Development of harmonic aggregation operator with trapezoidal Pythagorean fuzzy numbers

Aydin S., Kahraman C., KABAK M.

SOFT COMPUTING, vol.24, no.15, pp.11791-11803, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 15
  • Publication Date: 2020
  • Doi Number: 10.1007/s00500-019-04638-4
  • Journal Name: SOFT COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
  • Page Numbers: pp.11791-11803
  • Istanbul Technical University Affiliated: Yes


Pythagorean fuzzy sets are one of the extensions of ordinary fuzzy sets and allow a larger domain to be utilized by decision makers with respect to other extensions. Pythagorean fuzzy sets have been often used as an effective tool for handling the vagueness of multi-criteria decision making problems. Aggregation operators are a useful tool in order to collect different information provided by different sources. The objective of this paper is to develop harmonic aggregation operators for trapezoidal Pythagorean fuzzy numbers. We developed trapezoidal Pythagorean fuzzy weighted harmonic mean operator, trapezoidal Pythagorean fuzzy ordered weighted harmonic mean operator, and trapezoidal Pythagorean fuzzy hybrid harmonic mean operator. We proved some theorems for the developed operators. Finally, we presented an illustrative example using the proposed aggregation operators in order to rank the alternatives.