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Pythagorean fuzzy prioritized aggregation operators and their application to multi-attribute group decision making

  • Muhammad Sajjad Ali Khan
  • Saleem Abdullah
  • Asad Ali
  • Fazli Amin
Original Paper

Abstract

Pythagorean fuzzy set is a useful tool to deal with the fuzziness and vagueness. Many aggregation operators have been proposed by many researchers based on Pythagorean fuzzy sets. But the current methods are under the assumption that the decision makers and the attributes are at the same priority level. However, in real group decision-making problems the attribute and decision makers may have different priority level. Therefore, in this paper, we develop multi-attribute group decision-making based on Pythagorean fuzzy sets where there exists a prioritization relationship over the attributes and decision makers. First, we develop Pythagorean fuzzy prioritized weighted average operator and Pythagorean fuzzy prioritized weighted geometric operator. Then we study some of its desirable properties such as idempotency, boundary and monotonicity in detail. Moreover, we propose a multi-attribute group decision-making approach based on the developed operators under Pythagorean fuzzy environment. Finally, a numerical example is provided to illustrate the practicality of the proposed approach.

Keywords

Pythagorean fuzzy set Pythagorean fuzzy prioritized weighted average (PFPWA) operator Pythagorean fuzzy prioritized weighted geometric (PFPWG) operator Multi-attribute group decision making 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Muhammad Sajjad Ali Khan
    • 1
  • Saleem Abdullah
    • 2
  • Asad Ali
    • 1
  • Fazli Amin
    • 1
  1. 1.Department of MathematicsHazara University MansehraMansehraPakistan
  2. 2.Department of MathematicsAbdul Wali Khan University MadranMadranPakistan

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