An Algorithm for Producing Fuzzy Implications via Conical Sections

In the present study, a novel parametric family of fuzzy implications is introduced and its properties are examined. The parametric family of implications is produced only via a fuzzy negation. This in turn enables the effortless production of a wide range of implications from which to select the one that best fits a given problem, for example in fuzzy inference systems or fuzzy neural networks. The fuzzy negations that have been selected as a basis for the proposed methodology are strong, i.e., involutions, thus leading, in general, to the generated fuzzy implications possessing many desirable additional properties. We have examined which of these properties hold for the implications produced by our algorithm and under which conditions. Finally, it is demonstrated that the family of implications generated via the proposed methodology generalizes other well-established implications, including the Łukasiewicz implication.