Connectivity Concepts in m-Polar Fuzzy Incidence Graphs

This paper introduces and investigates the connectivity properties with [Formula: see text]-PFIG, a novel extension of fuzzy incidence graphs characterized by multiple membership values corresponding to different polarities. The study systematically defines and explores key connectivity concepts, including paths, cycles, and connectedness, under the [Formula: see text]-polar fuzzy framework. The authors present theoretical findings that expand traditional graph connectivity concepts to a more generalized context, offering a deeper understanding of the behavior and structure of [Formula: see text]-PFIG. This study introduces an innovative method for connectivity concept and incidence graph within [Formula: see text]-polar fuzzy graphs ([Formula: see text]-PFG). Several properties, along with detailed descriptions are thoroughly investigated. The proposed approach accounts for the various merits of each member in a railway network system by considering individual merits (self-weight) in the nature.