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Geometric aggregation operators with interval-valued Pythagorean trapezoidal fuzzy numbers based on Einstein operations and their application in group decision making

  • M. ShakeelEmail author
  • S. Abdullah
  • M. Shahzad
  • Nasir Siddiqui
Original Article
  • 75 Downloads

Abstract

The aim of this paper is to investigate information aggregation methods under interval-valued Pythagorean trapezoidal fuzzy environment. Some Einstein operational laws on interval-valued Pythagorean trapezoidal fuzzy numbers are defined based on Einstein sum and Einstein product. Based on Einstein operations, we define interval-valued Pythagorean trapezoidal fuzzy aggregation operators, such as interval-valued Pythagorean trapezoidal fuzzy Einstein weighted geometric operator, interval-valued Pythagorean trapezoidal fuzzy Einstein ordered weighted geometric operator and interval-valued Pythagorean trapezoidal fuzzy Einstein hybrid geometric operator. Furthermore, we apply the proposed aggregation operators to deal with multiple attribute group decision making problem. Finally we construct a numerical example for multiple attribute group decision making problem and compare the result with existing methods.

Keywords

Multiple attribute group decision making Aggregation operations Interval-valued Pythagorean trapezoidal fuzzy numbers Einstein operation 

Notes

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Copyright information

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

Authors and Affiliations

  • M. Shakeel
    • 1
    Email author
  • S. Abdullah
    • 2
  • M. Shahzad
    • 1
  • Nasir Siddiqui
    • 3
  1. 1.Department of MathematicsHazara University Mansehra KpkDhodialPakistan
  2. 2.Department of MathematicsAbdul Wali Khan University Mardan KpkMardanPakistan
  3. 3.Department of MathematicsUniversity of Engineering and Technology TaxilaTaxilaPakistan

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