Affiliations: College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China | School of Mathematics and Physics, Anhui University of Technology, Ma'anshan, China | Logistics School, Linyi University, Linyi, China
Note: [] Corresponding author. Jianjun Zhu, College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China. Tel.: +86 13505152630; Fax: +86 02584896149; E-mail: [email protected]
Abstract: The linear programming technique for multidimensional analysis of preference (LINMAP) and the technique for order preference by similarity to ideal solution (TOPSIS) are two well-known methods for dealing with the multiple attribute decision making (MADM) problems. In this paper, we further extend the LINMAP to accommodate hesitant fuzzy environment and propose a new approach to solve the MADM problems with hesitant fuzzy information. Then, an integrated method that combines the LINMAP and TOPSIS is developed. In this methodology, we take advantage of the LINMAP to determine the attribute weights objectively and thus overcome the drawbacks of the TOPSIS. Meanwhile the TOPSIS that considers both the positive ideal solution (PIS) and the negative ideal solution (NIS) can make up the disadvantages of the LINMAP. In order to measure consistency and inconsistency between the ranking order of alternatives and the decision maker's preference, two indices based on PIS and NIS are defined. Moreover, a linear programming model that can be used for minimizing the total inconsistency is constructed to determine the attribute weights. By using the TOPSIS, we obtain the most appropriate alternative. Finally, two numerical examples are given to demonstrate the implementation process of the developed approach.
Keywords: Hesitant fuzzy set, multiple attribute decision making, linear programming technique for multidimensional analysis of preference (LINMAP), technique for order preference by similarity to ideal solution (TOPSIS)
