novel concepts of connectivity in vague incidence graphs with application

Vague sets (vss) being the most advanced form of fuzzy sets has more capacity to analyze the network state more intelligently. it is proven that vs is more useful to solve many real life problems having uncertainties. fuzzy graphs (fgs) are efficient mathematical models for analyzing many problems of daily life. one of the most widely used types of fg is vague incidence graph (vig). vigs play an important role in various fields such as computer science, pcychology, medicine, and political sciences and are used to find effective people in an organization or social institution. they can be used to describe the problems which cannot be handled through fgs and vgs. so, in this paper, specific ideas analogous to vague cut vertices and vague bridges in vgs,  vague incidence cut-vertices, and vague incidence bridges are explored. the notion of vague incidence  gain and vague incidence less for vague incidence paths and pairs of vertices is also initiated.