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Spherical fuzzy Dombi aggregation operators and their application in group decision making problems

  • Shahzaib AshrafEmail author
  • Saleem Abdullah
  • Tahir Mahmood
Original Research

Abstract

Spherical fuzzy sets (SFSs), recently proposed by Ashraf, is one of the most important concept to describe the fuzzy information in the process of decision making. In SFSs the sum of the squares of memberships grades lies in close unit interval and hence accommodate more uncertainties. Thus, this set outperforms over the existing structures of fuzzy sets. In real decision making problems, there is often a treat regarding a neutral character towards the membership and non-membership degrees expressed by the decision-makers. To get a fair decision during the process, in this paper, we define some new operational laws by Dombi t-norm and t-conorm. In the present study, we propose Spherical fuzzy Dombi weighted averaging (SFDWA), Spherical fuzzy Dombi ordered weighted averaging (SFDOWA), Spherical fuzzy Dombi hybrid weighted averaging (SFDHWA), Spherical fuzzy Dombi weighted geometric (SFDWG), Spherical fuzzy Dombi ordered weighted geometric (SFDOWG) and Spherical fuzzy Dombi hybrid weighted geometric (SFDHWG) aggregation operators and discuss several properties of these aggregation operators. These aforesaid operators are enormously used to help a successful solution of the decision problems. Then an algorithm by using spherical fuzzy set information in decision-making matrix is developed and applied the algorithm to decision-making problem to illustrate its applicability and effectiveness. Through this algorithm, we proved that our proposed approach is practical and provides decision makers a more mathematical insight before making decisions on their options. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our method. Results indicate that the proposed method is suitable and effective for decision process to evaluate their best alternative.

Notes

Acknowledgements

This work was supported by Higher Education Commission, Pakistan under National Research Program for Universities (NRPU), Project no. 10701/KPK/ NRPU/R&D/HEC/ 2017.

Compliance with ethical standards

Conflict of Interest

The authors declare that they have no 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 MathematicsAbdul Wali Khan UniversityMardanPakistan
  2. 2.Department of Mathematics and StatisticsInternational Islamic UniversityIslamabadPakistan

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