Abstract
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 non-strictly 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.
Highlights
As an important branch of modern decision theory, multi-attribute decision making (MADM) is widely used in many fields such as economy, management, military, and engineering
In view of the Choquet integral operator can be used to consider the relationship between information, this paper proposes the normal Pythagorean neutrosophic set (NPNS) and generalize Choquet integral operator to the NPNS environment
According to some relevant operation rules of normal Pythagorean neutrosophic element (NPNE), we can get the form of the NPNS Choquet integral average (NPNSCIA) operator shown in Theorem 1
Summary
As an important branch of modern decision theory, MADM is widely used in many fields such as economy, management, military, and engineering. Liu et al [12] proposed a weighted aggregation operator and decision making method based on interval value neutrosophic sets (IVNS). Xu [24] applied Choquet integral to multi-attribute decision making of intuitional fuzzy sets and proposed intuitional fuzzy correlated average operator, intuitional fuzzy correlated geometric operator, etc. Peng et al [27] applied Choquet integral to The Pythagorean fuzzy decision making environment and proposed the Pythagorean fuzzy Choquet integral average operator and geometric operator. Wan et al [29] proposed Generalized Shapley Choquet integral operator based method for interactive interval-valued hesitant fuzzy uncertain linguistic. In view of the Choquet integral operator can be used to consider the relationship between information, this paper proposes the normal Pythagorean neutrosophic set (NPNS) and generalize Choquet integral operator to the NPNS environment.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
