Air Pollution Model using Neutrosophic Cubic Einstein Averaging Operators

Abstract

The neutrosophic cubic averaging and Einstein averaging aggregation operators are presented and applied to the air pollution model of the city of Peshawar, Pakistan. Neutrosophic cubic set (NCS) is a more generalized version of the neutrosophic set (NS) and an interval neutrosophic set (INS). It is in a better position to express consistent, indeterminant and incomplete information, thus it is able to be applied to aggregate the air pollution model. Aggregation operators have a key role in science and engineering problems. Firstly, the neutrosophic cubic weighted averaging (NCWA) operator, neutrosophic cubic ordered weighted averaging (NCOWA) operator, neutrosophic cubic hybrid aggregation (NCHA) operator, neutrosophic cubic Einstine weighted averaging (NCEWA) operator, neutrosophic cubic Einstine ordered weighted averaging (NCEOWA) operator and neutrosophic cubic Einstine hybrid aggregation (NCEHA) operator are defined. Secondly, these operators are applied to the air pollution model of particulate matter with the size of less than 10 micron (PM10) in Peshawar. Subsequently, the results are compared with the World Health Organization (WHO) standards using score/accuracy function. The pollution of PM10 is found to be very much higher than WHO standards. Hence, strong measures are required to control air pollution.

Keywords

• air pollution; neutrosophic cubic weighted averaging; neutrosophic cubic hybrid averaging; neutrosophic cubic einstein weighted averaging; neutrosophic cubic einstein hybrid averaging.