Pythagorean fuzzy ordered weighted averaging aggregation operator and their application to multiple attribute group decision-making

Multi-attribute group decision-making problem based on some induced Einstein aggregation operators under complex fuzzy environment

The aim of the paper is to introduce some complex Einstein aggregation operators for aggregating the different complex Pythagorean fuzzy sets (CPFSs) by considering the dependency between the pairs of its membership degrees. In the existing studies of fuzzy and its extensions, the uncertainties present in the data are handled with the help of degrees of membership that are the subset of real numbers, which may also loss some valuable data and hence consequently affect the decision results. A modification to these, complex Pythagorean fuzzy set handles the uncertainties with the degree whose ranges are extended from real subset to the complex subset with unit disc and hence handle the two dimensional information in a single set. Thus motivated by this and this paper we present some novel Einstein aggregation operators, namely complex Pythagorean fuzzy Einstein weighted averaging (CPFEWA) operator, complex Pythagorean fuzzy Einstein ordered weighted averaging (CPFEOWA) operator, complex Pythagorean fuzzy Einstein hybrid averaging (CPFEHA) operator, induced complex Pythagorean fuzzy Einstein ordered weighted averaging (I-CPFEOWA) operator, and induced complex Pythagorean fuzzy Einstein hybrid averaging (I-CPFEHA) operator. Also develop some of their desirable properties. Furthermore, based on these operators a multi-attribute group decision making problems developed. An illustrative example related to the selection of the best alternative is considered to show the effectiveness, of the novel developed methods.

Mathematical calculation of COVID-19 disease in Pakistan by emergency response modeling based on complex Pythagorean fuzzy information

The new emerged infectious disease that is known the coronavirus disease (COVID-19), which is a high contagious viral infection that started in December 2019 in China city Wuhan and spread very fast to the rest of the world. This infection caused millions of infected cases globally and still poses an alarming situation for human lives. Pakistan in Asian countries is considered the third country with higher number of cases of coronavirus with more than 649824. Recently, some mathematical models have been constructed for better understanding the coronavirus infection. Mostly, these models are based on classical integer-order derivative using real numbers which cannot capture the fading memory. So at the current position it is a challenge for the world to understand and control the spreading of COVID-19. Therefore, the aim of our paper is to develop some novel techniques, namely complex Pythagorean fuzzy weighted averaging (abbreviated as CPFWA) operator, complex Pythagorean fuzzy ordered weighted averaging (abbreviated as CPFOWA) operator, complex Pythagorean fuzzy hybrid averaging (abbreviated as CPFHA) operator, induced complex Pythagorean fuzzy ordered weighted averaging (abbreviated as I-CPFOWA) operator and induced complex Pythagorean fuzzy hybrid averaging (abbreviated as I-CPFHA) operator to analysis the spreading of COVID-19. At the end of the paper, an illustrative the emergency situation of COVID-19 is given for demonstrating the effectiveness of the suggested approach along with a sensitivity analysis, showing the feasibility and reliability of its results.