Simplified interval-valued Pythagorean fuzzy graphs with application

Interval-valued Pythagorean fuzzy set (IVPFS) as a generalization of Pythagorean fuzzy set (PFS) increases its elasticity drastically. However, the expressions and calculations of IVPFS are slightly complicated. To overcome this drawback, in this research study, we greatly simplify the expressions of IVPFS by introducing a new concept of simplified interval-valued Pythagorean fuzzy set (SIVPFS), constituted by two Pythagorean fuzzy numbers (PFNs) with the relationships of intersection and union simultaneously. We develop systematic aggregation operators to aggregate simplified interval-valued Pythagorean fuzzy information. Meanwhile, we propose a new generalization of fuzzy graph, called simplified interval-valued Pythagorean fuzzy graph (SIVPFG), to describe uncertain information in graph theory. We develop a series of operations on two SIVPFGs and investigate their desirable properties. Finally, we develop a SIVPFG-based multi-agent decision-making approach to solve a common kind of situation where the graphic structure of agents is obscure. A numerical example is provided to illustrate the proposed approach as well as the applicability of SIVPFS and SIVPFG in decision making.