In order to explore the impact of environmental regulation on the coordinated development of energy and the environment with the background of governance transition, we propose a three-stage integrated approach and use the panel data of China’s manufacturing industry 27 sub-sectors during the period of 2006–2015. In the first stage, according to the environmental pollution intensity, the manufacturing industry is divided into heavily polluting industry, moderately polluting industry, and lightly polluting industry. The second stage is employed the slacks-based measure (SBM)-undesirable method to study the sub-industries’ green energy-environmental efficiency under different environmental pollution intensities. Besides, the dynamic changes of technical innovation and efficiency among different industries are analyzed through the Malmquist productivity index. For the purpose of investigating the transmission mechanism of the Porter’s hypothesis and exploring the compound effects of environmental regulation and governance transition on green development, in the third stage, we use the panel data analysis to conduct more in-depth research on the relationship between environmental regulation, governance transition, and technical innovation. Results show that the highest average green energy-environmental efficiency is lightly polluting industry, which is 0.52, followed by the heavily polluting industry at 0.40, and the lowest is the moderately polluting industry, which is 0.32. By decomposing total factor productivity, heavily polluting industry is at the forefront of technical innovation. Panel data analysis results indicate that investment in research and development and governance transition could promote the growth of total factor productivity for manufacturing.

Distance and similarity measures have recently been investigated in-depth within the context of hesitant fuzzy sets. By analyzing the existing studies concerning distance measures for hesitant fuzzy sets, we find that they have some limitations. To address the flaws, this study develops some novel distance measures for hesitant fuzzy sets, including the normalized Euclidean distance measure, the Hausdorff metric distance measure, the normalized generalized distance measure, and their corresponding weighted distance measures. The proposals of this study not only hold many ideal characteristics but also do not consider the lengths of hesitant fuzzy elements as well as the arrangement of their possible values. To deal with the situations where both of the universe of discourse and the weight of element are continuous, some continuous hesitant fuzzy distance measures are also investigated. Based on the relationship between distance measure and similarity measure, some novel similarity measures for hesitant fuzzy sets can be further deduced from the proposed distance measures. Finally, two numerical examples are given to demonstrate the applicability and validity of the proposed hesitant fuzzy distance measures.