Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis

• We propose a novel concept of the hesitancy index for the HFE.
• We introduce two novel hesitant fuzzy distance measures.
• We present a signed distance-based comparison method for HFEs.
• We develop a hesitant fuzzy QUALIFLEX outranking method.
• We modify the hesitant fuzzy ELECTRE method to conduct a comparative study.

QUALIFLEX (QUALItative FLEXible multiple criteria method) is a very useful outranking method to deal simultaneously with the cardinal and ordinal information in decision making process. The purpose of this paper is to develop a hesitant fuzzy QUALIFLEX with a signed distance-based comparison method for handling multi-criteria decision-making problems in which both the assessments of alternatives on criteria and the weights of criteria are expressed by hesitant fuzzy elements (HFEs). We propose a novel concept of hesitancy index for the HFE to measure the degree of hesitancy of the decision-maker or the decision organization. By taking their hesitancy indices into account, we present a signed distance-based method to compare the magnitude of HFEs. Using the signed distance-based comparison approach, we define the concordance/discordance index, the weighted concordance/discordance index and the comprehensive concordance/discordance index. By investigating all possible permutations of alternatives with respect to the level of concordance/discordance of the complete preference order, the optimal ranking orders of alternatives can be obtained. An application study of the proposed method on green supplier selection is conducted. The study indicates that the proposed method does not require the complicated computation procedures but still yields a reasonable and credible solution.