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math.PR updates on arXiv.org

Visibility in the Boolean Model on Harmonic Manifolds Global estimates on the Brenier map Geodesics and Wandering Exponents in Brochette First-Passage Percolation State-dependent inverse-subordinator time changes of regenerative processes: Excursion structure and multiscale occupation-time limits Randomly twisted transfer operators and singular values statistics Generalized Bessel-Dunkl diffusions An almost sure invariance principle for the Takagi-van der Waerden class functions Central limit theorems for high dimensional lattice polytopes: cosmological polytopes Convergence rate estimates for semigroups and heat kernels associated with resistance forms Second-order Poincaré inequalities and localization on the Poisson space Maximum Probability of Independence in Transitive Matroids On global solutions to the semidiscrete stochastic heat equation The Poisson Tail Conjecture for primes in short intervals A Complete Spectral Analysis of the CEV Operator with Applications to Arbitrage Holographic functions and neural networks From Betting to Empirical Bernstein LIL Concentration of General Stochastic Approximation Under Heavy-Tailed Markovian Noise Pointwise Generalization in Deep Neural Networks Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors Wasserstein bounds for denoising diffusion probabilistic models via the Föllmer process A note on connections between the Föllmer process and the denoising diffusion probabilistic model Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations A Fourier perspective on the learning dynamics of neural networks: from sample complexities to mechanistic insights Propagation of Chaos in Contextual Flow Maps Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures $α$-TCAV: A Unified Framework for Testing with Concept Activation Vectors Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model On the Limits of Latent Reuse in Diffusion Models State-of-art minibatches via novel DPP kernels: discretization, wavelets, and rough objectives
Interval-Valued Fuzzy Fault Tree Analysis through Qualita...
Hitesh Khungla, Kulbir Singh, Mohit Kumar · 2024-11-22 · via math.PR updates on arXiv.org

Marine accidents highlight the crucial need for human safety. They result in loss of life, environmental harm, and significant economic costs, emphasizing the importance of being proactive and taking precautionary steps. This study aims to identify the root causes of accidents, to develop effective strategies for preventing them. Due to the lack of accurate quantitative data or reliable probability information, we employ qualitative approaches to assess the reliability of complex systems. We collect expert judgments regarding the failure likelihood of each basic event and aggregate those opinions using the Similarity-based Aggregation Method (SAM) to form a collective assessment. In SAM, we convert expert opinions into failure probability using interval-valued triangular fuzzy numbers. Since each expert possesses different knowledge and various levels of experience, we need to assign weights to their opinions to reflect their relative expertise. We employ the Best-Worst Method (BWM) to calculate the weights of each criterion, and then use the weighting scores to determine the weights of each expert. Ranking of basic events according to their criticality is a crucial step, and in this study, we use the FVI measure to prioritize and rank these events according to their criticality level. To demonstrate the effectiveness and validity of our proposed methodology, we apply our method to two case studies: (1) chemical cargo contamination, and (2) the loss of ship steering ability. These case studies serve as examples to illustrate the practicality and utility of our approach in evaluating criticality and assessing risk in complex systems.