Affiliations: [a] College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan Province, P.R. China | [b] Data Recovery Key Lab of Sichuan Province, Neijiang Normal University, Neijiang, Sichuan, P.R. China | [c] School of Computing and Mathematics, Ulster University, Jordanstown Campus, Northern Ireland, UK
| [d] School of Computer Science, Wuyi University, Jiangmen, Guangdong, P.R. China
Correspondence:
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Corresponding author. Yi Liu. Email: liuyiyl@126.com.
Note: [1] This work is supported by National Natural Science Foundation of P.R. China (Grant no. 61673320); The Application Basic Research Plan Project of Sichuan Province (No. 2015JY0120); The Scientific Research Project of Department of Education of Sichuan Province (15TD0027, 14ZA0245, 15ZB0270); Natural Science Foundation of Guangdong Province (2016A030310003).
Abstract: Pythagorean fuzzy sets (PFSs), as an extension of intuitionistic fuzzy sets (IFSs) to deal with uncertainty, have attracted much attention since its introduction, in both theory and application aspects. The present work aims at investigating new distance measures in the PFSs and then employing them into multiple criteria decision-making application. To begin with, generalized Pythagorean fuzzy weighted averaging distance operator (GPFWAD) and generalized Pythagorean fuzzy ordered weighted averaging distance (GPFOWAD) measure are firstly introduced in the PFSs. Afterwards, probabilistic generalized Pythagorean fuzzy weighted averaging distance (P-GPFWAD) operator, probabilistic generalized Pythagorean fuzzy order weighted averaging distance (P-GPFOWAD) operator are proposed which are new distance measures and are able to integrate the (ordered) weighted averaging operator, probabilistic weight and individual distance of two Pythagorean fuzzy numbers (PFNs) in the same formulation. These generalized weighted averaging distance measures are very suitable to deal with the situation where the input data are represented in Pythagorean fuzzy numbers (PFNs). Then we present a kind of multiple criteria decision-making method with Pythagorean fuzzy information based on the developed distance measures. Finally, a numerical example is provided to illustrate the practicality and feasibility of the developed method.
