Formulation of Fuzzy Implication Modeling Theory

This work introduces Fuzzy Implication Modeling Theory, a connective-centered framework that supplies an intermediate structural layer between the class and family levels in the subset of fuzzy implications generated by compositions of the three basic fuzzy connectives. The theory distinguishes Fuzzy Implication Models from Fuzzy Implication Model Instances and formalizes their relationship through three propositions addressing generation, traceability and non-uniqueness. Two model-level quantitative descriptors—a Behavior Index and an Intra-Model Variability Index—are proposed to enable comparative analysis across models, and a new Fuzzy Implication Model is introduced and proven to satisfy the defining conditions of a fuzzy implication. A MATLAB-based companion tool with a dedicated model-design module operationalizes the theory. Taken together, the framework provides a structured lens for organizing, analyzing and selecting fuzzy implication operators, and opens paths for both further theoretical development and applied studies.