The generalized Dice measures for multiple attribute decision making under simplified neutrosophic environments

A simplified neutrosophic set (SNS) is a subclass of neutrosophic set and contains a single-valued neutrosophic set (SVNS) and an interval neutrosophic set (INS). It was proposed as a generalization of an intuitionistic fuzzy set (IFS) and an interval-valued intuitionistic fuzzy set (IVIFS) in order to deal with indeterminate and inconsistent information. The paper proposes another form of the Dice measures of SNSs and the generalized Dice measures of SNSs and indicates that the Dice measures and asymmetric measures (projection measures) are the special cases of the generalized Dice measures in some parameter values. Then, we develop the generalized Dice measures-based multiple attribute decision-making methods with simplified neutrosophic information. By the weighted generalized Dice measures between each alternative and the ideal solution (ideal alternative) corresponding to some parameter value required by decision makers' preference, all the alternatives can be ranked and the best one can be obtained as well. Finally, a real example on the selection of manufacturing schemes demonstrates the applications of the proposed decision-making methods under simplified neutrosophic environment. The effectiveness and flexibility of the proposed decision-making methods are shown by choosing different parameter values.