Some new Hamacher aggregation operators under single-valued neutrosophic 2-tuple linguistic environment and their applications to multi-attribute group decision making

This paper proposes an approach to linguistic multiple attribute group decision making (MAGDM) problem with single-valued neutrosophic 2-tuple linguistic (SVN2TL) assessment information by adding a subjective imprecise estimation of reliability of the 2-tuple linguistic terms (2TLTs). SVN2TL includes the truth-membership (TM), indeterminacy-membership (IM) and faulty-membership (FM), which can express the incomplete, indeterminate and inconsistent information perfectly and avoid information and precision losing in aggregation process ideally. We first propose the concept of SVN2TL set (SVN2TLS) and single valued neutrosophic 2-tuple linguistic element (SVN2TLE), basic operational rules on SVN2TLEs via Hamacher triangular norms, and ranking method for SVN2TLEs. Then, some SVN2TL aggregation operators including SVN2TL Hamacher weighted averaging (SVN2TLHWA) operator, SVN2TL Hamacher geometric weighted averaging (SVN2TLHGWA) operator, are developed, their some properties are investigated as well. Moreover, we apply new operators to develop approach to MAGDM problem with SVN2TL assessment information, where a model for optimal weighting vector is constructed. Finally, an numerical example related to evaluation of emergency response solutions for sustainable community development is provided to show the utility and effectiveness of the method described in this paper. A sensitivity and comparative analysis are also conducted to demonstrate the strength and practicality of the proposed method.