LAUSR

An interval-valued fuzzy graph (IVFG) and degree of vertices have been applied for performance evaluation in an educational system. The approach is mainly developed based on real membership values of vertices of an IVFG. In this manuscript, some definitions of generalized fuzzy graphs and neutrosophic graphs structures are improved. First, we have concentrated to improve the existing definitions for union and join of two IVFG’s, complete IVFG with supporting examples. Then, their modified version is developed. Secondly, the modified version of interval-valued neutrosophic graph (IVNG) is given. Third, an algorithm and a flowchart of the proposed method are described. Fourth, the generalized form of complete and strong IVNG is given with examples. Finally, a real-life application using interval-valued fuzzy graph in education system in Taiwan is exhibited.