A Note on Multi-Neutro-Topological Space

Jeevan Krishna Khaklary; Bhimraj Basumatary

doi:https://doi.org/10.54216/IJNS.270235

Galoitica: Journal of Mathematical Structures and Applications | 2025

Extending Classical Uncertainty Models via Hyperpolar Structures: Fuzzy, Neutrosophic, and Soft Set Perspectives

Concepts such as the Fuzzy Set, Neutrosophic Set, and Soft Set are known for handling uncertainty. As extensions of Fuzzy Sets, Neutrosophic Sets, and Soft Sets, concepts such as Bipolar Fuzzy Sets, Bipolar Neutrosophic Sets, and Bipolar Soft Sets have been introduced. In this paper, we further extend these notions and explore Hyperpolar Fuzzy Sets, Hyperpolar Neutrosophic Sets, and Hyperpolar Soft Sets. These structures integrate multi-perspective or multi-agent evaluations into a unified framework by leveraging higher-dimensional mappings and hypercubic representations. This work lays a theoretical foundation for advanced uncertainty modeling in complex, multi-source environments.

groups

Takaaki Fujita mail -

Arif Mehmood mail

link https://doi.org/10.54216/GJMSA.120202

Volume & Issue

Vol. Volume 12 / Iss. Issue 2

Details open_in_new

International Journal of Neutrosophic Science | 2026

A Conceptual Approach for Algebraic Structure of Multi-Neutrosophic BCI/BCK Algebras

A multi-neutrosophic set is a collection in which each element has a vector of truth indeterminacy, and falsity membership degree, rather than a Neutrosophic set. These vectors may correspond to multiple criteria, perspectives, or layers of information. Multi-neutrosophic sets are a more adaptive strategy for handling ambiguity in complex systems because they broaden neutrosophic sets and allow for better modeling of uncertain information. In this study, we have proposed the fundamental structure of multi-neutrosophic BCI/BCK Algebra and extended it to the category of multi-neutrosophic BCI(BCK) algebras. Theoretical results are presented along with examples. This study advances algebraic structure to multi-neutrosophic set and provides novel directions for future research in non-classical logic.

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Omaima Al-Shanqiti mail -

Santhakumar S. mail -

Sumathi I. R. mail

link https://doi.org/10.54216/IJNS.270232

Volume & Issue

Vol. Volume 27 / Iss. Issue 2

Details open_in_new

International Journal of Neutrosophic Science | 2026

Analytic Solution of Higher Order Fractional Abstract Cauchy Problem

In this paper, we utilize the concept of point-wise independent set of closed operators that enabled us to find atomic solutions of the non-homogeneous α−fractional abstract Cauchy problem of order n. The proposed fractional abstract Cauchy problem isAnu(nα)(t) + An−1u((n−1)α)(t) + · · · + A1u(α)(t) + A◦u(t) = f (t)where the involved operators An, An−1, · · · , A◦ are closed and linear on a given Banach space and the unknown function u(t) is assumed to be n-times α−differentiable. Beyond the deterministic setting, we indicate how the atomic-solution framework extends naturally when coefficients, data, or initial states are modeled as neutrosophic (single-valued) quantities, thereby accommodating uncertainty and indeterminacy at the operator or forcing level.

groups

Waseem Ghazi Alshanti mail

link https://doi.org/10.54216/IJNS.270233

Volume & Issue

Vol. Volume 27 / Iss. Issue 2

Details open_in_new

International Journal of Neutrosophic Science | 2026

Optimizing Crop Selection for Small Scale Farmers Using Neutrosophic Hypersoft Set Theory and Cubic Spherical Neutrosophic Sets

This study addresses the inherent challenges of uncertainty, vagueness, and imprecision in real-world decision-making, particularly focusing on the problem small-scale farmer’s face in optimally selecting short-term crops across diverse planting seasons. The central challenge is the absence of a systematic framework to evaluate multiple, often conflicting, criteria such as initial investment, expected yield, market demand, water and soil requirements, specific fertilizer needs, and pest susceptibility. To overcome this, a robust Multi-Criteria Decision-Making (MCDM) framework is introduced, integrating Cubic Spherical Neutrosophic Sets (CSNS) with Neutrosophic Hyper Soft Sets (NHSS). The research proposes the cubic spherical neutrosophic Bonferroni mean operator as a novel geometric representation for aggregating neutrosophic sets, which enables a more refined modeling of uncertainty and indeterminacy in complex environments. Cubic Spherical Neutrosophic Sets embed neutrosophic information within a spherical structure using interval-based (Truth, Indeterminacy, Falsity) triplets and a radius, offering robust aggregation and ranking capabilities. Neutrosophic hypersoft sets further enhance logical expressiveness by associating each multi-parameter tuple with a neutrosophic triplet, effectively managing complex multi-attribute decision-making tasks with deep interdependencies. The applicability and effectiveness of this approach are demonstrated through a practical case study involving the selection of the most suitable crop for different climatic zones (Pattams) in Tamil Nadu, considering agricultural, environmental, and economic factors. Expert linguistic assessments are converted into neutrosophic values and aligned with seasonal cropping patterns. A subsequent sensitivity analysis confirms the robustness of the model, revealing a perfect correlation between the outcomes of different decision-making methods and thereby validating the consistency and reliability of the proposed approach. This context-aware, data-driven tool aims to enhance decision-making, improve resource utilization, reduce risks, and promote agricultural sustainability and improved farmer livelihoods.

groups

F. Smarandache mail -

B. Kalins mail -

D. Anandakumar mail -

N. Selvanayaki mail -

S. Krishnaprakash mail

link https://doi.org/10.54216/IJNS.270234

Volume & Issue

Vol. Volume 27 / Iss. Issue 2

Details open_in_new

Fusion: Practice and Applications | 2026

Predicting Next-Day Closing Prices in Emerging Stock Markets Using Machine Learning Framework and Engineered Features—Iraq as a Case Study

The complex nature, non-linear dynamics, and inherent volatility of stock markets make it difficult to provide accurate predictions. Recent developments in the area have shown the efficiency of some machine learning methodologies in predicting financial stock prices. However, emerging markets, such as Iraq, face additional challenges due to the lack of fundamental data needed to support predictive analysis. In this study, we present a novel framework that focuses on overcoming this issue and predicting the next-day closing prices of the Iraq Stock Exchange (ISX) main index, using only available historical closing prices to engineer 12 technical indicators. The goal is to compensate for the lack of important Open, High, and Low prices data while improving prediction accuracy. We used four machine-learning algorithms in the form of Random Forest (RF), Support Vector Machine (SVM), Artificial Neural Network (ANN), and K-Nearest Neighbor (KNN), which were optimized using grid search hyperparameter tuning technique. The performance of the models was evaluated using Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Coefficient of Determination (R²). The comparison analysis resulted in the SVM with the linear kernel yielding the best performance (RMSE = 16.25, MAPE = 1.15, R² = 0.989), followed closely by the ANN (RMSE = 18.25), RF (RMSE = 26.76), then KNN (RMSE = 55.77). The current study introduces two main contributions: (1) the feasibility of using engineered features to achieve reliable predictions in markets with incomplete data, and (2) the critical role of using hyperparameter optimization to enhance models accuracy. The framework we propose provides a practical model for predicting stock prices in resource-constrained emerging markets.

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Ali Subhi Alhumaima mail -

Wisam Hayder Mahdi mail -

Marwa M. Eid mail -

El-Sayed M. El-Kenawy mail

link https://doi.org/10.54216/FPA.210216

Volume & Issue

Vol. Volume 21 / Iss. Issue 2

Details open_in_new

Fusion: Practice and Applications | 2026

Optimized Time-Series Forecasting for Electricity Consumption in Tetouan: A Machine Learning Approach with Greylag Goose Optimization

This paper addresses the challenge of predicting and analyzing electricity consumption patterns in Tetouan, Morocco, using time-series data. The dataset consists of 52,416 observations with 9 features, collected from the SCADA system of electricity consumption across three zones. The primary goal is to enhance forecasting accuracy and optimize prediction models through machine learning (ML) algorithms, including both timeseries models and advanced optimization techniques. We compare the performance of several baseline ML models, such as BiLSTM and Continuous Time Stochastic Modelling (CTSM), with their optimized versions, utilizing optimization algorithms like Greylag Goose Optimization (GGO), Bat Algorithm (BA), and Whale Optimization Algorithm (WOA). The results show that the optimized CTSM model, using GGO, achieved substantial improvements, including the lowest Mean Squared Error (MSE) of 7.09E-07 and the highest R² of 0.990, demonstrating superior accuracy and stability. The contributions of this work include (i) benchmarking various ML models for time-series forecasting, (ii) introducing the use of optimized CTSM with meta-heuristics, and (iii) evaluating model performance using a comprehensive set of statistical metrics.

groups

Marwa M. Eid mail

link https://doi.org/10.54216/FPA.210217

Volume & Issue

Vol. Volume 21 / Iss. Issue 2

Details open_in_new

Fusion: Practice and Applications | 2026

Optimizing Smart-Home Energy Forecasting with Evolutionary Attention-based LSTM and Greylag Goose Optimization

This study addresses the challenge of smart-home energy forecasting across multiple appliances under varying temperature and seasonal regimes, aiming to improve demand planning and household energy efficiency. The analysis leverages a 100,000-row dataset from Kaggle, encompassing appliance type, time of consumption, outdoor temperature, season, and household size. The study benchmarks several recurrent neural network models, including Long Short-Term Memory (LSTM), Bidirectional LSTM (BiLSTM), Gated Recurrent Unit (GRU), and Bidirectional RNN (BiRNN), as well as a feedforward Artificial Neural Network (ANN). A novel enhancement, the Evolutionary Attention-based LSTM (EALSTM), is introduced, and its hyperparameters are optimized using the Greylag Goose Optimization (GGO) algorithm. The performance of GGO-optimized EALSTM is compared to other metaheuristics, such as Differential Evolution (DE), Genetic Algorithm (GA), Quantum-Inspired Optimization (QIO), JAYA, Bat Algorithm (BA), and Stochastic Fractal Search (SFS). The results indicate that GGO-optimized EALSTM outperforms all other models, achieving superior accuracy across multiple metrics, including MSE, RMSE, MAE, r, R2 , RRMSE, NSE, and WI. Key contributions of the paper include (i) the establishment of an appliance- and season-aware forecasting benchmark, (ii) a comprehensive optimizer comparison for EALSTM using GGO, and (iii) the provision of actionable visual analytics to enhance the understanding of energy demand patterns and model errors.

groups

El-Sayed M. El-Kenawy mail

link https://doi.org/10.54216/FPA.210218

Volume & Issue

Vol. Volume 21 / Iss. Issue 2

Details open_in_new

Fusion: Practice and Applications | 2026

Greylag Goose Optimization-Driven EALSTM for Accurate HVAC Chiller Energy Prediction

Forecasting the energy consumption of heating, ventilation, and air conditioning (HVAC) chillers is vital for enhancing building efficiency, reducing operating costs, and supporting sustainability goals. However, the task remains challenging due to nonlinear system dynamics, strong dependence on weather conditions, and the scarcity of high-quality real-world datasets. In this work, we employ the Chiller Energy Data from Kaggle, which contains 13,561 cleaned records collected between August 2019 and June 2020, incorporating ten operational and meteorological features. Six baseline models, namely the Evolutionary Attention-based Long Short-Term Memory (EALSTM), Bidirectional LSTM (BILSTM), standard LSTM, Gated Recurrent Unit (GRU), Temporal Convolutional Network (TCN), and Artificial Neural Network (ANN), are first benchmarked to assess their forecasting capability. To further improve predictive accuracy, we integrate EALSTM with ten meta-heuristic optimization algorithms, focusing on the Greylag Goose Optimization Algorithm (GGO) and comparing it with alternatives such as Harris Hawks Optimization (HHO), Artificial Physics Optimization (APO), Simulated Annealing Optimization (SAO), Grey Wolf Optimizer (GWO), and others. The optimized GGO+EALSTM framework achieves state-of-the-art performance with a mean squared error of 6.83×10−6 and an R2 value of 0.98, reflecting a 96% reduction in error relative to simple feedforward models and significant improvements over other recurrent networks and optimizer-enhanced variants. The main contributions of this study include a structured benchmarking of neural architectures for chiller forecasting, the first systematic comparison of ten meta-heuristic optimizers applied to deep learning in this domain, and a visualization-based error analysis that strengthens interpretability and supports practical deployment. These results establish optimization-enhanced EALSTM as a robust and generalizable framework for HVAC energy forecasting, paving the way toward more efficient, reliable, and sustainable building energy management.

groups

Doaa Sami Khafaga mail

link https://doi.org/10.54216/FPA.210219

Volume & Issue

Vol. Volume 21 / Iss. Issue 2

Details open_in_new

Journal of Intelligent Systems and Internet of Things | 2025

An Efficient Wireless Sensor Network Developed Election Protocol for Extendable Lifetime

Wireless sensor networks (WSNs) are made up of thousands of sensor nodes that are distributed in an area where their energy is limited. To overcome the issue of energy consumption. This paper study different deployment configuration as well as evaluating the two different clustering-based routing protocols. This work describes a hybrid distance, energy, and zonal SEP (HDEZ-SEP), which combines the strengths of the Distance and Energy-Aware Stable Election Routing Protocol (DE-SEP) and Zone-Based Stable Election Protocol (Z-SEP) to improve WSN energy efficiency and longevity. The suggested HDEZ-SEP was executed and compared to other protocols, including DE-SEP and Z-SEP. Using the MATLAB R2022b simulator; we assess the suggested protocol and contrast it with the others. According to the simulation results, the overall performance is improved. This study shows how hybrid techniques can effectively optimize data transmission and energy use in WSNs.

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Aya A. Ramadan mail -

Marwa M. Eid mail -

El-Sayed S. A. Said mail -

Shereen H. Ali mail -

Mohamed Yasin I. Afifi mail

link https://doi.org/10.54216/JISIoT.170210

Volume & Issue

Vol. Volume 17 / Iss. Issue 2

Details open_in_new

International Journal of Neutrosophic Science | 2026