Volume 27, Issue 1 (2016), pp. 85–110
Heronian mean (HM) has the characteristic of capturing the correlations of the aggregated arguments and the neutrosophic set can express the incomplete, indeterminate and inconsistent information, in this paper, we applied the Heronian mean to the neutrosophic set, and proposed some Heronian mean operators. Firstly, we presented some operational laws and their properties of single valued neutrosophic numbers (SVNNs), and analyzed the shortcomings of the existing weighted HM operators which have not idempotency, then we propose the improved generalized weighted Heronian mean (IGWHM) operator and improved generalized weighted geometric Heronian mean (IGWGHM) operator based on crisp numbers, and prove that they can satisfy some desirable properties, such as reducibility, idempotency, monotonicity and boundedness Further, we proposed the single valued neutrosophic number improved generalized weighted Heronian mean (NNIGWHM) operator and single valued the neutrosophic number improved generalized weighted geometric Heronian mean (NNIGWGHM) operator, and some desirable properties and special cases of them are discussed. Moreover, with respect to multiple attribute group decision making (MAGDM) problems in which attribute values take the form of SVNNs, the decision making approaches based on the proposed operators are developed. Finally, an application example has been given to show the decision making steps and to discuss the influence of different parameter values on the decision-making results.