Multiple Attribute Projection Methods with Neutrosophic Sets

Abstract

Projection measure (PM) is an appropriate method for dealing with multiple attribute decision making (MADM) problems since they can contain the distance and included angle between objects evaluated. Then, the simplified neutrosophic set (SNS) includes the information of single-valued neutrosophic set (SVNS) and interval neutrosophic set (INS) as a sub-class of a neutrosophic set, which can be used for real science and engineering fields under incomplete, indeterminate, and inconsistent environments. First, the general PM and bidirectional PM were presented between two SNSs (SVNSs and INSs), and then a harmonic averaging PM of SNSs was further introduced based on two (bidirectional) projections. Further, MADM methods were provided based on the general PM, bidirectional PM, and harmonic averaging PM in the simplified neutrosophic setting. In the introduced multiple attribute projection methods, the ranking order of all alternatives and the best alternative can be efficiently identified by these PMs between the ideal solution (the ideal alternative) and each alternative in MADM problems with simplified neutrosophic information. Finally, the effectiveness and applicability of these multiple attribute PMs were demonstrated by two numerical examples. The contribution of the chapter is that the three kinds of simplified neutrosophic PM methods are proposed and used for simplified neutrosophic MADM problems.