⚡ electrical engineering

Quantum Spherical Fuzzy Decision Framework with Golden Cut and ARTASI for Sustainable Mining Method Selection in Geologically Complex Thin Seams

This study proposes a novel Quantum Spherical Fuzzy Large-Scale Decision-Making framework, integrating Golden Cut, Consensus-Based Expert Weighting, Ant Colony Optimization, and ARTASI to systematically identify automated 3D-trajectory shearer mining as the optimal method for safely and sustainably extracting geologically complex thin coal seams in Meghalaya.

Original authors: Nidahamteinsar Papang, Bishal Gurung, Priya Sharma

Published 2026-10-29

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CC BY 4.0

Original authors: Nidahamteinsar Papang, Bishal Gurung, Priya Sharma

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep within the earth, where coal seams are thin, fractured, and geologically complex, the choice of how to extract fuel is a high-stakes gamble. In regions like Meghalaya, India, where coal layers can be as thin as a few inches, traditional methods have often relied on crude, unscientific digging that endangers workers and scars the landscape. The core challenge for engineers and planners is not just finding coal, but selecting a mining technique that balances safety, cost, environmental impact, and technical feasibility. This decision is rarely straightforward because the factors involved often pull in opposite directions; a method that is cheap might be unsafe, while one that is highly efficient might be too expensive for a specific site. To navigate these conflicting demands, researchers turn to a field of mathematics designed to handle human uncertainty, where judgments are not forced into rigid numbers but are allowed to exist in shades of gray, capturing the hesitation and doubt that naturally accompany expert opinion.

A team of researchers has developed a new, sophisticated system to solve this specific problem, aiming to replace guesswork with a structured, scientific approach. They created a decision-making framework that treats expert opinions not as simple "yes" or "no" votes, but as complex assessments containing layers of agreement, disagreement, and uncertainty. By using a mathematical model that incorporates "quantum" concepts—specifically, the idea that information can have both a magnitude and a phase, much like a wave—they can represent the full nuance of an expert's hesitation. To ensure the system remains grounded and consistent, the researchers applied a principle based on the golden ratio, a famous mathematical proportion found in nature, to automatically generate the necessary parameters for these complex assessments, removing the need for arbitrary choices.

The study focused on the coalfields of Meghalaya, where seams range from 0.30 to 2.12 meters thick. The researchers gathered a group of experts to evaluate twelve different mining methods, from traditional drilling and blasting to advanced automated machinery. These methods were tested against twelve distinct criteria, including the thickness and depth of the coal, the stability of the rock above it, ventilation needs, safety records, and environmental consequences. Instead of simply averaging the experts' scores, the new system looked for how much the experts agreed with one another. Those whose judgments aligned closely with the group consensus were given more influence in the final calculation, ensuring that the collective wisdom of the team guided the outcome rather than the outlier opinions of a single individual.

Once the experts' views were combined, the system had to decide which criteria mattered most. Rather than asking experts to guess the importance of each factor, the researchers used a computer algorithm inspired by how ants find food. This algorithm, known as Ant Colony Optimization, simulated thousands of scenarios to find the perfect balance of weights that would best distinguish between the different mining methods. It searched for a set of priorities that would make the differences between the options as clear as possible. The final step involved ranking the methods using a technique that compares each option against an ideal best-case scenario and a worst-case scenario, calculating a single score that reflects how close each method comes to perfection.

The results of this rigorous analysis pointed clearly to one winner: automated 3D-trajectory shearer mining. This method, which uses advanced machinery to cut coal along a precise, computer-controlled path, emerged as the top choice with a utility score of 0.674. It was followed closely by shearer-based thin-seam longwall mining and continuous-miner bord-and-pillar mining. The study found that the potential for mechanization was the single most important factor in this decision, outweighing other concerns like seam depth or geological continuity. The researchers tested the stability of their findings by randomly shifting the importance of the criteria and the data inputs, and the top-ranked methods remained consistent, suggesting the result is robust and not a fluke of the calculation.

This work does not claim to have solved every mining problem or to be a universal rule for all coalfields. Instead, it offers a reliable, scientific foundation for moving away from dangerous, unregulated extraction practices in Meghalaya. By providing a clear, data-driven ranking of available technologies, the framework gives decision-makers a way to justify choosing safer, more sustainable methods over those that might seem easier but carry hidden risks. The study demonstrates that when human uncertainty is handled with the right mathematical tools, it is possible to cut through the complexity of geology and economics to find the path that offers the best chance for a safe and sustainable future.

Technical Summary: Quantum Spherical Fuzzy Decision Framework with Golden Cut and ARTASI for Sustainable Mining Method Selection

Problem Statement
The selection of appropriate mining methods for geologically complex, thin coal seams (specifically those ranging from 0.30 to 2.12 m in thickness) presents a critical challenge, particularly in regions like Meghalaya, India. Conventional extraction practices in these areas, such as rat-hole mining, are associated with significant safety hazards, resource losses, and environmental degradation. The decision-making process is complicated by the need to simultaneously evaluate multiple, often conflicting criteria—including geological characteristics, technical feasibility, economic viability, safety, and environmental impact—under conditions of uncertainty, imprecision, and subjective expert judgment. Existing methods often struggle to adequately represent the hesitation and vagueness inherent in human assessments or to objectively determine criterion weights without relying on fixed analytical rules.

Methodology
The study proposes a Quantum Spherical Fuzzy Large-Scale Decision-Making (QSF-LSDM) framework designed to address multidimensional uncertainty and expert subjectivity. The methodology follows a structured, multi-stage process:

Quantum Spherical Fuzzy Sets (QSFS) Representation: Expert judgments are modeled using QSFS, which extend conventional Spherical Fuzzy Sets by incorporating amplitude and phase information. This allows for the simultaneous representation of membership, non-membership, and hesitancy amplitudes alongside their corresponding phase parameters, providing a richer description of uncertain information.
Golden Cut Mechanism: To reduce subjectivity in parameter selection, a Golden Cut procedure based on the Golden Ratio ( $\approx 1.618$ ) is employed. This mechanism systematically derives non-membership, hesitancy, and phase parameters directly from initial linguistic assessments (e.g., "Very High," "Low"), eliminating arbitrary scaling choices.
Consensus-Based Expert Weighting (CBEW): Instead of treating all experts equally, the framework calculates expert weights based on the degree of agreement (consensus) among the decision-making group. Similarity measures between individual decision matrices determine the relative importance of each expert, assigning higher weights to assessments that align more closely with the collective opinion.
Aggregation via QSFWBM: Individual expert assessments are aggregated using the Quantum Spherical Fuzzy Weighted Bonferroni Mean (QSFWBM) operator. Unlike standard arithmetic or geometric means, this operator explicitly captures non-linear pairwise interactions and dependencies among criteria and expert opinions during the fusion of group information.
Objective Criterion Weighting via ACO: To avoid subjective bias in weighting criteria, the study formulates criterion weight determination as a continuous optimization problem. A continuous Ant Colony Optimization (ACO) algorithm is used to search for an optimal weight vector that maximizes the overall pairwise score deviation among the candidate alternatives, thereby deriving weights directly from the decision matrix's inherent discriminatory power.
Ranking via ARTASI: The final ranking is established using the Alternative Ranking Technique based on Adaptive Standardized Intervals (ARTASI). This method transforms diverse benefit and cost attributes into a unified standardized interval while preserving the relative disposition of raw data. It evaluates alternatives based on their distance from ideal and anti-ideal conditions to produce a utility index.

Key Contributions
The paper outlines six primary contributions to the field of Multi-Criteria Decision Making (MCDM) and mining engineering:

Framework Development: Establishment of a QSF-LSDM framework that models complex cognitive uncertainty and human hesitation by integrating QSFS with phase parameters and a Golden Cut mechanism for systematic parameter construction.
Objective Expert Weighting: Introduction of a Consensus-Based Expert Weighting (CBEW) model that assigns weights based on group agreement levels, preventing individual biases from skewing collective evaluations.
Interaction-Aware Aggregation: Application of the QSFWBM operator to capture interrelationships among criteria and expert opinions, moving beyond the assumption of independence found in conventional aggregation methods.
Optimization-Based Weighting: Formulation of criterion weighting as a continuous optimization problem solved via ACO, maximizing score discrimination without relying on fixed analytical rules.
Adaptive Ranking: Utilization of the ARTASI method to provide a flexible ranking framework that handles both benefit and cost criteria consistently through adaptive standardization.
Practical Validation: Application of the framework to a real-world case study in Meghalaya, evaluating 12 candidate mining methods against 12 diverse criteria to support the transition from unscientific to sustainable mining practices.

Results
The framework was applied to evaluate 12 mining methods ( $M_1$ to $M_{12}$ ) across 12 criteria. The computational implementation, performed using Python 3.11, yielded the following findings:

Top-Ranked Method: Automated 3D-trajectory shearer mining ( $M_{10}$ ) emerged as the highest-ranked alternative with a utility index ( $\Omega$ ) of 0.674.
Subsequent Rankings: This was followed by shearer-based thin-seam longwall mining ( $M_5$ ) with $\Omega = 0.662$ and continuous-miner bord-and-pillar mining ( $M_3$ ) with $\Omega = 0.632$ .
Lowest Ranked: Auger mining ( $M_7$ ) and stope-and-pillar mining ( $M_9$ ) received the lowest utility values.
Criterion Importance: The ACO-based weighting identified mechanization potential ( $C_{11}$ ) as the most influential criterion ( $w_{11} = 0.529$ ), followed by seam geometry and continuity ( $C_4$ ), seam depth ( $C_3$ ), and coal recovery ( $C_{10}$ ).
Robustness: Sensitivity analyses (Monte Carlo simulations and COMSAM perturbation) demonstrated that the ranking of the top alternatives remained highly stable despite variations in criterion weights and input data.
Comparative Analysis: The QSF-ARTASI results showed perfect agreement (Spearman correlation of 1.000) with EDAS and MARCOS methods and strong agreement with TOPSIS. A significant divergence was observed with VIKOR, attributed to methodological differences in handling the decision information.

Significance and Claims
The paper claims that the proposed QSF-LSDM framework provides a systematic, scientific basis for evaluating mining methods in geologically complex thin seams. By integrating quantum-inspired fuzzy logic with optimization and consensus mechanisms, the framework effectively handles the uncertainty and hesitation inherent in expert assessments while minimizing subjective bias in parameter and weight selection.

The study positions its results not as universal recommendations for all mining conditions, but as decision-support outcomes tailored to the specific geological, technical, and operational context of Meghalaya's thin coal seams. The primary significance lies in offering a structured alternative to unscientific extraction practices, supporting the transition toward safer, regulated, and sustainable mining operations. The authors emphasize that while the framework identifies the most suitable methods based on the defined criteria, actual implementation requires further site-specific geological investigations, engineering validation, safety assessments, and regulatory approval.

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