Compatibility analysis and coupling evaluation method of extension set and variable set

Materialism holds that objective reality does not shift by human consciousness. Therefore, for the same practical problem, different evaluation methods should be compatible and complementary, and their evaluation results tend to be basically consistent. Extension sets and variable sets are taken as examples to study the theoretical compatibility between the two from three aspects, i.e. problem context, research methods and philosophical implication. Then, on the basis of analyzing the numerical characteristics and relationship of extension correlation function and variable opposite difference function, a coupling evaluation model based on extension matter element theory and opposite difference function was constructed. A comparative study on the application of water resources carrying capacity in 13 cities in Heilongjiang Province shows that the evaluation results of the model established in this paper are basically consistent with those of the extenics method, and are consistent with the actual situation, thus verifying the compatibility of variable sets and extension sets at the application level. The model introduces the opposite difference function into the extension evaluation method, which can not only determine the level of water resources carrying capacity, but also reflect its strength relative to adjacent levels, which provides support for further revealing the characteristics of the studied system and enriching its expression forms. © 2021, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.