i. ahmad

In this study, we explore the theoretical features of a multiobjective interval-valued programming problem with vanishing constraints. In view of this, we have defined a multiobjective interval-valued programming prob-lem with vanishing constraints in which the objective functions are consid-ered to be interval-valued functions, and we define an LU-efficient solution by employing partial ordering relations. Under the assumption of general-ized convexity, we investigate the optimality conditions for a (weakly) LU-efficient solution to a multiobjective interval-valued programming problem with vanishing constraints. Furthermore, we establish Wolfe and Mond–Weir duality results under appropriate convexity hypotheses. The study concludes with examples designed to validate our findings.

In the presence of outliers in the data set, the utilization of robust regression tools for mean estimationis a widely established practice in survey sampling with single auxiliary variable. Abid et al. (2018),with the aid of some non-conventional location measures and traditional OLS, proposed a class of meanestimators using information on two supplementary variates under a simple random sampling framework. The utilization of non-traditional measures of location, especially in the presence of outliers,performed better than existing conventional estimators. In this study, we have proposed a new class ofestimators of mean utilizing quantile regression. The general forms of MSE and MMSE are also derived.The theoretical findings are being reinforced by different real-life data sets and simulation study.

The presence of extreme events gives rise to outrageous results regarding population parametersand their estimates using traditional moments. Traditional moments are usually influenced by extremeobservations. In this paper, we propose some new calibration estimators under L-Moments scheme for variance which is one of the most important population parameters. Some suitable calibration constraints under double stratified random sampling are also defined for these estimators. Our proposed estimators based on L-Moments are relatively more robust in presence of extreme values. The empirical efficiency of proposed estimators is also calculated through simulation. Covid-19 pandemic data from January 22, 2020, to August 23, 2020, is considered for simulation study.

The design of a stable slope in a rock mass environment is a quite complicated job due to the anisotropic behaviour of the rock mass. In this research work, the cut slopes at the Swat motorway in the weakest schist rock is numerically analyzed by the shear strength reduction (SSR) approach using the Finite Element-based 2D RS2 software. The slope is divided into two cases according to the nature of the rock. Each case of the cut slope is analyzed by two stabilization methods 1) changing the characteristics of the slope 2) support system installation based on the Mohr-Coulomb (MCC) and Generalized Hoek and Brown (GHB) failure criteria in order to propose the most appropriate method for slope stabilization. The results obtained reveal that the Critical Strength Reduction Factor (CSRF) before applying the stabilization methods is 1.34 (MCC) and 1.04 (GHB) for Case-I and 1.21 (MCC) and 0.53 (GHB) for Case-II. CSRF for Case-I after changing the characteristics of the slope is observed to be 2.43 (MCC) and 2.33 (GHB), while for Case-II is 1.82 (MCC) and 1.26 (GHB), respectively. CSRF for Case-I after the support installation criteria is 1.59 (MCC) and 1.07 (GHB), while for Case-II is 1.65 (MCC) and 0.5 (GHB), respectively. Based on the comparative analysis, it is revealed that changing the characteristics of the slope method shows prominent results in both cases; therefore, this method can be effectively used in order to stabilize the slope in the weakest rock mass environment.