Rock Mass Quality Rating Based on the Multi-Criteria Grey Metric Space

Assessment of rock mass quality significantly impacts the design and construction of underground and open-pit mines from the point of stability and economy.This study develops the novel Gromov-Hausdorff distance for rock quality(GHDQR)methodology for rock mass quality rating based on multi-criteria grey metric space.It usually presents the quality of surrounding rock by classes(metric spaces)with specified properties and adequate interval-grey numbers.Measuring the distance between surrounding rock sample characteristics and existing classes represents the core of this study.The Gromov-Hausdorff distance is an especially useful discriminant function,i.e.,a classifier to calculate these distances,and assess the quality of the surrounding rock.The efficiency of the developed methodology is analyzed using the Mean Absolute Percentage Error(MAPE)technique.Seven existing methods,such as the Gaussian cloud method,Discriminant method,Mutation series method,Artificial neural network(ANN),Support vector machine(SVM),Grey wolf optimizer and Support vector classification method(GWO-SVC)and Rock mass rating method(RMR)are used for comparison with the proposed GHDQR method.The share of the highly accurate category of 85.71%clearly indicates compliance with actual values obtained by the compared methods.The results of comparisons showed that the model enables objective,efficient,and reliable assessment of rock mass quality.

Assessing Criteria Weights by the Symmetry Point of Criterion (Novel SPC Method)–Application in the Efficiency Evaluation of the Mineral Deposit Multi-Criteria Partitioning Algorithm

Information about the relative importance of each criterion or theweights of criteria can have a significant influence on the ultimate rank of alternatives.Accordingly,assessing the weights of criteria is a very important task in solving multi-criteria decision-making problems.Three methods are commonly used for assessing the weights of criteria:objective,subjective,and integrated methods.In this study,an objective approach is proposed to assess the weights of criteria,called SPCmethod(Symmetry Point of Criterion).This point enriches the criterion so that it is balanced and easy to implement in the process of the evaluation of its influence on decision-making.The SPC methodology is systematically presented and supported by detailed calculations related to an artificial example.To validate the developed method,we used our numerical example and calculated the weights of criteria by CRITIC,Entropy,Standard Deviation and MEREC methods.Comparative analysis between these methods and the SPC method reveals that the developedmethod is a very reliable objective way to determine the weights of criteria.Additionally,in this study,we proposed the application of SPCmethod to evaluate the efficiency of themulti-criteria partitioning algorithm.The main idea of the evaluation is based on the following fact:the greater the uniformity of the weights of criteria,the higher the efficiency of the partitioning algorithm.The research demonstrates that the SPC method can be applied to solving different multi-criteria problems.