Research on Normal Pythagorean Neutrosophic Set Choquet Integral Operator and Its Application

We first propose the normal Pythagorean neutrosophic set (NPNS) in this paper, which synthesizes the distribution of the incompleteness, indeterminacy, and inconsistency of the Pythagorean neutrosophic set (PNS) and normal fuzzy number. We also define some properties of NPNS. For solving the decision-making problem of the nonstrictly independent and interacting attributes, two kinds of NPNS Choquet integral operators are proposed. First, the NPNS Choquet integral average (NPNSCIA) operator and the NPNS Choquet integral geometric (NPNSCIG) operator are proposed. Then, their calculating formulas are derived, their properties are discussed, and an approach for solving the interacting multi-attribute decision making based on the NPNS is studied. Finally, the two kinds of operators are applied to validate the stability of the new method.

Automated summary

This paper first proposes the normal Pythagorean neutrosophic set (NPNS), which integrates the distribution of incompleteness, indeterminacy, and inconsistency of the Pythagorean neutrosophic set (PNS) and normal fuzzy number. The properties of NPNS are defined. Two types of NPNS Choquet integral operators are introduced to solve the decision-making problem of nonstrictly independent and interacting attributes. Finally, the stability of the new method is validated using these operators.