In this work, we introduce a Flexible Job-shop Scheduling Problem with Resource Recovery Constraints (FRRC). In the FRRC, besides the constraints of the classical Flexible Job-shop Scheduling Problem (FJSP), operations may require resources to be processed. The resources are available in batches and a recovery time is required between each batch. This problem is inspired by a real situation faced by a brewing company where different yeasts are available in a limited quantity and are recovered only once they have been completely used. The objective is to schedule the operations such that the makespan is minimised. A mathematical model and a metaheuristic based on a General Variable Neighborhood Search is proposed for the solution of the FRRC. Computational results over a large set of instances, adapted from the FJSP literature, are presented.

This research introduces innovative rough approximation techniques for multidimensional fuzzy sets by integrating rough sets and multidimensional fuzzy sets. Departing from traditional methods that rely on predefined equivalence relations to delineate rough spaces, we propose a novel approach utilizing a function termed the ‘convenient function’. The values generated by this function facilitate the establishment of lower and upper estimations, enhancing the precision of rough approximations. The adept utilization of the parameter α, in conjunction with a multidimensional distance measure, allows for the attainment of desirable approximations within specified bandwidths. Additionally, we explore a more generalized version of α approximation, known as α-β approximation, along with its associated properties, thereby expanding the applicability and flexibility of the proposed methodology. Finally, we present a comprehensive case study demonstrating the efficacy of the α approximation methodology in real-world decision-making processes, highlighting its practical utility and effectiveness.

Additive Manufacturing (AM) has emerged as a transformative technology for rapid prototyping and fabrication of geometrically complex structures. However, the inherent thermal cycling and rapid solidification in processes such as Selective Laser Sintering (SLS) frequently induce deformation and residual stresses, leading to dimensional deviations and potential premature failure. This paper presents OpenAM-SimCCX, an open-source workflow for finite element-based thermo-mechanical simulation of AM processes using CalculiX 2.21. The framework employs a time-dependent thermo-mechanical model with layer-by-layer element activation to capture key aspects of SLS, including laser–material interaction and scanning strategy effects. Systematic comparisons of different scanning strategies demonstrate clear correlations between path planning, residual stress distributions, and distortion, while computational time analyses confirm the framework’s efficiency. By providing comprehensive documentation, implementation guides, and open repositories, OpenAM-SimCCX offers an accessible and economically viable alternative to commercial software, particularly for academic institutions and small- to medium-sized enterprises. This framework advances open-source simulation tools for AM and promotes broader adoption in both research and industry.

This article examines distance and similarity measures in multidimensional fuzzy sets, which are essential in decision-making and aggregation across various fields. It defines the axioms for multidimensional distance measures and introduces a framework for normalized distance and similarity measures within a suitable fuzzy space. The concept of complement-invariant proximity measures is also discussed. The paper further explores the relationship between distance and similarity, linking them with multidimensional entropy. It presents \(\sigma\)-distance, \(\sigma\)-similarity, and \(\sigma\)-entropy measures that balance values between fuzzy sets and their complements. Finally, two decision-making problems are analyzed, with a comparative study showing the proposed model’s advantage over existing approaches.

Deep learning techniques are transforming stock market forecasting by significantly improving the accuracy of predicting price movements and market patterns. In this research work, we propose two novel hybrid architectures – MSLSTM (Multivariate Sequential Long Short-Term Memory) and MSLSTMA (Multivariate Sequential Long Short-Term Memory Autoencoder). Both models leverage the Long Short-Term Memory (LSTM) ability to capture complex temporal dependencies in sequential financial data. Our method performs well in a variety of industries and surpasses a few other LSTMs and their autoencoder-augmented variations, as well as conventional deep learning models like CNNLSTM. MSLSTMA achieves the highest sector-wise winning rates, notably 95.83% in the telecommunication sector, 87.5% in technology, and 83.33% in industrials. Model performance was rigorously evaluated using mean squared error, root mean squared error, mean absolute error, and mean absolute percentage error. Across all these metrics, MSLSTMA consistently delivered the lowest error rates, showcasing its superior accuracy and practical relevance for real-world financial forecasting. MSLSTM also demonstrated strong performance, with winning rates of 50% in consumer staples and 45.83% in the healthcare sector. This research introduces an effective and scalable tool for investors, with the potential to enhance investment decisions through precise stock price prediction. Received: 18 March 2025 | Revised: 17 June 2025 | Accepted: 11 July 2025 Conflicts of Interest The authors declare that they have no conflicts of interest to this work. Data Availability Statement Data sharing is not applicable to this article as no new data were created or analyzed in this study. Author Contribution Statement Sheba Elizabeth Thomas: Methodology, Validation, Investigation, Data curation, Writing – review & editing, Visualization, Supervision. Rubell Marion Lincy George: Conceptualization, Validation, Resources, Writing – original draft, Project administration. Nevin Selby: Conceptualization, Software, Formal analysis, Writing – original draft, Project administration. Aditya Taparia: Software, Formal analysis, Supervision. Jobish Vallikavungal: Methodology, Validation, Investigation, Resources, Data curation, Writing – review & editing, Visualization, Supervision.