Fuzzy fractional factors in fuzzy graphs-II

The fractional factor implicates the characteristics of fractional flow in network data transmission, and it is a crucial tool for analyzing network information transfer. When there is uncertain information in the network, the corresponding network graph should be characterized by fuzzy graphs, in which the vertex membership function (MF) describes the uncertainty of sites, and the edge membership reveals the uncertainty of channels. The previous work introduced the concept of fuzzy fractional factor (FFF) on fuzzy graphs, but the correlated concepts are still open on other fuzzy graph classes. In order to overcome this defect, in this contribution, the concept of fuzzy fractional factor is extended to intuitionistic fuzzy graph, Pythagorean fuzzy graph, and picture fuzzy graph. Sign-alternating walk and increasing walk are extended to the corresponding settings, and the transformation operations are redefined in light of various situations. By means of constructive approaches, the corresponding theoretical results are further generalized in these settings, which characterize the existence of (resp. maximum) fuzzy fractional factors in different kinds of fuzzy graphs.