Fuzzy mathematics is a tool to deal with fuzzy information. It describes fuzzy phenomena abstractly by mathematical methods and reveals the essence and law of fuzzy phenomena. Grey system theory studies and deals with complex systems from incomplete information. By mathematically processing the observation data at a certain level of the system, we can understand the internal change trend and the mechanism of the relationship at a higher level.
In the grey system theory, the grey correlation degree is the expression of the degree and quantity of correlation between things and factors. By calculating the correlation coefficient and correlation degree, we can quantitatively analyze the degree of correlation and influence between things as a whole or dynamically, and provide quantitative basis for establishing the main factors of things' development and change [1-2]. Because many factors in the evaluation object are fuzzy, grey and difficult to quantify, we combine the fuzzy comprehensive evaluation method in fuzzy mathematics with the grey relational clustering analysis theory in grey theory, and put forward a multi-level fuzzy grey relational clustering analysis comprehensive evaluation method on the basis of establishing a multi-level index system. The application of this method in oil and gas drilling technology evaluation has achieved satisfactory results.
The composition of evaluation index system is different, so is the composition of evaluation index system. Many evaluation indicators reflecting problems are grouped according to different attributes, and each group is regarded as a level. For general evaluation problems, the evaluation index system consists of the highest level and the first level. For complex evaluation problems, we should arrange the levels of evaluation indicators and form a multi-level evaluation index system, such as forming a three-level evaluation index system. The top layer A represents the problem to be comprehensively evaluated, the first layer B 1, B2, …, Bk represents the first-level evaluation index, and the second layer Cij represents the second-level evaluation index.
The basic idea of grey relational analysis is to judge whether a series of curves are closely related according to their geometric similarity. The closer the curves are, the greater the correlation between the corresponding series. Grey correlation clustering is based on grey correlation analysis, and clustering is based on the principle of maximum correlation recognition. Fuzzy grey relational clustering analysis takes the fuzzy comprehensive evaluation result matrix of the evaluation object as a comparison sequence, calculates the correlation degree between each comparison sequence and each reference sequence, and carries out clustering analysis according to the correlation degree, thus ranking the evaluation objects.