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Mathematical Problems in Engineering
Volume 2015, Article ID 892549, 9 pages
Research Article

A Novel Model of Set Pair Analysis Coupled with Extenics for Evaluation of Surrounding Rock Stability

School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China

Received 3 May 2015; Accepted 5 July 2015

Academic Editor: Jurgita Antucheviciene

Copyright © 2015 Mingwu Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The evaluation of surrounding rock stability is a complex problem involving numerous uncertainty factors. Here, based on set pair analysis (SPA) coupled with extenics, a novel model, considering incompatibility, certainty, and uncertainty of evaluation indicators, was presented to analyze the surrounding rock stability. In this model, extension set was first utilized to describe the actual problem of surrounding rock stability. Then, the connectional membership degree of the set pair was introduced to compare the measured values with classification standards from three aspects embracing identity, discrepancy, and contrary. Also, according to identity-discrepancy-contrary (IDC) analysis in the universe of the extension set, the connection numbers were proposed to specify the connectional membership degree of an evaluation indicator to each class. Combined with the weights of evaluation indicators, integrated connectional membership degrees were calculated to determine their classes of rock stability. Finally, a case study and comparison with variable fuzzy set method, triangular fuzzy number method, and basic quality (BQ) grading method were performed to confirm the validity and reliability of the proposed model. The results show that this model can effectively and quantitatively express the differences within a group, transformation of different groups, and uncertainty of complex indicators as a whole.