Some Novel Concepts of Bipolar Picture Fuzzy Influence Graphs Models With Application Toward MADM

The main objective of this study is to introduce the concepts of some connectivity parameters and dominations in the frame of bipolar picture fuzzy influence graphs and explore their application in multi-attribute decision-making. Due to its inherent prosperities, bipolar picture fuzzy influence graphs is a powerful mathematical tool for addressing uncertain problems where fuzzy influence graphs, bipolar fuzzy influence graph and picture fuzzy influence graph may fail to yield precise results. Initially, some useful terms related to connectivity parameters like bipolar picture fuzzy influence path and its strength, bipolar picture fuzzy influence pair, weak bipolar picture fuzzy influence pair, strongest bipolar picture fuzzy influence pair, strong bipolar picture fuzzy influence pair etc are introduced. Following this, several characteristics of these terms in the domain of bipolar picture fuzzy influence graphs are explored. The concepts of complete-BPPFIGs, size of BPPFIG, minimum strong bipolar picture fuzzy influence pair domination numbers are also investigated. To demonstrate effectiveness of this study, we present a bipolar picture fuzzy influence graphs model to identify the brand’s store with the best shopping variety. Comparative study establishes the fact that our presented model based on BPPFIGs is more efficient and flexible than the other existing models in the literature.