Harmonic Aggregation Operator with Trapezoidal Picture Fuzzy Numbers and Its Application in a Multiple-Attribute Decision-Making Problem

Chittaranjan Shit, Ganesh Ghorai, Qin Xin, Muhammad Gulzar

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator, trapezoidal picture fuzzy order weighted harmonic mean (TrPFOWHM) operator and trapezoidal picture fuzzy hybrid harmonic mean (TrPFHHM) operator. The related properties about these operators are also studied. At last, an MADM problem is considered to interrelate among these operators. Furthermore, a numerical instance is considered to explain the productivity of the proposed operators.
Original languageUndefined/Unknown
Article number135
Number of pages19
Issue number1
Publication statusPublished - 11 Jan 2022


  • trapezoidal picture fuzzy number (TrPFN)
  • TrPFWHM operator
  • TrPFOWHM operator
  • TrPFHHM operator
  • MADM

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