Composition-Generated Higher-Order and Two-Branch Fuzzy Implications: Interaction Mechanisms and Asymptotic Behavior

In this paper, we study composition-generated fuzzy implications induced by strict fuzzy negations. Starting from the known Yager-type generated implication IN(x,y)=NxN−1(y), we first isolate a general monotone precomposition principle and use it to organize power-type families as structured preliminary constructions. These families clarify how order parameters act on the antecedent-side component and on the internal consequent-side scale N−1(y), and they provide a basis for studying saturation phenomena. The main constructional part of the paper introduces Yager-induced two-branch fuzzy implications with explicit admissibility conditions. Their n-order extensions are obtained through repeated product-composition of internal Yager-type components. We also introduce a recursive feedback mechanism based on a new auxiliary two-branch implication, where the order parameter counts feedback iterations rather than powers of an internal product. The asymptotic analysis shows that power-type constructions may converge pointwise toward the maximal truth value on large parts of the unit square, while the two-branch and recursive mechanisms may produce branch-dependent limiting behavior. Thus, the paper separates closure-based transformations, direct two-branch composition mechanisms, and recursive implication–composition within fuzzy implication theory.