6533b7ddfe1ef96bd12740aa

RESEARCH PRODUCT

Asymptotic comparison of the implicative fragments of certain fuzzy logics

Sławomir KostZofia Kostrzycka

subject

Fuzzy logicAlgebraFuzzy systems

description

An asymptotic similarity of some fragments of two fuzzy logics is proved. We focus on two 3-valued fuzzy logics: the Gödel-Dummett one and the Łukasiewicz one and we consider their purely implicative fragments of two variables. This paper shows the existence of the densities of truth of these logics and determines their values. For this purpose we build the appropriate Tarski-Lindenbaum algebra and use extensively generating functions. Our method can be generalized to n-valued logics, n > 3, but all computations will be extremely complicated.

yearjournalcountryeditionlanguage
2022-07-18
10.1109/fuzz-ieee55066.2022.9882699https://doi.org/10.1109/FUZZ-IEEE55066.2022.9882699