Neighborhood HyperRough Set and Neighborhood SuperHyperRough Set

Takaaki Fujita

doi:https://doi.org/10.54216/PMTCS.050104

Galoitica: Journal of Mathematical Structures and Applications | 2025

The Characterization of 4-Cyclic Refined Vector Spaces

This paper is dedicated to study 4-cyclic refined vector spaces, where we classify these spaces by using semi-module isomorphisms as direct product of classical complex vector spaces. In addition, we study the inner products defined over these structures and we present sufficient conditions for 4-cyclic refined orthogonality.

groups

Mohammad Abobala mail -

Hasan Sankari mail

link https://doi.org/10.54216/GJMSA.0120101

Volume & Issue

Vol. Volume 12 / Iss. Issue 1

Details open_in_new

Galoitica: Journal of Mathematical Structures and Applications | 2025

Turiyam Set Based Four Way Mathematical Characterization of Retracted Paper

Recent time retraction analysis is considered as one of the major issues. The retraction is a regular process where some time it is true, some time happen due to conflict, some time due to indescribable parameters or last via self retraction by authors or Editor. It is happening due to pressure on academia and its quality measurement by quantitative publications and citation rather than qualitative. It forces researchers to add the co-authors for increment, promotion, or citation rather than focusing on true research. Some time the retraction happens due to self correction, genuine mistake or conflict of interest with editor. These types of genuine or self retraction happended using Turiyam awareness of authors or editor which can be considered as positive retraction. It is also noted that negative results are also part of the research as equal to positive or noble research. It is difficult to characterize these types of retraction. In this paper author has introduced a mathematical model for precise analysis of retracted paper and its characterization in true (t), false(f), indeterminant (i) and liberal (l) region for intellectual measurement. Same time the extension of work for undefined or unknown paramerters of retraction or unretraction is also discussed using the complement of Turiyam operator with an example.

groups

Prem Kumar Singh mail

link https://doi.org/10.54216/GJMSA.0120102

Volume & Issue

Vol. Volume 12 / Iss. Issue 1

Details open_in_new

Journal of Artificial Intelligence and Metaheuristics | 2026

An Enhanced LSTM Framework for Solar Radiation Forecasting Using Hybrid Grey Wolf–Waterwheel Plant Optimization

Accurate solar radiation prediction is critical for optimizing renewable energy utilization, yet traditional machinelearning models struggle with suboptimal forecasting accuracy. To address this challenge, we propose a novel hybrid optimization algorithm, the Grey Wolf and Water Whale Plant Optimizer (GWWWPA), to enhance Long Short-Term Memory (LSTM) networks for improved solar radiation forecasting. The proposed method leverages the exploration-exploitation synergy of the Grey Wolf Optimizer (GWO) and Water Whale Plant Algorithm (WWPA) to optimize LSTM hyperparameters effectively. Experimental results on the NASA Space Apps Moscow dataset demonstrate that GWWWPA-LSTM outperforms existing optimization techniques, achieving the lowest Mean Squared Error (MSE) of 0.00019392 and the highest R2 score of 0.917262, surpassing standalone GWO, WWPA, PSO, and WOA. These findings highlight the potential of hybrid metaheuristic approaches in enhancing predictive accuracy, facilitating more reliable solar energy forecasting, and supporting sustainable energy management systems.

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Alaa Mohamed Abdel-Moati mail -

Abdullah Muhammad Ibrahim mail

link https://doi.org/10.54216/JAIM.110106

Volume & Issue

Vol. Volume 11 / Iss. Issue 1

Details open_in_new

Journal of Artificial Intelligence and Metaheuristics | 2026

An Intelligent DGGO-Based Machine Learning Framework for Predicting Student Adaptability in Online Education

The recent shift to online education worldwide has highlighted the urgent need to evaluate and improve students’ flexibility in the online learning environment. The paper solves that problem by creating a predictive framework that enables measuring students’ adaptability using modern techniques for advanced perception of adaptability and advanced machine learning (ML) and metaheuristic optimization methods. The research proposes an improved variant of geese’s cooperative flight behavior, called the Dynamic Greylag Goose Optimization (DGGO) algorithm, to optimize the hyperparameters of a base model, a Decision Tree (DT). A comparison of the baseline DT showed an accuracy of 93.81% and a sensitivity (True Positive Rate, TPR) of 93.14%. The DGGO optimization further improved the DT model’s performance to 97.15% accuracy and 96.86% sensitivity, with improved convergence and tuning. To be flexible to changes, the optimized model reduces classification errors and improves predictive consistency. The findings demonstrate the effectiveness of metaheuristic-based optimization for educational data mining and provide preliminary evidence that DGGO can serve as a robust, scalable, and intelligent framework to enhance predictive analytics and decision-support capabilities in the modern e-learning environment.

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Osama Alabedallat mail

link https://doi.org/10.54216/JAIM.110107

Volume & Issue

Vol. Volume 11 / Iss. Issue 1

Details open_in_new

Journal of Artificial Intelligence and Metaheuristics | 2026

An Intelligent Learning Analytics Framework for Predicting AI Proficiency Using BER-SC-Optimized MLP

The fast adoption of artificial intelligence (AI) and machine learning (ML) in the sphere of higher education has become a catalyst that requires more precise and data-driven models that could assess the level of proficiency and interest in new technologies in students. This work is driven by the fact that there are currently no personalized and analytically rigorous frameworks for assessing the level of AI literacy among college students and proposes an optimized learning analytics model that hyperparameters a Multilayer Perceptron (MLP) by utilizing the Binary Al-Biruni Earth Radius with Sine Cosine Algorithm (BER-SC) metaheuristic algorithm to close the performance gap between human and artificial intelligence. The suggested BER-SC + MLP hybrid was created and evaluated using a sample consisting of 258 student responses from Grand Canyon University, which encompassed AI knowledge and usage behavior as well as career interest. The model achieved an accuracy of 0.9312 after optimization, compared to the MLP’s pre-optimization accuracy (0.8996), and a significant decrease in Mean Squared Error (MSE = 0.0002808). The results demonstrate that BER-SC is far superior to nontraditional optimization techniques in terms of convergence efficiency and prediction accuracy. The contribution of the study is that it created a scalable and interpretable, and high-performing educational data modeling framework that has the potential to support adaptive educational learning analytics and institutional decision-making. The results suggest that intelligent optimization added to the ML-based assessment systems has a high possibility of enhancing the quality, efficiency, and feasibility of AI-based education and allowing more adaptable, more affordable, and more individually focused learning settings.

groups

Hessa Al-Junaid mail

link https://doi.org/10.54216/JAIM.110108

Volume & Issue

Vol. Volume 11 / Iss. Issue 1

Details open_in_new

Journal of Artificial Intelligence and Metaheuristics | 2026

Global Crop Yields Forecasting Using Informer Architecture Optimized with Football-Inspired Metaheuristic

Accurate forecasting of agricultural production is essential for managing food supply chains, guiding policy decisions, and building resilience against climate variability. However, modeling long-range, country-level crop production remains challenging due to temporal complexity, nonlinear dependencies, and the need for highly generalizable prediction systems. This study addresses these challenges by developing a hybrid forecasting framework that combines deep learning architectures with metaheuristic hyperparameter optimization. A global dataset spanning tomato and potato production from 1961 to 2021 was used to evaluate multiple forecasting models, including Informer, N-BEATS, LogTrans, N-HITS, EALSTM, TST, and LSTM. The Informer model achieved the best baseline performance (RMSE = 0.0799; NSE = 0.9070) and was selected for optimization. A comparative analysis was conducted using several metaheuristic algorithms, with particular focus on the Football Optimization Algorithm (FbOA), a novel strategy inspired by cooperative team dynamics. FbOA delivered the highest gains across all evaluated metrics, reducing RMSE to 0.00109, MSE to 1.19×10−6, and increasing NSE to 0.9260, R2 to 0.9600, and the correlation coefficient r to 0.9550. These results confirmed that metaheuristic tuning substantially enhances the forecasting capability of deep models, particularly when guided by domain-inspired search logic. The proposed framework demonstrates strong potential for integration into real-time, AI-driven agricultural decision support systems, offering scalable solutions for food security planning, climate-smart agriculture, and long-term sustainability forecasting.

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Toufik Mzili mail

link https://doi.org/10.54216/JAIM.110207

Volume & Issue

Vol. Volume 11 / Iss. Issue 2

Details open_in_new

Journal of Neutrosophic and Fuzzy Systems | 2025

HyperFuzzy Graph and HyperFuzzy HyperGraph

Fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, plithogenic sets, and other uncertainty handling frameworks are the subject of intensive daily research. Analogous investigations have been pursued in the contexts of graphs, hypergraphs, and superhypergraphs. In this paper, we introduce new definitions of the hyperfuzzy hypergraph and superhyperfuzzy hypergraph, which extend the notion of the fuzzy hypergraph. We also revisit and refine the concepts of the hyperfuzzy graph and the superhyperfuzzy graph.

groups

Takaaki Fujita mail -

Prem Kumar Singh mail

link https://doi.org/10.54216/JNFS.100101

Volume & Issue

Vol. Volume 10 / Iss. Issue 1

Details open_in_new

Galoitica: Journal of Mathematical Structures and Applications | 2025

A Short Contribution to the Classification of the Group of Units of the Rings (NCR)_(Z_pq ), (NCR)_(Z_(2^n ) ) and NCRZ_(p^2 )

In this paper, we study the group of units problem of three different non-commutative logical extensions rings, where we classify the group of units of the rings (NCR)_(Z_pq ), (NCR)_(Z_(2^n ) )and (NCR)_(Z_(p^2 ) )as semi direct products of well-known abelian groups as the following: U(N⊂R)_(Z_pq )&cong;(Z_(p-1)×Z_(q-1) )&prop;[(Z_p×Z_q )&prop;(Z_(p-1)×Z_(q-1)), U(NCR)_(Z_(2^n ) )&cong;(Z_2×Z_(2^(n-2)))&prop;(Z_(2^n )&prop;(Z_2×Z_(2^(n-2)))),   U(N⊂R)_(Z_(p^2 ) )&cong;Z_(p^2-p)&prop;(Z_(p^2 )&prop;Z_(p^2-p)).

groups

Lee Xu mail -

Olalekan Joosati mail

link https://doi.org/10.54216/GJMSA.0120103

Volume & Issue

Vol. Volume 12 / Iss. Issue 1

Details open_in_new

Pure Mathematics for Theoretical Computer Science | 2025

HyperWeighted Graph, SuperHyperWeighted Graph, and MultiWeighted Graph

A weighted graph is a graph in which each edge is assigned a numerical value (weight), typically representing cost, distance, or intensity. In this paper, we revisit and further explore three generalizations of weighted graphs: the Hyperweighted Graph, the Superhyperweighted Graph, and the MultiWeighted Graph. These advanced structures were initially introduced in.10 Our objective is to enhance understanding and broaden awareness of their theoretical foundations and potential applications through renewed analysis and formal refinement

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Takaaki Fujita mail

link https://doi.org/10.54216/PMTCS.050103

Volume & Issue

Vol. Volume 5 / Iss. Issue 1

Details open_in_new

Pure Mathematics for Theoretical Computer Science | 2025

Neighborhood HyperRough Set and Neighborhood SuperHyperRough Set

Fuzzy sets,20 rough sets,14 intuitionistic fuzzy sets,3 neutrosophic sets,15 soft sets,13 hesitant fuzzy set,17 plithogenic sets,16 and other uncertainty-handling frameworks have been the focus of intensive and ongoing research. Rough set theory provides a mathematical framework for approximating subsets through lower and upper approximations defined by equivalence relations, effectively capturing uncertainty in classification and data analysis.5, 10 Building upon these foundational concepts, further generalizations such as Hyperrough Sets8 and Superhyperrough Sets have been introduced. In this paper, we investigate the concepts of Neighborhood Hyperrough Sets and Neighborhood Superhyperrough Sets. These models extend the classical Neighborhood Rough Set framework by incorporating the structural richness of Hyperrough Sets and Superhyperrough Sets.

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Takaaki Fujita mail

link https://doi.org/10.54216/PMTCS.050104

Volume & Issue

Vol. Volume 5 / Iss. Issue 1

Details open_in_new