Pythagorean Fuzzy LINMAP Method Based on the Entropy Theory for Railway Project Investment Decision Making

The uncertainty and complexity of the decision-making environment and the subjectivity of the decision makers will lead to the inevitable errors of the decision-making data. A poor decision will be produced with those errors, whereas the linear programming technique for multidimensional analysis of preference (LINMAP) method can adjust such errors through constructing an optimal programming model based on the consistency of the decision-making information, and it has been applied widely in multiple attribute group decision making (MAGDM). Moreover, Pythagorean fuzzy information is useful to simulate the ambiguous and uncertain decision-making environment. Therefore, the LINMAP method under the Pythagorean fuzzy circumstance will be proposed in this paper to solve MAGDM problems. To measure the fuzziness and uncertainty of Pythagorean fuzzy set (PFS) and interval-valued PFS, Pythagorean fuzzy entropy (PFE) and interval-valued PFE (IVPFE) grounded on the similarity and hesitancy parts have been defined, respectively. Then, Pythagorean fuzzy LINMAP (PF LINMAP) methods are constructed on the basis of the PFE and IVPFE correspondingly. Under the given preference relations, the maximum consistency and the amount of knowledge can be realized by the proposed methods. After investigating the relevant indicator system, the decision-making problem concerning railway project investment has been solved through the proposed PF LINMAP method with PFE. Finally, the practicability and effectiveness of the PF LINMAP method has been verified via the comparative analysis with the existing methods. (C) 2017 Wiley Periodicals, Inc.