Novel Concepts of Bipolar Picture Fuzzy Graphs With Applications in Image Segmentation and Road Maps Designs

Bipolar picture fuzzy sets (BPPFSs), being the most extended form of fuzzy sets (FSs), has more capability to analyze the state of any network, more intelligently. It is proven that BPPFSs having poles is most efficient in solving daily life problems with uncertainties, compared to the other extensions of fuzzy sets (FSs). The ideas of fuzzy planar graphs (FPGs) and intutiionistic fuzzy planar graphs (IFPGs) have been introduced in the literature, the concepts of bipolar picture fuzzy planar graph (BPPFPG) has not yet been explored. In this study, we fill the gap existing in the literature by introducing the idea of BPPFPGs. We present various key features and characteristics of BPPFPGs. In this context, we describe the degree of a vertex of a BPPFMG, strong multi-edge of a BPPFMG, complete BPPFMG, strength of a bipolar picture fuzzy multi-edge of a BPPFMG, a strong multi-edge of a BPPFMG etc. Moreover, we initiate the concepts of geometric and combinatorial duals of BPPFPGs. At the end, we present the utilizations of BPPFPGs in creating image segmentation and making road map designs. In this regard, we analyze image segmentation based on strong BPPFPG, and by utilizing the term “degree of planarity” of BPPFPGs, we introduce a new scheme for designing safer road map.