Fuzzy graph theory is a rapidly developing area of research with numerous applications across various fields, such as communication networks, hospital networks, transportation systems, decision-making, and optimization problems. In recent years, bipolar intuitionistic fuzzy networks have emerged as an effective framework for modelling complex human decision-making processes. {In this paper, the concepts of connectivity status (CS) and average edge connectivity (AEC) on bipolar intuitionistic fuzzy graphs (BIFGs) are introduced to enhance network analysis by incorporating both positive and negative membership and non-membership values. This approach provides a more accurate understanding of network dynamics. A novel algorithm for computing the CS on BIFGs is proposed, achieving substantially lower time complexity compared to existing algorithms for CS. In addition, an algorithm for computing AEC on BIFGs is presented. Several theorems concerning CS and AEC are established. To demonstrate practical utility, the proposed methods are applied to hospital networks. Furthermore, the optimal path on BIFGs is defined and its application in transportation systems is illustrated.
Lee et al. (Thu,) studied this question.