Abstract
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.
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