New discriminant-function-based multidimensional discrimination of mid-ocean ridge and oceanic plateau

From a compilation of geochemical data for the discrimination of the tectonic settings of mid-ocean ridge(MOR;3730 samples)and oceanic plateau(OP;3656 samples),we present two new discriminant functions and diagrams obtained from censored multivariate discordant outlier-free datasets.Ten different sets of data(original concentrations as well as isometric log-ratio transformed(ilr)variables;all 10 major(M)elements as well as all 10 major and 6 trace elements MT)were used to evaluate the quality of discrimination from linear discriminant analysis(LDA)and canonical analysis.Two selected multidimensional models ilrM(9 ilr transformed variables of multi-normally distributed 10 major elements)and ilrMT(15 ilr transformed variables of multi-normally distributed combined 10 major and 6 trace elements),considered as the best or most representative(total of5650 samples for ilrM and 2858 for ilrMT),provided percent success values,respectively,of 80.9%for the MOR and 81.1%for the OP(ilrM)and 88.5%for the MOR and 90.1%for the OP(ilrMT).Both processes(log-ratio transformation and multi-normality)rendered the percent success values similar for both groups(MOR and OP).The respective discriminant functions were successfully used for four tests from known tectonic settings and four application cases(two for ophiolites and two for Precambrian rocks),documenting thus the utility of the new discrimination procedure for the MOR and OP tectonic settings.Furthermore,we showed that our multidimensional procedure is robust against analytical errors or uncertainties,as well as post-emplacement compositional changes caused by element mobility from both low or high temperature alteration.The robustness against the gain or loss of a single element at a time was also documented,from which the ilrMT model was evaluated as more robust than the ilrM model.A new online computer program MOROPdisc was written in Java Framework ZK,which is freely available for use at our web portal http://tlaloc.ier.unam.mx.

Research on consistency measurement and weight estimation approach of hybrid uncertain comparison matrix

The consistency measurement and weight estimation approach of the hybrid uncertain comparison matrix in the analytic hierarchy process （AHP） are studied. First, the decision-making satisfaction membership function is defined based on the decision making＇s allowable error. Then, the weight model based on the maximal satisfactory consistency idea is suggested, and the consistency index is put forward. Moreover, the weight distributing value model is developed to solve the decision making misleading problem since the multioptimization solutions in the former model. Finally, the weights are ranked based on the possibility degree approach to obtain the ultimate order.