Some Generalized Neutrosophic Number Hamacher Aggregation Operators and Their Application to Group Decision Making

Peide Liu, Yanchang Chu, Yanwei Li, Yubao Chen
2014 International Journal of Fuzzy Systems   unpublished
1 The neutrosophic set (NS) can be better to express the incomplete, indeterminate and inconsistent information , and Hamacher aggregation operators extended the Algebraic and Einstein aggregation operators and the generalized aggregation operators can generalize the arithmetic, geometric, and quad-ratic aggregation operators. In this paper, we combined Hamacher operations and generalized aggre-gation operators to NS, and proposed some new ag-gregation operators. Firstly, we presented some new
more » ... presented some new operational laws for neutrosophic numbers (NNs) based on Hamacher operations and studied their properties. Then, we proposed the generalized neu-trosophic number Hamacher weighted averaging (GNNHWA) operator, generalized neutrosophic number Hamacher ordered weighted averaging (GNNHOWA) operator, and generalized neutroso-phic number Hamacher hybrid averaging (GNNHHA) operator, and explored some properties of these operators and analyzed some special cases of them. Furthermore, we gave a new method based on these operators for multiple attribute group decision making problems with neutrosophic numbers, and the operational steps were illustrated in detail. Finally , an application example is given to verify the proposed method and to demonstrate its effectiveness .