Multiple Attribute Decision-Making Methods Based on the Expected Value and the Similarity Measure of Hesitant Neutrosophic Linguistic Numbers

The existing neutrosophic linguistic decision-making approach uses only one neutrosophic linguistic number (NLN) to express its evaluation value of an attribute in decision making. Sometimes, it may not reflect exactly what decision makers mean due to the ambiguity and indeterminacy of their cognitions to complex decision-making problems. In this situation, decision makers might hesitate among several NLNs to express their opinions. To deal with the issue, this paper defines hesitant neutrosophic linguistic numbers (HNLNs), the expected value of HNLN and proposes the generalized distance and similarity measure between two HNLN sets based on the least common multiple cardinality for HNLNs. Then, multiple attribute decision-making (MADM) methods are established based on the expected value and the similarity measure under a HNLN environment. In the proposed decision-making methods, the evaluation values of alternatives over attributes provided by decision makers are HNLNs, and then all the alternatives are ranked by the expected values of HNLNs and the similarity measure values between each alternative and the ideal alternative (ideal solution) to select the best one. An actual example on the selection problem of manufacturing alternatives is provided to demonstrate the applicability of the developed decision-making approaches. The decision results of manufacturing alternatives and the comparative analysis indicate that the proposed methods are effective and superior to existing ones. The MADM methods based on the expected value and the similarity measure can effectively deal with MADM problems with HNLN information and are more objective and more useful than the existing ones.