Abstract
Multiple attribute decision making (MADM) is full of uncertainty and vagueness due to intrinsic complexity, limited experience and individual cognition. Representative decision theories include fuzzy set (FS), intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS), dual hesitant fuzzy set (DHFS) and so on. Compared with IFS and HFS, DHFS has more advantages in dealing with uncertainties in real MADM problems and possesses good symmetry. The membership degrees and non-membership degrees in DHFS are simultaneously permitted to represent decision makers’ preferences by a given set having diverse possibilities. In this paper, new distance measures for dual hesitant fuzzy sets (DHFSs) are developed in terms of the mean, variance and number of elements in the dual hesitant fuzzy elements (DHFEs), which overcomes some deficiencies of the existing distance measures for DHFSs. The proposed distance measures are effectively applicable to solve MADM problems where the attribute weights are completely unknown. With the help of the new distance measures, the attribute weights are objectively determined, and the closeness coefficients of each alternative can be objectively obtained to generate optimal solution. Finally, an evaluation problem of airline service quality is conducted by using the distance-based MADM method to demonstrate its validity and applicability.
Highlights
Multiple attribute decision making (MADM) is one of the most significant components of decision theory, which aims to generate an optimal solution among several alternatives by selecting and ranking a set of alternatives profiled from conflictive attributes with respect to decision makers’ cognitions [1].In the process of analyzing MADM problem, we are usually plagued by uncertain and vagueness due to intrinsic complexity, limited experience and individual cognition.A growing number of methods and theories have been applied to deal with different kinds of uncertainties in MADM
The third deficiency is that these existing distance measures are not precise because they cannot depict the volatility of the values of membership and non-membership degrees in a dual hesitant fuzzy elements (DHFEs)
We propose a variety of new distance measures for dual hesitant fuzzy set (DHFS) in terms of the mean, the variance and the number of elements in the DHFEs, which overcomes some deficiencies of the existing DHF distance measures
Summary
Multiple attribute decision making (MADM) is one of the most significant components of decision theory, which aims to generate an optimal solution among several alternatives by selecting and ranking a set of alternatives profiled from conflictive attributes with respect to decision makers’ cognitions [1]. Symmetry 2020, 12, 191 a dual hesitant fuzzy element (DHFE), which has more advantages in dealing with uncertainties in real MADM problems and possesses good symmetry The existing distance measures were defined only depending on the difference among numerical values of the membership and non-membership degrees but paid few attentions on the volatility of the DHF information To overcome such deficiencies, some new distance measures are developed in terms of the mean, the variance and the number of elements in the DHFEs. The proposed distance measures are effectively applicable to solve MADM problems where the attribute weights are completely unknown [32,33,34,35,36]. We summarize the main work of this paper
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