A Robust Fuzzy Decision Making on Global Warming

Abstract

In this article we develop a global warming indicator model under fuzzy system. It is the light of sun that environmental pollution is responsible for the cause and immediate effect of global warming. Limited amount of oxygen in the air, continuous decrease of fresh water volume, more especially the amount of drinking water and the rise of temperature in the globe are the major symptoms (variants) of global warming. Thus, to capture the facts we need to develop a mathematical model which has not yet been developed by the earlier researchers. An efficient literature survey has been done over the three major parameters of the environment namely oxygen, fresh water and surface temperature exclusively. In fact we have accumulated 150 years-data structure for these major components and have analyzed them under fuzzy system so as to develop an efficient global warming indicator model. First of all, we gave few definitions on fuzzy set. Utilizing the data set we have constructed appropriate membership functions of the three major components of the environment. Then applying goal programming problem, we have constructed a fuzzy global warming indicator (GWI) model subject to some goal constraints with respective priority vectors (Scenario 1 and Scenario 2). An extension has also been included for multi-valued goal programming problem and numerical illustrations have been done with the help of LINGO software. Numerical study reveals that the GWI takes maximum and minimum values in a decreasing manner as time increases. It is seen that for scenario 1, the global environmental system will attain its stability after 30 years by degrading 31% of GWI with respect to present base line. For scenario 2, after the same time the global environmental system will attain its stability quite slowly by degrading 28% of GWI with respect to present base line. Here we have studied a mathematical model of global warming first time using fuzzy system. No other mathematical models have been existed in the literature. Thus, the basic novelty lies in a robust decision-making approach which shows the expected time of extinction of major species in this world. However, extensive study on data analytics over major environmental components can tell the stability of the global warming indicator and hence the future fate of the globe also.