Multi Criteria Decision Making Method in Neutrosophic Environment Using a New Aggregation Operator, Score and Certainty Function

141 Abstract Neutrosophic sets, being generalization of classic sets, fuzzy sets and intuitionistic fuzzy sets, can simultaneously represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. Neutrosophic theory has been developed in twenty first century and not much of arithmetic has been developed for this set. To solve any problem using neutrosophic data, it is desirable to have suitable operators, score function etc. Some operators like single valued neutrosophic weighted averaging (SVNWA) operator, single valued neutrosophic weighted geometric (SVNWG) operator are already defined in neutrosophic set (NS). In this paper an improved weighted average geometric (IWAG) operator which produces more meaningful results has been introduced to aggregate some real numbers and the same has been extended in neutrosophic environment. We further generalize this to include a wide range of aggregation operators for both real numbers and neutrosophic numbers. A new score function and certainty function have been defined which have some benefit compared to the existing ones. Further comparative study highlighting the benefit of this new approach of ranking in neutrosophic set has been presented. A multiple-attribute decision-making method is established on the basis of the proposed operator and newly defined score function.