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Pythagorean hesitant fuzzy Choquet integral aggregation operators and their application to multi-attribute decision-making

  • Muhammad Sajjad Ali Khan
  • Saleem Abdullah
  • Asad Ali
  • Fazli Amin
  • Fawad Hussain
Methodologies and Application
  • 21 Downloads

Abstract

Pythagorean hesitant fuzzy sets play a vital role in decision-making as it permits a set of possible elements in membership and non-membership degrees and satisfy the condition that the square sum of its memberships degree is less than or equal to 1. While aggregation operators are used to aggregate the overall preferences of the attributes, under Pythagorean hesitant fuzzy environment and fuzzy measure in the paper we develop Pythagorean hesitant fuzzy Choquet integral averaging operator, Pythagorean hesitant fuzzy Choquet integral geometric operator, generalized Pythagorean hesitant fuzzy Choquet integral averaging operator and generalized Pythagorean hesitant fuzzy Choquet integral geometric operator. We also discuss some properties such as idempotency, monotonicity and boundedness of the developed operators. Moreover, we apply the developed operators to multi-attribute decision-making problem to show the validity and effectiveness of the developed operators. Finally, a comparison analysis is given.

Keywords

Pythagorean hesitant fuzzy sets Generalized Pythagorean hesitant fuzzy Choquet integral averaging (GPHFCIA) operator Generalized Pythagorean hesitant fuzzy Choquet integral geometric (GPHFCIG) operator Multi-attribute decision-making 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Muhammad Sajjad Ali Khan
    • 1
  • Saleem Abdullah
    • 2
  • Asad Ali
    • 1
  • Fazli Amin
    • 1
  • Fawad Hussain
    • 3
  1. 1.Department of MathematicsHazara UniversityMansehraPakistan
  2. 2.Department of MathematicsAbdul Wali Khan UniversityMardanPakistan
  3. 3.Department of MathematicsAbbottabad University of Science and TechnologyAbbottabadPakistan

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