P-Indeterminate Vector Similarity Measures of Orthopair Neutrosophic Number Sets and Their Decision-MakingMethod with Indeterminate Degrees

In the complexity and indeterminacy of decision making(DM)environments,orthopair neutrosophic number set(ONNS)presented by Ye et al.can be described by the truth and falsity indeterminacy degrees.Then,ONNS demonstrates its advantages in the indeterminate information expression,aggregations,and DM problems with some indeterminate ranges.However,the existing research lacks some similarity measures between ONNSs.They are indispensable mathematical tools and play a crucial role in DM,pattern recognition,and clustering analysis.Thus,it is necessary to propose some similaritymeasures betweenONNSs to supplement the gap.To solve the issue,this study firstly proposes the p-indeterminate cosine measure,p-indeterminate Dice measure,p-indeterminate Jaccard measure of ONNSs(i.e.,the three parameterized indeterminate vector similarity measures of ONNSs)in vector space.Then,a DMmethod based on the parameterized indeterminate vector similarity measures of ONNSs is developed to solve indeterminate multiple attribute DM problems by choosing different indeterminate degrees of the parameter p,such as the small indeterminate degree(p=0)or the moderate indeterminate degree(p=0.5)or the big indeterminate degree(p=1).Lastly,an actual DM example on choosing a suitable logistics supplier is provided to demonstrate the flexibility and practicability of the developed DM approach in indeterminate DM problems.By comparison with existing relative DM methods,the superiority of this study is that the established DMapproach indicates its flexibility and suitability depending on decision makers’indeterminate degrees(decision risks)in ONNS setting.

Rock mass structural recognition from drill monitoring technology in underground mining using discontinuity index and machine learning techniques

A procedure to recognize individual discontinuities in rock mass from measurement while drilling(MWD)technology is developed,using the binary pattern of structural rock characteristics obtained from in-hole images for calibration.Data from two underground operations with different drilling technology and different rock mass characteristics are considered,which generalizes the application of the methodology to different sites and ensures the full operational integration of MWD data analysis.Two approaches are followed for site-specific structural model building:a discontinuity index(DI)built from variations in MWD parameters,and a machine learning(ML)classifier as function of the drilling parameters and their variability.The prediction ability of the models is quantitatively assessed as the rate of recognition of discontinuities observed in borehole logs.Differences between the parameters involved in the models for each site,and differences in their weights,highlight the site-dependence of the resulting models.The ML approach offers better performance than the classical DI,with recognition rates in the range 89%to 96%.However,the simpler DI still yields fairly accurate results,with recognition rates 70%to 90%.These results validate the adaptive MWD-based methodology as an engineering solution to predict rock structural condition in underground mining operations.