Orthopair indeterminate information expression, aggregations and multiattribute decision making method with indeterminate ranges

A neutrosophic number (NN) (d = mu + vI) can flexibly represent the indeterminate information corresponding to values/ranges of the indeterminacy I. Regarding the hybrid concept of intuitionistic fuzzy set (IFS) and NN, this study presents an orthopair indeterminate set (OIS), an orthopair indeterminate element weighted arithmetic averaging (OIEWAA) operator and an orthopair indeterminate element weighted geometric averaging (OIEWGA) operator to simplify and generalise the existing IFS and interval-valued IFS expressions and aggregation forms. Thus, a multiattribute decision making (DM) approach with indeterminate ranges of decision makers is developed based on the OIEWAA and OIEWGA operators and the score and accuracy functions of orthopair indeterminate elements in OIS setting. Finally, the proposed DM approach is applied to a multi-attribute DM example of manufacturing schemes (alternatives) in OIS setting to demonstrate the applicability and flexibility of the proposed DM approach in OIS setting.

Automated summary

This study introduces an orthopair indeterminate set, weighted arithmetic averaging, and weighted geometric averaging operators to simplify and generalize existing expression and aggregation forms for intuitionistic fuzzy sets and interval-valued fuzzy sets. A multiattribute decision making approach is developed based on these operators, applied to a manufacturing scheme example.