Some Neutrosophic Uncertain Linguistic Number Heronian Mean Operators and Their Application to Multi-Attribute Group Decision Making

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Heronian mean (HM) is a useful aggregation operator which is marked by catching the interrelations of the aggregated arguments and the neutrosophic uncertain linguistic set can be better to express the incomplete, indeterminate and inconsistent information. In this paper, we combine the Heronian mean and the neutrosophic uncertain linguistic set and proposed some Heronian mean operators based on neutrosophic uncertain linguistic numbers. Firstly, we introduce some definition and properties of uncertain linguistic numbers, the single valued neutrosophic set, and some heronian mean (HM) operators including the generalized weighted Heronian mean (GWHM) operator, the improved generalized weighted Heronian mean (IGWHM) operator, the improved generalized geometric weighted Heronian mean (IGGWHM) operator. Then, we propose the single valued neutrosophic uncertain linguistic set by combining the uncertain linguistic numbers and the single valued neutrosophic set. Further, the neutrosophic uncertain linguistic number improved generalized weighted Heronian mean (NULNIGWHM) operator and the neutrosophic uncertain linguistic number improved generalized geometric weighted Heronian mean (NLUNIGGWHM) operator are developed and the properties of them are analyzed. Furthermore, we develop the decision making methods for multi-attribute group decision making (MAGDM) problems with neutrosophic uncertain linguistic information and give the detail decision steps. At last, an illustrate example is given to show the process of decision making and the effectiveness of the proposed method.