Abstract
The target of current work is to propose a new approach to deal with multiattribute decision-making (MADM) problems with interval-valued Pythagorean fuzzy set (IVPFS) based on the concepts of covering-based rough set (CRS) and TOPSIS and give its application in MADM problems. To begin with, we integrate the fuzzy rough set (FRS), IVPFS and CRS and define the covering-based interval-valued Pythagorean fuzzy rough set (CIVPFRS). Firstly, the relative notions of the CIVPFRS model are introduced. In addition, the distance measure of interval-valued Pythagorean fuzzy numbers (IVPFNs) is defined; based on the proposed distance, the rough and precision degrees of CIVPFRS are discussed. Thirdly, on the basis of the theoretical analysis for CIVPFRS models, an interval-valued Pythagorean fuzzy TOPSIS method is designed to deal with the MADM problems with interval-valued Pythagorean fuzzy information (IVPFI). Last of all, the validity and merits of the proposed approach are illustrated by an example, and the sensitivity analysis of the parameters and the comparison with the existing related methods are carried out.β
Highlights
Fuzzy set theory (FS) [1] and rough set theory (RS) [2] are both used to address some problems with uncertainty
As can be seen from the latest hot research directions, the CIVPFS model is an important tool for dealing with uncertainty in the real world. erefore, it is necessary to build the coveringbased interval-valued Pythagorean fuzzy rough set (CIVPFRS) model by integrating the interval-valued Pythagorean fuzzy set (IVPFS) and CFRS in order to deal with some information with more complicated uncertainty
Conclusions e CIVPFS model is an important tool for dealing with uncertainty in the real world
Summary
Wan and Dong [8] studied the theory and method of decision-making based on interval-valued intuitionistic fuzzy sets. IFSs have some limitations in the application of MADM It can only describe the fuzzy phenomenon that the sum of MD and NMD is not more than one, but it cannot do anything to the phenomenon that the sum of MD and NMD is more than one. For this reason, Yager and Abbasov [9] put forward the Pythagorean fuzzy set (PFS) to solve the abovementioned limitations. Based on Yager’s research, many scholars have studied the PFS and obtained some research
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