Linguistic neutrosophic partitioned Maclaurin symmetric mean operators based on clustering algorithm and their application to multi-criteria group decision-making

Abstract

Linguistic neutrosophic number (LNN) can describe evaluation information by three linguistic variables indicating truth-membership, indeterminacy-membership and falsity-membership respectively, which is an effective tool to represent uncertainty, the partitioned Maclaurin symmetric mean (PMSM) operator can reflect the interrelationships among criteria where there are interrelationships among criteria in the same partition, but the criteria in different partitions are irrelevant, so, in this paper, we extend the PMSM operator to LNNs, define linguistic neutrosophic partitioned Maclaurin symmetric mean operator and linguistic neutrosophic weighted partitioned Maclaurin symmetric mean (LNWPMSM) operator, and discuss the properties and theorems of the proposed operators. Then we propose a clustering algorithm for linguistic neutrosophic sets based on the similarity measure to give some objective and reasonable partitions among criteria, and based on the LNWPMSM operator and the objective partition structure of the criteria, a novel multi-criteria group decision-making method is developed for linguistic neutrosophic environment. Finally, one practical example is presented to illustrate the applicability of the proposed method, and a comparison analysis is to show the advantages of the proposed method compared with the existing methods.