Many extension and generalization of fuzzy sets have been introduced and studied in the literature. Picture fuzzy set acquired more concentration in the domain of decision making, as many real time circumstances might have choices of more than one and researchers are looking for optimum choice/decision. Spherical fuzzy digraph is a generalization of intuitionistic fuzzy set and fuzzy graph. In this paper, we redefine some preliminary operations of Spherical fuzzy graph and it is referred as spherical fuzzy digraph. We discuss some arithmetic operations and relations among spherical fuzzy digraph. We further proposed a method to solve a shortest path problem using score function.

This work studies a new version of normality called epi-quasi normality, which lies between epi-normality and epi-mild normality. In this paper, we investigate this property and present some examples that illustrate the relationships between epi-quasi normality and other kinds of both normality and regularity.

Throughout this article, we propose an extension of the metric space due to M. Jleli and B. Samet (JS-metric space). This extension is made using the altering distance function, hence the name altering JS-metric. The idea of fixed points for the contraction mappings endowed with graph was first introduced by J. Jachymski in 2008. After that many researchers followed this idea and proposed various contraction mappings endowed with a graph. Motivated by these ideas, we have generalised some well-known contraction mappings in the literature that are endowed with a graph. Additionally, we have provided some fixed point results concerning these contractions in an altering JS-metric space.