A unified method for Pythagorean fuzzy multicriteria group decision-making using entropy measure, linear programming and extended technique for ordering preference by similarity to ideal solution

  • Biswajit Sarkar
  • Animesh BiswasEmail author
Methodologies and Application


This paper presents an innovative method for solving Pythagorean fuzzy (PF) multicriteria group decision-making problems with completely unknown weight information about criteria using entropy weight model, linear programming (LP) and modified technique for ordering preference by similarity to ideal solution (TOPSIS). At first, a new distance measure for PF sets is defined considering their degree of hesitancy and based on weighted Hamming distance and Hausdorff metric. To handle the fuzziness in criteria weights, PF entropy weight model is used to find the initial weights of the criteria in PF format. Following the concept of TOPSIS, an LP model is constructed on the basis of the view point that the chosen alternative should have the smallest distance from the positive ideal solution and the largest distance from the negative ideal solution. Then, the LP model is utilized to find optimal weights of the criteria. Using the newly defined distance measure, entropy weight model and LP model, TOPSIS is extended in PF environments. The existing methods are able to find criteria weights in the form of crisp values only, whereas proposed method is able to obtain those weights in PF format. Thus, the proposed method can overcome the drawback in computing criteria weight for multicriteria group decision-making in PF environments and reduce the information loss significantly. Several numerical examples are considered and solved to validate the superiority of the proposed methodology.


Multicriteria group decision-making Pythagorean fuzzy sets Distance measure Entropy weight model Linear programming TOPSIS 



Dr. Animesh Biswas is thankful to University of Kalyani for providing partial financial assistance in carrying out the research work through DST-PURSE Programme of the University. The authors also remain grateful to the reviewers for their valuable comments and suggestions.

Compliance with ethical standards

Conflict of interest



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsBasirhat CollegeBasirhatIndia
  2. 2.Department of MathematicsUniversity of KalyaniKalyaniIndia

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