STUDY ON MULTIDIMENSIONAL FUZZY GRAPHS THROUGH MODIFIED PARTIAL ORDERING

This paper introduces the concepts of multidimensional fuzzy graphs and edge-powered multidimensional fuzzy graphs, which employ a hybrid structure that combines multidimensional fuzzy sets and graphs. This study redefines the axioms of multidimensional t− norms and t− conorms by providing a more general partial order that can link more components of the range set J∞^≺[0, 1]^≻. More studies on various operations such as direct product, composition, tensor product, join, etc. are conducted with relevant illustrations. A novel complement operator approach is also investigated to link the multidimensional fuzzy graph and the edge-powered multidimensional fuzzy graph. Finally, defining the infimum and supremum of an arbitrary family in J∞^≺[0, 1]≻ introduces many notions such as vertex degree, min− vertex degree, max− vertex degree, path strength, etc.