Abstract
Based on the idea of linear programming technique for multidimensional analysis of preference (LINMAP), a novel three-phase LINMAP method is presented here for solving hybrid multi-criteria group decision making (MCGDM) with dual hesitant fuzzy (DHF) truth degrees and incomplete criteria weights information. Firstly, by simultaneously taking into account the difference between each alternative and all the others for the decision maker (DM), the difference of each alternative between the individual DM and the decision group, and the difference of each alternative between the individual DM and all the others, a tri-objective nonlinear programming model is created to determine the DMs' weights. Secondly, to derive the criteria weights, objective positive ideal solution (OPIS), and the objective negative ideal solution (ONIS), a new four-objective DHF mathematical programming model is established by minimizing inconsistency and maximizing consistency based on OPIS and ONIS, and a pair of parametric nonlinear programming models are technically established by unequal weighted summation approach for solving the four-objective DHF mathematical programming model, which can provide DMs with more agility and flexible space to change their preference. Thirdly, by considering the distances of each alternative from the OPIS and ONIS for individual DM and the decision group, a minimizing deviation optimal model is established to derive the group ranking order of alternatives. Finally, a new method is put forward for solving hybrid MCGDM with DHF truth degrees, and the validity and practicability of the proposed method is analyzed through a case of water quality monitoring system (WQMS) selection.
Highlights
With the fast progress of social economy, information resources appear with diversity and complexity
This paper develops a new dual hesitant fuzzy (DHF) mathematical programming method to solve hybrid multi-criteria group decision making (MCGDM) problems
(2) On the basis of the deviation degree of each alternative from objective PIS (OPIS) and the objective NIS (ONIS), this paper introduces two consistency indices and two inconsistency indices, including the DHF positive ideal group consistency index (DHFPGCI), DHF positive ideal group inconsistency index (DHFPGICI), DHF negative ideal group consistency index (DHFNGCI), and DHF negative ideal group inconsistency index (DHFNGICI)
Summary
With the fast progress of social economy, information resources appear with diversity and complexity. Based on the classical LINMAP, Li [11] and [12] utilized IFSs to describe the criteria values of alternatives and presented two linear programming methods for solving multi-criteria decision making (MCDM) and MCGDM problems, respectively. Li and Wan [18] and Li and Wan [19] utilized TrFNs to represent the fuzzy truth degrees of pair-wise comparisons of alternatives and developed two LINMP methods for solving hybrid MCDM and MCGDM problems, respectively. A DHF mathematical programming method is put forward to solve hybrid MCGDM problems (3) To get the group criteria weights, OPIS, and ONIS, a four-objective DHF mathematical programming model is created based on the consistency and inconsistency indices.
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