Distance and Similarity Measures for Multiple Attribute Decision Making with Single-Valued Neutrosophic Hesitant Fuzzy Information

With respect to a combination of hesitant sets, and single-valued neutrosophic sets which are a special case of neutrosophic sets, the single valued neutrosophic hesitant sets (SVNHFS) have been proposed as a new theory set that allows the truth-membership degree, indeterminacy membership degree and falsity-membership degree including a collection of crisp values between zero and one, respectively. There is no consensus on the best way to determine the order of a sequence of singlevalued neutrosophic hesitant fuzzy elements. In this paper, we first develop an axiomatic system of distance and similarity measures between single-valued neutrosophic hesitant fuzzy sets and also propose a class of distance and similarity measures based on three basic forms such that the geometric distance model, the set-theoretic approach, and the matching functions. Then we utilize the distance measure between each alternative and ideal alternative to establish a multiple attribute decision making method under single-valued neutrosophic hesitant fuzzy environment. Finally, a numerical example of investment alternatives is provided to show the effectiveness and usefulness of the proposed approach. The advantages of the proposed distance measure over existing measures have been discussed.