A Novel Trapezoidal Bipolar Fuzzy TOPSIS Method for Group Decision-Making

  • Muhammad AkramEmail author
  • Maham Arshad


In this research article, the notions of bipolar fuzzy numbers, trapezoidal bipolar fuzzy numbers, triangular bipolar fuzzy numbers and bipolar fuzzy linguistic variables are introduced. Ranking function on the set of all bipolar fuzzy numbers, and the expressions for the ranking of trapezoidal and triangular bipolar fuzzy numbers are derived. A group decision making method based on trapezoidal bipolar fuzzy TOPSIS method is proposed, and the implementation of the proposed method in the selection of best project proposal is presented. Finally, a theoretical comparison of the proposed trapezoidal bipolar fuzzy TOPSIS method with other multi-criteria decision making methods such as TOPSIS, bipolar fuzzy TOPSIS and bipolar fuzzy ELECTRE I is discussed.


Bipolar fuzzy numbers Trapezoidal bipolar fuzzy numbers Triangular bipolar fuzzy numbers Bipolar fuzzy linguistic values Trapezoidal bipolar fuzzy TOPSIS 



The authors are highly thankful to the Associate Editor, and the anonymous referees for their valuable comments and suggestions.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest regarding the publication of the research article.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan

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