Pythagorean Fuzzy Monotonic Argument Dependent OWA Operator and Its Applications in Multiple Attribute Decision Making

After analyzing the existing ranking methods of Pythagorean fuzzy numbers (PFNs) by several examples, some shortcomings of the existing ranking methods are pointed out. To conquer such shortcomings, we propose a novel approach to rank PFNs by using power index measure and score function of PFN. Simultaneously, the rationality of the proposed ranking method is analyzed theoretically. Besides, the techniques of aggregating Pythagorean fuzzy information are investigated. To expand the practical application scope of the DOWA operator to Pythagorean fuzzy environments, we present two kinds of Pythagorean fuzzy monotonic DOWA (PFMDOWA) operators by utilizing the power index measure of PFN. If the weights of attributes are considered, we further develop two kinds of Pythagorean fuzzy hybrid monotonic DOWA (PFHMDOWA) operators. The main advantage of the PFMDOWA operator and PFHMDOWA operator is that the weights associated to the operators can be generated and adjusted dynamically. Lastly, a decision making example is given to verify the flexibility and rationality of the presented techniques.