Based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. Further, we discuss some of their properties and give three numerical examples to illustrate our proposed method reasonable.

Rock abrasivity, as one of the most important parameters affecting the rock drillability, significantly influences the drilling rate in mines. Therefore, rock abrasivity should be carefully evaluated prior to selecting and employing drilling machines. Since the tests for a rock abrasivity assessment require sophisticated laboratory equipment, empirical models can be used to predict rock abrasivity. Several indices based on five known methods have been introduced for assessing rock abrasivity including rock abrasivity index (RAI), Cerchar abrasivity index (CAI), Schimazek’ s abrasivity factor (Fabrasivity), bit wear index (BWI), and LCPC abrasivity coefficient (LAC). In this work, 12 rock types with different origins were investigated using the uniaxial compressive strength (UCS), Brazilian test for tensile strength, and longitudinal wave velocity and LCPC tests, and microscopic observations were made to obtain a correlation for estimating the LCPC abrasivity coefficient by conducting the conventional rock mechanics tests. Using the equivalent quartz content, velocity of longitudinal waves, and rock brittleness index, a linear correlation was obtained with a coefficient of determination (R2) of 93. 3% using SPSS in order to estimate LAC.

Background & Aim: A single outlier can even have a large disturbing effect on a classical statistical method that is optimal under the classical assumptions. One of the powerful goodness-of-fit tests is the correlation coefficient test, however this test suffers from the presence of outliers.Methods & Materials: This study provides a simple robust method for test of goodness of fit for the Gumbel distribution [extreme value distribution (EVD) type I family] through using the new diagnostic tool called the "Forward Search" (FS) method. The FS version of this test was introduce in the present study, which is not affected by the outliers.Results: A new robust method for testing the goodness-of-fit for Gumbel distribution has been presented. The approach gives information about the distribution of majority of the data and the percentage of contamination.Conclusion: A new robust method for testing the goodness-of-fit for the Gumbel distribution has been presented. The simple and fast method have been used to find distribution of proposed statistic. In addition, using the transformation study, an application to the two-parameter Weibull distribution has been investigated. The performance and the ability of this procedure to capture the structure of data have been illustrated by some simulation studies.