Multiple attribute decision-making approach for Pythagorean neutrosophic normal interval-valued fuzzy aggregation operators

We present a communication which deals with some new methods to solve multiple attribute decision-making (MADM) problems based on Pythagorean neutrosophic normal interval-valued set (PNSNIVS). The Pythagorean neutrosophic interval-valued sets are based on further generalization of Pythagorean neutrosophic sets and interval-valued neutrosophic sets. Here we discuss about various aggregating operations that have been interpreted up to date. The focus of the article is to discuss a new notion of Pythagorean neutrosophic normal interval-valued weighted averaging (PNSNIVWA), Pythagorean neutrosophic normal interval-valued weighted geometric (PNSNIVWG), generalized Pythagorean neutrosophic normal interval-valued weighted averaging (GPNSNIVWA) and generalized Pythagorean neutrosophic normal interval-valued weighted geometric (GPNSNIVWG). Also, we obtain an algorithm that deals with the MADM problems based on these operators. We interact applicability of the Euclidean and hamming distance measures which are further extended in real life example. Finally, some important properties of these sets under various algebraic operations are to be elaborated in this communication.

Automated summary

This communication presents new methods for solving multiple attribute decision-making problems based on Pythagorean neutrosophic normal interval-valued set (PNSNIVS). Various aggregating operations and new notions are discussed, including Pythagorean neutrosophic normal interval-valued weighted averaging (PNSNIVWA), Pythagorean neutrosophic normal interval-valued weighted geometric (PNSNIVWG), generalized Pythagorean neutrosophic normal interval-valued weighted averaging (GPNSNIVWA), and generalized Pythagorean neutrosophic normal interval-valued weighted geometric (GPNSNIVWG). The article also includes an algorithm for MADM problems based on these operators, and the applicability of Euclidean and Hamming distance measures in real-life examples. Finally, the communication elaborates on important properties of these sets under various algebraic operations.