This study presents the Neutrosophic Transmuted Log-logistic Distribution (NTLLD), which is particularly designed to handle indeterminacy and transmuted data. Since neutrosophic theory successfully manages uncertainty, indeterminacy, and inconsistency in data, it solves the drawbacks of fuzzy set and classical theories. For modelling uncertainty, neutrosophic sets provide a complete framework by capturing truth, indeterminacy, and falsity all at once. Transmuting the log-logistic, another name for the distribution is the quadratic transmuted log-logistic distribution, which extends the log-logistic distribution and is a major advancement for managing intricate decision-making situations. A comprehensive neutrosophic description of the statistical properties of the NTLLD is presented. For estimating neutrosophic parameters, the maximum likelihood estimation approach, based on a neutrosophic environment, is employed. A Monte Carlo simulation study was used to examine the performance of these neutrosophic estimators in terms of their neutrosophic mean squared errors (NMSEs) and neutrosophic average biases (NAB) of the parameters. According to simulation studies, NAB and NMSE decline with increasing sample numbers, suggesting a robust and precise parameter estimate. Superior fit and performance are offered by NTLLD, which also offers important insights for applications in health sciences and reliability engineering. In particular, the produced distribution is useful for modelling uncertain data. The usefulness of the NTLLD for data modelling is illustrated using wastewater treatment data, and a few recently suggested neutrosophic distributions are also contrasted.
Virtualization in cloud computing enables multiple virtual servers to be deployed on a single physical infrastructure. The increasing number of cloud applications also increases resource overload during service execution. However, the main challenge with the migration of interoperable applications is the process of establishing optimal resource allocation, performance, quality of service, the tradeoff between cost-effectiveness and satisfying the requirements of service level agreement. Deep learning methods are useful for load balancing because they can identify noisy workload fluctuations. In this paper, Weight Adaptive Temporal CNN and Secretary Bird Optimization Algorithm (WATCSBOA)-based container architecture is proposed for predicting the workload, which optimizes the degree of resource utilization and reduces the overload during the process of executing the migrated interoperable applications. This container architecture uses Weight Adaptive Temporal CNN (WATCNN) to determine long-term sequence dependencies for deciding the actual workload thereby improving the accuracy and response speed of container clusters. It mainly helps enhance the capabilities of feature extraction when the deep learning model is employed to address long sequences. It uses the Secretary Bird Optimization Algorithm (SBOA), which helps in parameter optimization to maximize resource allocation and attain optimized migration of interoperable applications. It supports resource allocation and migration by evaluating a fitness function that considers demand, transmission cost, load prediction, and resource availability. The simulation results show that the proposed WATCSBOA scheme improves load prediction performance by reducing RMSE by 11.26%, MAE by 9.64%, and MAPE by 8.96%, while improving PCC by 12.36% compared with the baseline approaches. Under the moderate and high workload scenarios, WATCSBOA reduces migration time by 11.64% and 10.98%, respectively, and improves resource utilization by 12.39% and 11.64%, respectively.
This study introduces the concept of Complex Interval-Valued Fermatean Fuzzy Sets and presents a comprehensive investigation of their theoretical properties. The proposed framework extends the traditional Fermatean fuzzy set by incorporating complex-valued and interval-valued information, thereby enhancing its capability to represent uncertainty, ambiguity, and indeterminacy in complex decision-making environments. To strengthen the theoretical foundation, fundamental concepts and comparative measures are developed. In addition, essential set-theoretic operations such as union, intersection, complement, conjunction (“and”), and disjunction (“or”) are formally defined, along with illustrative examples and rigorous proofs of their properties. Furthermore, a Complex Interval-Valued Fermatean Fuzzy Weighted Averaging operator is proposed to aggregate decision information. The operator is shown to satisfy important properties, including idempotency, boundedness, and monotonicity, ensuring its reliability and consistency. To demonstrate the applicability and effectiveness of the proposed model, a multi-criteria decision-making problem is considered. The results illustrate that the proposed approach can effectively evaluate alternatives and determine their ranking under complex uncertain conditions, highlighting its potential for practical applications in decision-making problems.
The shortest path problem is a fundamental optimization problem with numerous applications in transportation, communication, and logistics networks. In many real-world situations, arc lengths are subject to uncertainty and may contain both positive and negative aspects reflecting satisfaction and dissatisfaction. Bipolar fuzzy sets provide an effective framework for modeling such dual uncertainty. In this paper, we investigate the n-sided bipolar fuzzy shortest path problem (NBFSPP) in which arc lengths is represented by n-sided bipolar fuzzy numbers. A decomposition-based framework is proposed to transform the NBFSPP into two satisfaction models corresponding to positive and negative membership components. These models are further converted into deterministic multi-objective shortest path problems. To obtain a single optimal solution, three solution strategies are employed: a bipolar fuzzy approach, the weighted-sum method, and an n-sided bipolar Euclidean distance technique. Two numerical examples involving triangular and trapezoidal bipolar fuzzy numbers are presented to demonstrate the applicability of the proposed framework. The obtained results are compared with existing ranking-based methods, showing that the proposed approaches can effectively determine optimal paths under bipolar fuzzy uncertainty. The proposed framework provides a flexible decision-making tool for shortest path problems in uncertain environments where both positive and negative preferences must be considered simultaneously.
Additive manufacturing through three-dimensional (3D) and four-dimensional (4D) printing has transformed modern production with improved design flexibility, efficiency, and material utilization. Despite these advantages, the selection and prioritization of process parameters remains a complex challenge. This study employs the Fuzzy Analytical Hierarchy Process (FAHP) to systematically evaluate expert survey data on parameters such as tool path setting, print speed, extrusion temperature, material choice, bed temperature, support removal, surface finishing, and time–cost considerations. Using pairwise comparison matrices converted into triangular fuzzy numbers (TFNs), the FAHP framework calculates fuzzy weights, applies de-fuzzification, and normalizes the results to derive parameter priorities. The findings reveal that Extrusion Temperature and Bed Temperature are critical for 4D printing, whereas Surface Finishing and Support Removal dominate in 3D printing. This highlights the shift in the significance of the parameters between the two technologies. Additionally, the FAHP-based desirability index supports the justification of 4D printing applications, particularly in mechatronics and the Internet of Things, offering valuable optimization insights for researchers and industry. The novelty of the study lies in establishing an FAHP-based decision framework that prioritizes eight printing and post-processing criteria and compares 3D and 4D printing at the technology level for IoT and mechatronic applications under uncertain expert judgments.
