We first propose the normal Pythagorean neutrosophic set (NPNS) in this paper, which synthesizes distribution of incompleteness, indeterminacy, and inconsistency (PNS) fuzzy number. also define some properties NPNS. For solving decision-making problem non-strictly independent interacting attributes, two kinds NPNS Choquet integral operators are proposed. First, average (NPNSCIA) operator geomet...