Rashmi Singh

The analysis of complex networks under uncertainty represents a fundamental challenge in modern graph theory and network science. This paper introduces a compre...

This paper presents a comprehensive of the algebraic and lattice structure of fuzzy groups in fuzzy approximation spaces. The structure of ℱ(𝒫, 𝒬), the collecti...

This paper is an analytic enquiry of the integration of the nearset theory with a study of chaotic systems in order to determine patterns upon which to adhere t...

Cow dung cakes remain an important renewable energy source in many rural regions of South Asia; however, traditional designs often suffer from poor drying efficiency, inconsistent combustion, and handling limitations. The objective of this study is to identify and optimize cow dung cake geometries using the Fuzzy Technique for Order Preference by Similarity to Ideal Solution. Ten conventional and novel geometric designs were evaluated with respect to four criteria: drying efficiency, burning performance, storage and handling, and versatility. The analysis ranked the Honeycomb Hexagonal Prism as the most effective design—which achieved the highest closeness coefficient (1.0000)—owing to its enhanced airflow, rapid drying, efficient combustion, and compact storage characteristics. Sensitivity analysis demonstrated ranking stability under ±20% variations in criterion weights, while statistical validation confirmed the robustness of the results. Economic and environmental assessments indicated improved energy output, higher return on investment, reduced carbon monoxide emissions, lower particulate matter generation, and decreased ash content compared with conventional flat patties. The findings suggest that geometric optimization can substantially enhance the performance and sustainability of cow dung-based fuels, offering a promising pathway for cleaner and more efficient rural energy systems.

Soft sets and their extensions emerge as a powerful tool for handling uncertainty in decision making applications dealing with only one expert. Decision-making involving opinions of more than one expert can be effectively modeled by soft expert sets (SES) and fuzzy soft expert set (FSES). Building upon these concepts this article presents the concept and operations of Inverse Fuzzy Soft Expert Set (inverse FSES) by developing an enhanced algorithmic approach. The Inverse FSES combines the principles of inverse fuzzy sets and SES to model complex decision-making scenarios involving multiple experts. Inverse FSES provides a mechanism to quantify, aggregate and interpret expert judgement with precision. The proposed algorithm is validated using sustainable supplier case study. Sensitivity analysis by changing weights of parameters and by adding credibility weights to experts is also conducted. This article combines the mathematical concept with practical applicability thereby opening a new avenue in decision-making. JEL Codes: D81. Received: 20/04/2025. Accepted: 03/02/2026. Published: 06/08/2026.

The present article discusses the extension of classical proximity theory to multi valued systems. Existing distance measures for hesitant fuzzy sets operate primarily at the computational level without establishing the rigorous mathematical foundations. This paper develops a comprehensive axiomatic framework for proximity spaces on hesitant fuzzy sets. First, five fundamental axioms (HFP0–HFP5) for hesitant fuzzy proximity relations are introduced, generalizing classical proximity theory to fit multi-valued membership structures. Second, it is proven that hesitant fuzzy proximity spaces induce completely regular topologies, and the Smirnov compactification theorem is established for these spaces. Third, a bijective correspondence between hesitant fuzzy proximities and totally bounded uniformities is demonstrated, along with a metrization theorem characterizing when compatible metrics exist. Fourth, a new concept of variable length proximity measure is proposed that naturally handles hesitant fuzzy elements of different cardinalities without requiring artificial data extension or reduction. Finally, the practical applicability of the framework is validated through a facial recognition case study, where the proposed discrete hesitant fuzzy proximity successfully identifies images of the same individual under varying lighting and rotation conditions while correctly discriminating different subjects. This work bridges classical proximity theory and modern uncertainty modeling, giving both theoretical foundations and applicability for decision-making under hesitancy.

We introduce a hybrid framework that combines Topological Data Analysis (TDA) and deep learning architectures to detect and classify chaotic attractors in high-dimensional dynamical systems with real-time capability. Our approach exploits persistent homology to extract robust topological features, which are then processed by convolutional neural networks (CNNs) for pattern recognition. Our algorithm is both more accurate and more computationally efficient than state of the art tools such as traditional Lyapunov exponent analysis, phase space reconstruction methods and more recent deep learning tools Experimental results show that our algorithm is 95.8\% more accurate and 50ms faster to run on 1000-dimensional input data (95\% CI: [94.6\% 97.0\%]) than compared to state of the art methods, including the traditional Lyapunov exponent analysis and phase space reconstruction methods and more recent deep learning methods. The model is extremely resistant to noise, and its accuracy with signal-to-noise ratios as low as 15dB is 92.3\% with 1.5\% standard deviation. Extensive ablation experiments show that the hybrid method is better than the single TDA (82.4\% accuracy) and deep learning (78.9\% accuracy) modules, which proves the synergy advantage. Performance analysis O(n log n) computational complexity and linear scaling properties The performance analysis has a 3.2x speedup over traditional algorithms and has a 45 percent memory reduction. The study is an improvement on nonlinear dynamics as it offers an efficient, scalable, and robust algorithm to identify chaotic system dynamics in real-time and can be applied in climate modeling, financial markets, and neurological signal processing.