An integrated quantum picture fuzzy rough sets with golden cuts for evaluating carbon footprint-based investment decision policies of sustainable industries

The purpose of this study is to make evaluation related to the significant determinants of the effectiveness of the carbon footprint-based investments while constructing a novel decision-making model. At the first stage, selected five determinants are evaluated with multi stepwise weight assessment ratio analysis (M-SWARA) methodology based on quantum picture fuzzy rough sets. In the second part, sustainable industry alternatives are ranked by quantum picture fuzzy rough sets extended multi-objective optimization on the basis of ratio analysis (MOORA) technique. Similarly, elimination and choice translating reality (ELECTRE) approach is also taken into consideration to make a comparative evaluation. The main contribution of this study is that a novel methodology is proposed by integrated picture fuzzy row sets and quantum theory. While using the combination of rough sets and picture fuzzy logic, uncertain data in the complex process can be evaluated in a more effective manner. Moreover, due to the criticisms to stepwise weight assessment ratio analysis (SWARA) methodology by not considering causal relationship of the determinants, this methodology is extended with the help of some improvements so that a new approach (M-SWARA) is proposed to overcome this deficiency by creating impact direction map of the items. The ranking results of these two techniques are the same that indicates the coherency of the findings. It is concluded that carbon-free project financing with green bonds is the most important indicator for this situation. On the other side, the ranking results demonstrate that renewable energy investment is the most appropriate sustainable industry alternative. Considering the results obtained in this study, the development of green bonds should be given priority. Establishing an international certification system is important in terms of clearly defining green bonds. Government supports are also of critical importance in the development of green bonds. Tax reductions provided by governments can increase the profitability of green bonds. This may contribute to investors showing more interest in green bonds.