Operations on Alternate Quadra–Submerging Polar (AQSP) Fuzzy Graphs and Its Applications

Combining the fuzzy graphs with Alternate Quadra–Submerging Polar (AQSP) level is a new innovation to measure the difference between maximum and minimum in quadrants based on Cartesian coordinates. In this chapter, the level of fixation (−0.5, 0.5) is introduced to measure the Submerging membership and nonmembership degree of function. The AQSP fuzzy graph is proposed to examine and study certain Operations, Properties, Theorems like Cartesian product, Union, Composition, Join, AQSP Fuzzy Automorphic, Isomorphic, and Strong Self-complementary theorems are given with results and illustrations, which are pertaining with fixation and submerging operations with uncertain vertices and edges. An application of AQSP fuzzy graphs is discussed with experiments in the level of fixation.