A New Idea to Evaluate Networking Problem and MCGDM Problem in Parametric Interval Valued Pythagorean Arena

In this article, the concept of parametric interval valued Pythagorean number (PIVPN) has been introduced, which is an extended version of Pythagorean number (PN). Here, a new score and accuracy function have been innovated in the PIVPN environment along with the De-Pythagorean value concept. The new tool and techniques have been fruitfully applied to two realistic problems, namely the networking critical path model (CPM) problem and the multicriteria group decision making problem (MCGDM) problem. In order to solve the MCGDM problem, we have prepared Parametric Interval valued Pythagorean Weighted Arithmetic Mean Operator (PIVPWAMO) and Parametric Interval valued Pythagorean Weighted Geometric Mean Operator (PIVPWGMO) operator in PIVPN environment. Finally, sensitivity analysis and industrious comprehensive numerical simulations have been performed to identify the reliability, efficiency, and usefulness of this novel work. In this article, we have shown that PIVPNs are a more well-organized representation to grip a real-life problem, and they can handle inconsistent conditions in a better compatible way in comparison to the other existing methods.