

Peng, Zuming and Pan, Jiazhu (2022) On the distributivity of T-power based implications. Iranian Journal of Fuzzy Systems, 19 (2). pp. 169-186. ISSN 2676-4334 (https://doi.org/10.22111/IJFS.2022.6797)

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Due to the fact that Zadeh's quantifiers constitute the usual method to modify fuzzy propositions, the so-called family of T-power based implications was proposed. In this paper, the four basic distributive laws related to T-power based fuzzy implications and fuzzy logic operations (t-norms and t-conorms) are deeply studied. This study shows that two of the four distributive laws of the T-power based implications have a unique solution, while the other two have multiple solutions.