Linguistic neutrosophic Hamacher aggregation operators and the application in evaluating land reclamation schemes for mines

Land reclamation has become a significant way for the improvement of ecological environment in mining areas. When selecting the optimal land reclamation scheme, LNNs (linguistic neutrosophic numbers) are suitable to describe the complex fuzzy evaluation information through linguistic truth, indeterminacy and falsity membership degrees. Furthermore, the Hamacher aggregation operators are good tools to handle multi-criteria decision making problems. Accordingly, the aim of this paper is to extend Hamacher aggregation operators with LNNs and then build a decision making framework for evaluating land reclamation schemes in mining areas. First, new operational laws of LNNs based on Hamacher t-norm and t-conorm are defined. Then, several linguistic neutrosophic Hamacher aggregation operators, including the linguistic neutrosophic Hamacher weighted mean aggregation operators and linguistic neutrosophic Hamacher hybrid weighted mean aggregation operators are developed. Meanwhile, their desirable properties are proved. Thereafter, a method for decision making with linguistic neutrosophic information based on these operators is proposed to deal with complex decision problems. At last, the validity of this method is confirmed by an illustrative example of evaluating the land reclamation schemes in mining areas. In addition, the impact of the parameter in extended Hamacher aggregation operators is discussed. The merits of the proposed method are also highlighted by comparing with other decision making methods. The results show that the proposed linguistic neutrosophic Hamacher aggregation operators have great flexibility and advantages, and can provide powerful ways for the evaluation of land reclamation schemes.