On the φ‐Index of Inclusion: Studying the Structure Generated by a Subset of Indexes

ABSTRACT Theφ $$ \varphi $$ ‐index of inclusion has proven to be a suitable generalization of the inclusion in the fuzzy setting. In this paper, the properties of theφ $$ \varphi $$ ‐index of inclusion, when its definition is restricted to a subset of indexes, are analyzed. The theoretical results obtained in this work are necessary in order to develop fuzzy inference systems based on theφ $$ \varphi $$ ‐index of inclusion.