This paper focuses on the methods for determining how uncertainties affect people in everyday life. Sincealmost nothing is deterministic, anything might become impractical in real life. We will encounter many difficulties ifwe lack anticipatory ideas. The business organizations are facing uncertainties in demand, supply, cost of raw materials,prices of finished products etc. in everyday life. To address these uncertainties, this study will analyse stochastic LinearProgramming Problems (SLPs) aiming to bridge the gap between theoretical concepts and practical applications. Thispaper specifically explores the effects of assuming stochastic pricing and demand in the Uncapacitated Facility LocationProblem (UCFLP), shedding light on the variations in profit. We will develop a stochastic UFLP for a company ofBangladesh known as Unilever Company of Bangladesh and it may use for any company in the world. For this, we willcollect and analyse the data from the company in stochastic atmosphere. The model will help the company to be able toaware of how uncertainties of demand, supply and other factors can affect the profit and loss of the company. Thisapproach underscores the importance of considering various factors, including demand patterns, cost-effectiveness, andregional dynamics. In the model, we will consider the data from five different regions of Bangladesh
Curve similarity plays a crucial role in various domains where comparing functional or dynamic shapes isessential, including bioassay analysis, trajectory studies, spectroscopy, medical signal interpretation, and functionalgenomics. Despite its broad impact, research on curve similarity methods remains fragmented across statistical,computational geometry, and signal processing communities, leading to a lack of unified terminology and systematiccomparison. To address this gap, this study adopts a structured literature review methodology, in which relevant studies areidentified through a comprehensive search of major academic databases and selected based on predefined inclusion criteria,including peer-reviewed publications focusing on similarity measures for curves and time series. The review systematicallyexamines mathematical and statistical approaches to curve similarity, focusing on their theoretical foundations, statisticalproperties, and practical applications. The selected methods are categorized into five groups: distance-based, alignmentbased, topology-oriented, statistical and hypothesis testing, and learning-based approaches. For each category, key aspectssuch as mathematical formulation, invariance properties, robustness to sampling variability, and computationalcharacteristics are analyzed. In addition, application domains, method comparisons, and common limitations are discussed,along with available software tools that support curve similarity analysis. By providing a structured and methodologicallygrounded synthesis, this review assists researchers in selecting appropriate techniques and highlights potential directions fordeveloping more robust and scalable similarity assessment frameworks.
This study presents a C*-algebraic framework for optimizing intrusion mitigation in Internet of Things (IoT)networks by integrating mathematical models for cyberattack propagation with optimization-based security strategies.Theoretical results demonstrate that the spectral radius of the attack operator ρ(A) governs the recovery of IoTnetworks under attack, where ρ(A) < 1 ensures system recovery, and ρ(A) ≥ 1 leads to persistent or growing attackimpact. The framework combines blockchain-based trust, AI-driven intrusion detection systems (IDS), and Zero-TrustArchitecture (ZTA) to provide a multi-layered, adaptive defence system. Unlike probabilistic models that simplifyattack dynamics, this approach rigorously models threats using bounded linear operators, thereby offering scalabilityand robustness. Optimization ensures computational efficiency, making the model suitable for resource-constrained IoTenvironments, with the operator norm and the spectral radius acting as key constraints. Validation on real-worlddatasets such as CIC-IoT2023, UNSW-NB15, and BoT-IoT revealed that the AI-IDS models achieved near-perfectperformance, while the unified model integrating blockchain, IDS, and ZTA showed an accuracy of 51.0
Reliability of a software system is an important attribute of software quality, and its importance has increased significantly due to the growing demand for high-quality software systems. Evaluating reliability during the design phase is essential for improving system performance and ensuring effective planning. At this stage, an important challenge is to identify suitable methods for achieving the desired reliability of the software system. Reliability allocation methods can be applied to assign reliability targets to individual components prior to the actual system design. To address this, a new hierarchical model is proposed that integrates the perspectives of users, software programmers, and software managers. The system is decomposed into multiple levels, including functions, programs, modules, and submodules, to enable systematic analysis. To handle uncertainty and vagueness in human judgments, the fuzzy analytic hierarchy process (FAHP) is employed, incorporating the geometric mean method with trapezoidal fuzzy numbers. The proposed approach determines reliable weights and effectively allocates reliability targets at each level. A comparison with the classical AHP method demonstrates that FAHP provides a more flexible and realistic representation by capturing uncertainty, making it more suitable for reliability allocation in complex software systems.
Artificial-intelligence workloads increasingly process proprietary and personally identifiable data, yetconventional security controls protect data only at rest and in transit, leaving computation itself exposed. This paperpresents CC-Shield, a five-layer confidential-computing architecture that combines hardware trusted executionenvironments (Intel SGX, AMD SEV-SNP), differentially private federated aggregation, remote attestation, encryptedmodel lifecycle management, and LSTM-based anomaly detection into a single, formally analysed defence-in-depthstack. We derive a closed-form leakage bound that jointly composes TEE side-channel capacity and differential-privacynoise, prove three attack-resistance theorems covering membership inference, model inversion, and active-adversaryintegrity, and connect security overhead to system throughput via a queuing-theoretic performance model. On ResNet50/ImageNet, BERT-base/SST-2, and a clinical MLP on MIMIC-III, CC-Shield with differential privacy ( )reduces membership-inference attack success to 51.8% (statistically indistinguishable from the 50% random-chancebaseline at a 95% confidence half-width of approximately 1.0 percentage point over 10,000 attack queries), versus 71.3%for an unprotected baseline, while introducing only 11.9%-13.9% inference latency overhead – more than three ordersof magnitude lower than a homomorphic-encryption baseline. A seven-dimension qualitative comparison against fiveprior frameworks shows CC-Shield is the only approach satisfying data-in-use protection, computation integrity,training- and inference-time protection, quantum resistance, sub-15% latency overhead, and a formal security proofsimultaneously.
