A two-phase multi-criteria decision-making with interval-valued Pythagorean normal fuzzy information and its application for module hospital site selection in combating COVID-19

Abstract

During the fight against COVID-19, module hospital saved tens of thousands of lives and families. Therefore, how to effectively select the site of module hospital is a critical issue. The site selection of module hospital is a multi-criteria decision-making (MCDM) problem. Recently, interval-valued Pythagorean normal fuzzy (IPNF) number has become an effective and powerful tool for handling ambiguity in decision-making. However, the weights of experts in existing IPNF decision-making are often directly given, lacking objectivity and persuasiveness. Moreover, the current research on aggregation operators in IPNFN only involves simple weighted average and geometry, while ignoring the interaction among fuzzy information. Motivated by these issues, this paper aims to develop a two-phase IPNF MCDM approach and apply it to the site selection of module hospital. Firstly, IPNF Einstein weighted averaging (IPNFEWA) operator, IPNF Einstein order weighted averaging (IPNFEOWA) operator, IPNF Einstein weighted geometric (IPNFEWG) operator, and IPNF Einstein order weighted geometric (IPNFEOWG) operator are proposed. Moreover, numerical and theoretical proofs of the proposed operators are carried out. Secondly, an algorithm for determining experts’ weights is developed using the proposed IPNF social network in the first phase, and the decision-making process is conducted in the second phase. Finally, a numerical example on the site selection of module hospital is provided to demonstrate the feasibility of the proposed method. The numerical results of comparisons and sensitivity analysis are further analyzed to confirm the advantages of the proposed method.