Incentive mechanism-based interval-valued q-rung orthopair fuzzy dynamic comprehensive evaluation method for measuring regional green development level

Abstract

Interval-valued q-rung orthopair fuzzy number (IVq-ROFN) is a popular tool for modeling complex uncertain information and has gained successful applications in the field of comprehensive evaluation. However, most of the existing studies are based on the absolute values of evaluation data but fail to take incentive effects into account. Reasonable and appropriate incentive can guide the evaluated objects to better achieve the decision goals. Therefore, this study develops an incentive mechanism-based interval-valued q-rung orthopair fuzzy dynamic comprehensive evaluation method. Firstly, new interval-valued q-rung orthopair fuzzy measures including deviation measure and correlation coefficient are proposed for managing IVq-ROFNs data. To overcome the limitations of the existing aggregating operators that are not suitable for scenarios with need of many times of data aggregation, we introduce two new interval-valued q-rung orthopair fuzzy aggregating operators. Furthermore, a new interval-valued orthopair fuzzy CRITIC method is developed to objectively determine the importance of the evaluated criteria. More importantly, the horizontal incentive effects within a single period and the vertical incentive effects during multiple periods under IVq-ROFNs environments are proposed to reward (or punish) the evaluated objects in the evaluation process. The evaluated results are determined based on the full compensatory model and the multiplicative form model. The main advantage of the developed method is that the expectations of decision-makers and the dynamic characteristics during multiple periods are taken fully into account, which can make the evaluation results more reasonable and reliable. Finally, this developed comprehensive evaluation method is applied to evaluate the green development level of Jiangxi province within eleven cities from 2016 to 2020. We observe that the cities x 2, x 3, x 4, x 5, x 7, x 8 are rewarded within positive incentive values and the cities x 1, x 6, x 9, x 10, x 11 are punished within negative incentive values. Especially, the positive incentive value for the city x 3 is the biggest and the negative incentive value for the city x 9 is the biggest. The best city in term of GDL is x 3. The evaluated results with consideration of incentive effects are in line with the expectation of the decision-maker.