A well-regarded as well as powerful method named the ‘analytic hierarchy process’ (AHP) uses mathematics and psychology for making and analysing complex decisions. This article aims to present a brief review of the consistency measure of the judgments in AHP. Judgments should not be random or illogical. Several researchers have developed different consistency measures to identify the rationality of judgments. This article summarises the consistency measures which have been proposed so far in the literature. Moreover, this paper describes briefly the functional relationships established in the literature among the well-known consistency indices. At last, some thoughtful research directions that can be helpful in further research to develop and improve the performance of AHP are provided as well.

Brain tumor classification (BTC) from Magnetic Resonance Imaging (MRI) is a critical diagnosis task, which is highly important for treatment planning. In this study, we propose a hybrid deep learning (DL) model that integrates VGG16, an attention mechanism, and optimized hyperparameters to classify brain tumors into different categories as glioma, meningioma, pituitary tumor, and no tumor. The approach leverages state-of-the-art preprocessing techniques, transfer learning, and Gradient-weighted Class Activation Mapping (Grad-CAM) visualization on a dataset of 7023 MRI images to enhance both performance and interpretability. The proposed model achieves 99% test accuracy and impressive precision and recall figures and outperforms traditional approaches like Support Vector Machines (SVM) with Histogram of Oriented Gradients (HOG), Local Binary Pattern (LBP) and Principal Component Analysis (PCA) by a significant margin. Moreover, the model eliminates the need for manual labelling—a common challenge in this domain—by employing end-to-end learning, which allows the proposed model to derive meaningful features hence reducing human input. The integration of attention mechanisms further promote feature selection, in turn improving classification accuracy, while Grad-CAM visualizations show which regions of the image had the greatest impact on classification decisions, leading to increased transparency in clinical settings. Overall, the synergy of superior prediction, automatic feature extraction, and improved predictability confirms the model as an important application to neural networks approaches for brain tumor classification with valuable potential for enhancing medical imaging (MI) and clinical decision-making.

Purpose: The purpose of this paper is to evaluate various reliability measures like availability, reliability, mean time to failure and profit function. Design/methodology/approach: The authors present a novel method for availability analysis of an engineering system incorporating waiting time to repair. The considered system consists of two subsystems, namely, A and B connected in series. The subsystem B has two identical units in standby arrangement. Each unit of the subsystem has two modes, i.e. normal efficiency or failed. The two standby units of the subsystem B are connected by an imperfect switching. The system is analyzed by supplementary variable technique, Laplace transformation and Gumbel-Hougaard family of copula. Findings: Numerical examples with a way to highlight the important results have been appended at last. Numerical calculation shows that availability and reliability of the system is decreasing with respect to time when failure rates are fixed at different values. Finally, cost analysis of system reveals that the expected profit decreases with increase in service cost. Originality/value: This paper presents a mathematical model in which an important aspect of switching has been taken into consideration, which is consistent with actual failures of switching by assuming two different types of failure between adjacent transition. It is evaluated with the help of the Gumbel-Hougaard family of copula.