Natural fuzzy negations and ordinal sums of uninorms

This article explores the construction of natural fuzzy negations induced by uninorms and the application of ordinal sums in fuzzy logic. It begins with a comprehensive review of fundamental concepts such as t-norms, t-conorms, fuzzy negations, uninorms, and ordinal sums. The text introduces the concept of natural fuzzy negations induced by uninorms and establishes key results related to this concept. It also investigates the properties of natural negations of convex sums of specific classes of uninorms and provides proofs for results associated with this concept. Additionally, the article generalizes two well-known families of uninorms by replacing the minimum and maximum operators with an arbitrary commutative and non-decreasing binary function. The article concludes by introducing a notion of ordinal sum of an indexed family of uninorms and investigating some properties. The main contribution of this work lies in constructing the natural fuzzy negation induced by a uninorm and exploring the ordinal sum of a family of uninorms. The article provides proofs and results related to these concepts and extends two well-known methods used for constructing uninorms from t-norms and t-conorms. It also investigates the natural negation of the ordinal sum within a specific class of uninorms. The article is structured to provide a comprehensive understanding of these concepts and their applications in fuzzy logic.