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Keywords = expert-based fuzzy weighting

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34 pages, 3896 KB  
Article
A Fuzzy AHP-Based Framework for Assessing Cybersecurity Readiness in Smart Circular Economy Systems Aligned with ISO/IEC 27001
by Seyedeh Azadeh Alavi-Borazjani and Muhammad Noman Shafique
Information 2026, 17(5), 429; https://doi.org/10.3390/info17050429 - 29 Apr 2026
Abstract
The increasing digitalization of smart circular economy (CE) systems intensifies reliance on interconnected cyber-physical infrastructures, thereby increasing exposure to cybersecurity risks that may affect operational continuity and regulatory compliance. This study proposes a Fuzzy Analytical Hierarchy Process (Fuzzy AHP)-based framework to systematically assess [...] Read more.
The increasing digitalization of smart circular economy (CE) systems intensifies reliance on interconnected cyber-physical infrastructures, thereby increasing exposure to cybersecurity risks that may affect operational continuity and regulatory compliance. This study proposes a Fuzzy Analytical Hierarchy Process (Fuzzy AHP)-based framework to systematically assess cybersecurity readiness in alignment with the ISO/IEC 27001:2022 Information Security Management System (ISMS) standard. The framework adopts a structured three-level hierarchy consisting of seven main criteria and 39 sub-criteria, derived from ISO/IEC 27001:2022 clause-based requirements and Annex A control families, and expanded with an additional regulatory criterion based on the Cyber Resilience Act (CRA) Requirements Standards Mapping. Expert judgments from ten specialists in cybersecurity and digital systems were elicited using linguistic assessments and converted into triangular fuzzy numbers to compute priority weights under uncertainty. The results indicate that ISMS governance and organizational context are the most influential determinants of cybersecurity readiness, followed by regulatory and compliance alignment, operational oversight, and technological controls, while organizational, human, and physical controls play supportive roles. Consistency and sensitivity analyses confirm the robustness and stability of the weighting structure. Overall, the framework provides a standards-aligned decision-support tool for prioritizing cybersecurity readiness in digitally intensive CE environments. Full article
(This article belongs to the Special Issue Digital Technology and Cyber Security)
46 pages, 1895 KB  
Article
Aero-Engine Quality Assessment Under the RAMS Framework: Coupling Interval Type-2 Fuzzy Group Decision-Making with PLS-SEM for Dimensional Correlation Modelling
by Yuhui Wang, Sining Xu, Xiangjun Cheng and Borui Xie
Systems 2026, 14(5), 464; https://doi.org/10.3390/systems14050464 (registering DOI) - 24 Apr 2026
Viewed by 133
Abstract
Aero-engine quality assessment under the RAMS framework faces two persistent challenges: the inherent epistemic and linguistic uncertainty in expert evaluation, and the systematic neglect of inter-dimensional coupling. This paper proposes an integrated assessment method that combines Interval Type-2 Fuzzy Sets (IT2FS)-based group decision-making [...] Read more.
Aero-engine quality assessment under the RAMS framework faces two persistent challenges: the inherent epistemic and linguistic uncertainty in expert evaluation, and the systematic neglect of inter-dimensional coupling. This paper proposes an integrated assessment method that combines Interval Type-2 Fuzzy Sets (IT2FS)-based group decision-making with Partial Least Squares Structural Equation Modeling (PLS-SEM). At the measurement level, IT2FS encodes dual-layered uncertainty through the Footprint of Uncertainty (FOU); multi-expert judgments are aggregated via the fuzzy weighted geometric average operator and defuzzified using the Karnik–Mendel algorithm. At the structural level, a reflective second-order PLS-SEM model built on the RAMS framework enables parametric estimation and significance testing of inter-dimensional coupling. Validation on a 63-engine turbofan dataset confirms that all measurement model criteria are satisfied, the second-order model explains 82.4% of the variance in overall quality (R2 = 0.824), and predictive relevance is strong (Q2 = 0.567). Comparative experiments against three benchmark methods demonstrate consistent advantages in quality grade discrimination, information richness, sensitivity to technical improvements, and ranking robustness. These properties position the framework as a statistically rigorous, model-based complement to existing condition-monitoring and digital health management systems for complex propulsion systems, supporting quantitative decision-making within digital engineering programmes. Full article
27 pages, 816 KB  
Article
Hybrid Model for Assessing the Carbon Footprint in Pilot Training
by Miroslav Kelemen, Volodymyr Polishchuk, Martin Kelemen, Ján Jevčák and Marek Košuda
Appl. Sci. 2026, 16(8), 4041; https://doi.org/10.3390/app16084041 - 21 Apr 2026
Viewed by 154
Abstract
The research aimed to create a hybrid model for assessing the carbon footprint of pilots’ education at a flight school, taking into account the level of implementation of green infrastructure by the educational institution, while excluding indirect emissions from the model. The study [...] Read more.
The research aimed to create a hybrid model for assessing the carbon footprint of pilots’ education at a flight school, taking into account the level of implementation of green infrastructure by the educational institution, while excluding indirect emissions from the model. The study implemented an approach that combines fuzzy set theory with expert evaluation methods, utilizing membership functions and convolution mechanisms to incorporate subjective expert assessments into formalized numerical measures. The research was focused on two research questions: Does the proposed hybrid model allow for a practical assessment of a pilot’s carbon footprint during his training? Does the hybrid model provide the ability to automatically determine the level of carbon footprint of an aviation educational institution and generate substantiated recommendations for the strategic management of sustainable development of the educational process? The resulting model enables a quantitative assessment of individual CO2 emissions during pilot training and provides collective insights into the overall carbon footprint, accounting for the green infrastructure’s level of implementation. The hybrid model was tested and validated using real data from the Technical University of Košice (Slovakia) within the “PILOT” study program (2022–2025). The experimental calculations are based on the Viper SD4, a homogeneous aircraft type. The model is designed to account for multiple aircraft types through weighted aggregation, a feature that can be used in future institutional implementations. These recommendations are practical for managers and specialists at aviation educational institutions, environmental analysts, curriculum developers, and policymakers focused on sustainable development. At the current stage, the model primarily captures direct training-related and institution-level operational emissions, while indirect emissions were included only to a limited extent because of insufficiently available and non-systematically recorded data. Therefore, the proposed framework should be interpreted as an operational decision-support model rather than a full greenhouse gas inventory covering all indirect emission sources. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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30 pages, 5438 KB  
Article
Prioritizing Energy-Efficient Envelope Retrofit Strategies for Existing Residential Buildings in Severe Cold Regions Through Multi-Dimensional Benefit Evaluation
by Jiajia Teng, Conrong Wang, Lei Zhang, Weipeng Yin, Yongze Li and Zijun Wu
Buildings 2026, 16(7), 1451; https://doi.org/10.3390/buildings16071451 - 7 Apr 2026
Viewed by 403
Abstract
Energy-efficient retrofit of existing residential buildings is essential for reducing heating energy demand and carbon emissions in severe cold regions. However, the absence of a structured quantitative evaluation approach often limits effective decision-making in practice. This study develops a multi-dimensional evaluation framework integrating [...] Read more.
Energy-efficient retrofit of existing residential buildings is essential for reducing heating energy demand and carbon emissions in severe cold regions. However, the absence of a structured quantitative evaluation approach often limits effective decision-making in practice. This study develops a multi-dimensional evaluation framework integrating the Fuzzy Delphi Method and Analytic Hierarchy Process (AHP) to assess and prioritize building envelope retrofit strategies. A representative non-energy-efficient residential building in Changchun, China, is selected as a case study. Based on expert consultation, a hierarchical indicator system is established, and indicator weights are determined with satisfactory consistency (CR < 0.1). The results indicate that envelope thermal performance and energy–carbon benefits are the dominant factors influencing retrofit decisions. At the parameter level, insulation thermal conductivity and external wall heat transfer coefficient are identified as the most critical variables. The findings suggest that prioritizing improvements in envelope thermal performance can effectively enhance energy-saving and carbon-reduction performance under practical constraints. The proposed framework provides a practical and transferable decision-support tool for energy-efficient retrofit planning for existing residential buildings in severe cold regions. Full article
(This article belongs to the Section Building Energy, Physics, Environment, and Systems)
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18 pages, 1962 KB  
Article
Information System for Determining the Prioritization of Vector Image Quality Factors
by Alona Kudriashova, Iryna Pikh, Vsevolod Senkivskyy, Liubomyr Sikora and Nataliia Lysa
Appl. Sci. 2026, 16(7), 3569; https://doi.org/10.3390/app16073569 - 6 Apr 2026
Viewed by 488
Abstract
The quality of vector images depends on a significant set of geometric and structural factors, which makes objective assessment a challenging task. This paper proposes a comprehensive approach to identifying and prioritizing these factors. Factor selection was performed based on expert evaluation and [...] Read more.
The quality of vector images depends on a significant set of geometric and structural factors, which makes objective assessment a challenging task. This paper proposes a comprehensive approach to identifying and prioritizing these factors. Factor selection was performed based on expert evaluation and analysis of inter-factor relationships. A reachability matrix of factors was constructed to analyze direct and indirect relationships. Models describing relationships between the factors were developed. The rank and weight of each factor were calculated using a dependency-weighting system. An information system was developed to automate the process of prioritizing factors based on the proposed methodology. The software architecture was implemented in Python 3.13.5 using the Tkinter, NumPy, and NetworkX libraries. Experimental results confirmed that the factor «coordinate accuracy» has the highest level of significance, whereas «file format» has the smallest influence on the quality of vector images. Due to the lack of dependence on specific selected factors, the developed system is universal and suitable for prioritizing factors in any application domain. Future research will focus on integrating the developed information system into a fuzzy-logic-based system for assessing the quality of vector images. Full article
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26 pages, 1111 KB  
Article
A Decision Indicator System for Takeoff and Landing Site Selection of Bucket Firefighting Helicopters in Wildfire Emergency Response
by Yuanjing Huang, Chen Zeng, Weijun Pan, Rundong Wang, Zirui Yin, Yangyang Li and Shiyi Huang
Fire 2026, 9(4), 148; https://doi.org/10.3390/fire9040148 - 4 Apr 2026
Viewed by 522
Abstract
With the increasing complexity of wildfire emergency response, the aerial emergency response system is imposing increasing demands on both safety and decision rationality of takeoff and landing site selection. Site selection decisions are influenced by multi-dimensional factors, including geographical location, meteorological factors, and [...] Read more.
With the increasing complexity of wildfire emergency response, the aerial emergency response system is imposing increasing demands on both safety and decision rationality of takeoff and landing site selection. Site selection decisions are influenced by multi-dimensional factors, including geographical location, meteorological factors, and operational safety considerations, resulting in a pronounced coupling of multiple factors in the decision-making process. However, existing studies primarily focus on spatial suitability evaluation or technical implementation, often relying on predefined indicator systems and independence assumptions, while lacking a systematic characterization of the influencing factor system and its interrelationships in takeoff and landing site selection. To address this gap, this study proposes a novel structured decision-making framework to systematically analyze and optimize the selection of takeoff and landing sites for bucket firefighting helicopters in wildfire aerial emergency response scenarios. First, a procedural grounded theory approach is employed to systematically identify the influencing factors associated with site selection, thereby constructing a traceable decision-making factor system. Second, fuzzy DEMATEL is applied to model the causal relationships and structural interdependencies among these factors. Finally, a cumulative contribution rate based on centrality is introduced to screen and optimize the decision indicators, resulting in a refined set of key decision indicators. The results reveal the structural roles of different influencing factors in site selection, reduce the reliance on experience-driven judgment, and reconceptualize the problem from traditional indicator weighting and ranking into a structured decision-making process involving multi-factor coupling. This provides systematic decision support for takeoff and landing site selection in wildfire aerial emergency response and establishes a foundation for subsequent spatial suitability analysis and case-based validation. Furthermore, the results are consistent with expert experience and practical operational constraints, indicating the potential applicability of the proposed method in real-world decision-making. Full article
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22 pages, 1332 KB  
Article
Identifying Barriers to Shipbuilding in India: A Delphi–DEMATEL Approach
by Rupesh Kumar and Saroj Koul
Logistics 2026, 10(4), 80; https://doi.org/10.3390/logistics10040080 - 3 Apr 2026
Viewed by 618
Abstract
Background: This study examines the systemic barriers constraining the development of India’s shipbuilding industry and identifies leverage points for effective policy intervention. Methods: A mixed-methods design was adopted, combining the Delphi technique with fuzzy DEMATEL to capture expert consensus and causal [...] Read more.
Background: This study examines the systemic barriers constraining the development of India’s shipbuilding industry and identifies leverage points for effective policy intervention. Methods: A mixed-methods design was adopted, combining the Delphi technique with fuzzy DEMATEL to capture expert consensus and causal interdependencies among barriers. A panel of 20 experts, drawn from academia, the government, shipbuilding and ship repair, ports, logistics, and maritime consultancy, participated in two iterative Delphi rounds. An initial list of 21 barriers was refined to 10 based on convergence thresholds. These barriers were then analysed using a seven-step fuzzy DEMATEL procedure to distinguish causal drivers from dependent factors. Results: High raw material costs emerged as the most dominant causal barrier, with the highest net influence (R−C = 0.540), followed by high working capital requirements (R−C = 0.103) and complex regulatory frameworks (R−C = 0.275). Shortages of skilled labour, inefficiencies in ship design, and delays in clearances were largely effect-type barriers shaped by upstream structural conditions. Sensitivity analysis confirmed the stability of barrier rankings under alternative expert weighting scenarios. Conclusions: Policy efforts should prioritise reducing input cost disadvantages, strengthening long-term policy support, and rationalising regulatory processes, rather than focusing solely on downstream operational symptoms. The study is limited to expert judgement in the Indian shipbuilding sector. Future research could extend this framework to comparative country settings or integrate causal analysis with econometric evidence to further strengthen policy design. Contribution: Unlike prior thematic studies, this research provides an integrated causal mapping of structural, financial, and institutional barriers specific to Indian shipbuilding, enabling policy sequencing rather than simple ranking. Full article
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17 pages, 3983 KB  
Article
Characteristics and Hazards Prevention of Bed Separation Water Inrush: A Case Study of the Cuimu Coal Mine, China
by Hewen Ma
Water 2026, 18(7), 813; https://doi.org/10.3390/w18070813 - 28 Mar 2026
Cited by 1 | Viewed by 379
Abstract
This paper presents an active prevention and control technology for bed separation water inrush hazards, the effectiveness of which has been validated. Based on the hazard degree identification of such hazards and corresponding preventive measures, the Fuzzy Analytic Hierarchy Process (FAHP) and Expert [...] Read more.
This paper presents an active prevention and control technology for bed separation water inrush hazards, the effectiveness of which has been validated. Based on the hazard degree identification of such hazards and corresponding preventive measures, the Fuzzy Analytic Hierarchy Process (FAHP) and Expert Grading System (EGS) are adopted to analyze the prevention mechanisms and determine the indicator weights of different influencing factors. The results show that enhancing drainage capacity and accurately predicting bed separation water inflow are two effective measures to prevent water inrush or reduce the hazard risk coefficient. In addition, controlling the development of water-conducting fractured zones and optimizing drainage measures are also effective approaches to reducing the risk coefficient. The research results provide a theoretical basis and practical guidance for the prevention and control of bed separation water inrush hazards, and offer an effective and cost-efficient method for addressing such mining-induced hazards. Full article
(This article belongs to the Special Issue Mine Water Environment and Remediation)
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27 pages, 1727 KB  
Article
Research on the Dynamic Evolution of Expert Trust Relationship in Flood Disaster Decision-Making Based on Preference Distance
by Feng Li, Pengcheng Wu and Jie Yin
Water 2026, 18(7), 811; https://doi.org/10.3390/w18070811 - 28 Mar 2026
Viewed by 350
Abstract
In flood disaster emergency decision-making, the dynamic changes in expert trust relationships directly affects the efficiency of reaching a decision consensus. This paper constructs a dynamic evolution model of expert trust relationships in flood disaster emergency decision-making from the perspective of preference distance: [...] Read more.
In flood disaster emergency decision-making, the dynamic changes in expert trust relationships directly affects the efficiency of reaching a decision consensus. This paper constructs a dynamic evolution model of expert trust relationships in flood disaster emergency decision-making from the perspective of preference distance: the initial trust matrix and weights of experts based on four dimensions including cooperation intensity, social relations, background similarity, and subjective initial trust; the cognitive trust is quantified by using the intuitionistic fuzzy Hamming distance, and the trust relationship is dynamically update through the exponential fusion method; the Louvain community discovery algorithm is introduce to achieve dynamic clustering of experts and weight updates of experts in combination with the dynamic changes in trust relationships; and a consensus feedback adjustment mechanism is designed to optimize the preferences of experts with lower consensus. At the same time, the dynamic trust model is verified by combining a flood disaster case. Case validation shows that the model completes consensus iteration in just four rounds, with the maximum increase in cognitive trust due to opinion convergence reaching 0.18 during the evolution process. The model effectively captures changes in trust among experts during decision-making, improving consensus convergence speed while ensuring that the final solution aligns with the comprehensive considerations required in emergency scenarios. This study provides a quantitative tool for large-group decision-making in flood emergencies under high-pressure, information-poor environments; one that balances dynamic trust evolution with efficient consensus building. Full article
(This article belongs to the Topic Disaster Risk Management and Resilience)
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36 pages, 5862 KB  
Article
Reliability Analysis of Aerospace Blade Manufacturing Equipment: A Multi-Source Uncertainty FMECA Method for Five-Axis CNC Machine Tool Spindle Systems
by Muhao Han, Yufei Li, Hailong Tian, Yuzhi Sun, Zixuan Ni, Yunshenghao Qiu and Haoyuan Li
Machines 2026, 14(4), 360; https://doi.org/10.3390/machines14040360 - 25 Mar 2026
Viewed by 332
Abstract
Five-axis Computerized Numerical Control (CNC) machine tools play a pivotal role in the precision manufacturing of aeroengine turbine blades, where ultra-high reliability and accuracy are essential. Failure Mode, Effects and Criticality Analysis (FMECA) has been widely applied in the reliability assessment of such [...] Read more.
Five-axis Computerized Numerical Control (CNC) machine tools play a pivotal role in the precision manufacturing of aeroengine turbine blades, where ultra-high reliability and accuracy are essential. Failure Mode, Effects and Criticality Analysis (FMECA) has been widely applied in the reliability assessment of such advanced machining systems due to its systematic evaluation of potential failure modes. However, traditional FMECA approaches often overlook the ambiguity of human cognition and the interdependence among expert evaluations, limiting their effectiveness in complex aerospace manufacturing environments. To address these issues, this paper proposes a novel FMECA framework based on generalized intuitionistic linguistic theory. A new Generalized Intuitionistic Linguistic Weighted Geometric Average (GILWGA) operator is introduced to couple multi-source expert information and quantify the fuzziness inherent in subjective assessments. Additionally, an intuitionistic linguistic entropy-based weighting scheme is developed to dynamically evaluate key risk factors, including severity, occurrence, detectability, and controllability. The proposed framework is applied to a case study involving the spindle system of a five-axis CNC machine tool used in aeroengine blade production. The results demonstrate that the proposed method offers more robust and consistent failure mode prioritization, providing effective decision support for reliability-centered maintenance in aerospace equipment manufacturing. Full article
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24 pages, 2012 KB  
Article
An Adaptive Consensus Model to Manage Non-Cooperative Behaviors in Large Group Decision-Making with Probabilistic Linguistic Information
by Xun Han, Xingrui Guan, Gang Chen, Jiangyue Fu and Xinchuan Liu
Mathematics 2026, 14(6), 1049; https://doi.org/10.3390/math14061049 - 20 Mar 2026
Viewed by 357
Abstract
To address challenges in complex group decision-making (GDM)—specifically preference fuzziness, intricate subgroup segmentation, and non-cooperative behavior—this study proposes an adaptive consensus model based on probabilistic linguistic term sets (PLTSs). By integrating fuzzy C-means (FCM) clustering with a Gaussian mixture model (GMM), a fuzzy [...] Read more.
To address challenges in complex group decision-making (GDM)—specifically preference fuzziness, intricate subgroup segmentation, and non-cooperative behavior—this study proposes an adaptive consensus model based on probabilistic linguistic term sets (PLTSs). By integrating fuzzy C-means (FCM) clustering with a Gaussian mixture model (GMM), a fuzzy Gaussian mixture model (FGMM) is constructed to achieve soft segmentation of expert preference distributions. On this basis, an adaptive consensus feedback mechanism is developed, which dynamically integrates interactive and automated adjustment strategies via multi-level consensus thresholds, thereby balancing decision efficiency and quality. To identify and control non-cooperative behaviors, a cooperation index and a three-tier management strategy, which incorporates intra-group negotiation, weight penalties and an exit-delegation mechanism, were introduced. In the case of strategic decision-making of new energy vehicles (NEV), after four rounds of feedback iterations, the group consensus level increased from the initial 0.316 to 0.804, reaching the preset threshold and verifying the effectiveness of the consensus mechanism. Compared with the existing literature methods, the framework in this paper achieves more comprehensive integration and innovation in four aspects: preference expression, clustering mechanism, consensus feedback and behavior management. Full article
(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)
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29 pages, 1195 KB  
Article
Multidimensional Evaluation of Sustainable Lettuce (Lactuca sativa L.) Production: Agronomic, Sensory, and Economic Criteria Using the Fuzzy PIPRECIA–Fuzzy MARCOS Model
by Radomir Bodiroga, Milena Marjanović, Vuk Maksimović, Đorđe Moravčević, Zorica Jovanović, Slađana Savić and Milica Stojanović
Horticulturae 2026, 12(3), 368; https://doi.org/10.3390/horticulturae12030368 - 16 Mar 2026
Viewed by 424
Abstract
Although greenhouse vegetable production is rapidly shifting toward innovative soilless systems, soil-based conventional cultivation still dominates globally. This production system faces growing pressure to transition to sustainable practices. However, introducing biofertilisers into intensive systems often yields inconsistent results. Specifically, their effects on different [...] Read more.
Although greenhouse vegetable production is rapidly shifting toward innovative soilless systems, soil-based conventional cultivation still dominates globally. This production system faces growing pressure to transition to sustainable practices. However, introducing biofertilisers into intensive systems often yields inconsistent results. Specifically, their effects on different lettuce traits vary due to complex relationships between genotype, biofertiliser, environmental conditions, and market demands. Single-parameter evaluations fail to balance conflicting criteria, necessitating multi-criteria decision-making (MCDM) methods for selecting optimal choices. This study aims to overcome these inconsistencies through an integrated fuzzy MCDM-based optimisation model. Three lettuce cultivars (‘Carmesi’, ‘Aquino’, and ‘Gaugin’) were grown in an unheated Surčin (Serbia) greenhouse during a 58-day autumn experiment using a complete block design. Four treatments were applied: a control (without fertilisation), effective microorganisms, a Trichoderma-based fertiliser, and their combination. Biofertilisers were applied before transplanting and four times foliarly during the vegetation period via battery sprayer. This defined 12 production models (cultivar–fertiliser pairs), evaluated across 10 criteria: agronomic (core ratio, number of leaves), quality (nitrate content, total antioxidant capacity, total soluble solids, and chlorogenic acid), sensory (overall taste, overall quality), and economic (total variable costs, total income). Four decision-making experts from the Faculty of Agriculture and the ready-to-eat salad industry assessed weighting coefficients using the fuzzy PIPRECIA (PIvot Pairwise RElative Criteria Importance Assessment) method. The fuzzy MARCOS (Measurement Alternatives and Ranking according to COmpromise Solution) method was used to rank the alternatives. To confirm the stability of the obtained ranking with the fuzzy MARCOS method, we performed sensitivity analysis through 20 different scenarios. Applied fuzzy methods identified alternative A11—‘Aquino’ cultivar with combined biofertilisers—as the best-ranked option, followed by A6 and A7. This study validates fuzzy PIPRECIA and fuzzy MARCOS as effective tools for optimising lettuce production models. They support farmers in selecting the most favourable solution based on multiple criteria, aiding the shift from mineral fertilisers to sustainable biofertiliser-based systems in intensive production—especially helpful for producers making this transition. Full article
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19 pages, 844 KB  
Article
Parallels and Meridians in the Intuitionistic Fuzzy Triangle: A Confidence-Aware Framework for Decision Making
by Vassia Atanassova and Peter Vassilev
Symmetry 2026, 18(3), 468; https://doi.org/10.3390/sym18030468 - 9 Mar 2026
Viewed by 285
Abstract
The paper proposes a completely new geometric interpretation of intuitionistic fuzzy sets for confidence-aware decision making. Instead of directly using ordered pairs of membership and non-membership degrees, we reinterpret the intuitionistic fuzzy triangle as a structured coordinate framework that simultaneously represents the evaluation [...] Read more.
The paper proposes a completely new geometric interpretation of intuitionistic fuzzy sets for confidence-aware decision making. Instead of directly using ordered pairs of membership and non-membership degrees, we reinterpret the intuitionistic fuzzy triangle as a structured coordinate framework that simultaneously represents the evaluation outcomes and the evaluators’ expertise in the following manner: experts’ confidence levels are modelled with line segments parallel to the hypotenuse, while evaluation scores are represented by line segments radiating from the origin of the coordinate system toward the hypotenuse. Their intersections form a finite lattice of points whose total number depends on the chosen confidence and assessment scales. The proposed construction preserves the semantic foundations of intuitionistic fuzziness: points closer to the origin reflect higher uncertainty in the evaluator’s confidence, while points onto the hypotenuse represent determinate judgments (with varying degrees of positivity or negativity) based on the complete evaluator’s confidence. The geometric distances between intersections provide a formal explanation of varying discriminative power: assessments from highly confident reviewers are more distinguishable than those from less confident ones. In addition, a colour-based visualization further supports the intuitive interpretation of confidence-weighted evaluations. The proposed framework offers an alternative yet fully consistent way to model expertise-dependent decision processes within the intuitionistic fuzzy setting, bridging geometric insight and practical evaluation scenarios via a structured system of parallels and meridians. Full article
(This article belongs to the Special Issue Symmetry and Fuzzy Set)
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22 pages, 1811 KB  
Article
A Dynamic Decision-Making Framework for Prioritizing Renewable Energy Technologies in Smart Cities Using Deep Learning and Hybrid Multi-Criteria Decision-Making
by Rashid Nasimov, Shukhrat Kamalov, Azamat Kakhorov, Jamila Kamalova and Rahma Aman
Energies 2026, 19(4), 1095; https://doi.org/10.3390/en19041095 - 21 Feb 2026
Viewed by 512
Abstract
Rapid energy planning in cities needs decision-support tools that can change based on the supply of renewable resources and the needs of stakeholders. This paper introduces an innovative adaptive decision-support framework that integrates Long Short-Term Memory (LSTM)-based short-term renewable energy forecasting with an [...] Read more.
Rapid energy planning in cities needs decision-support tools that can change based on the supply of renewable resources and the needs of stakeholders. This paper introduces an innovative adaptive decision-support framework that integrates Long Short-Term Memory (LSTM)-based short-term renewable energy forecasting with an interval-valued Pythagorean fuzzy Best-Worst Method–TOPSIS (IVPF-BWM–TOPSIS). This enables forecast-driven and temporally adaptive prioritisation of urban energy technologies, as opposed to static expert-based evaluation. Using criteria based on forecasted technical feasibility and scalability, the five green energy options that are looked at are rooftop solar, wind energy, smart grids, solar-integrated electric vehicle infrastructure, and battery energy storage. The best score is for rooftop solar (RDC = 0.65), followed by solar-integrated EV infrastructure (RDC = 0.566), and finally smart grids (RDC = 0.55). Wind energy gets the lowest score because it will not be very useful in cities. Sensitivity analysis (±20% weight change) and 15 scenario-based stress tests show that the framework is strong and does not change the order of the ranks. The results show that the proposed mixed AI and fuzzy method can be used to make plans for renewable energy in smart cities that are both based on data and can be used by many people. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
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21 pages, 1927 KB  
Article
A Dynamic Hybrid Weighting Framework for Teaching Effectiveness Evaluation in Multi-Criteria Decision-Making: Integrating Interval-Valued Intuitionistic Fuzzy AHP and Entropy Triggering
by Chengling Lu and Yanxue Zhang
Entropy 2026, 28(2), 241; https://doi.org/10.3390/e28020241 - 19 Feb 2026
Viewed by 479
Abstract
Multi-criteria decision-making (MCDM) problems in complex evaluation systems are often characterized by high uncertainty in expert judgments and dynamic variations in indicator importance. Traditional analytic hierarchy process (AHP) and entropy-based weighting methods typically suffer from two inherent limitations: the inability to explicitly quantify [...] Read more.
Multi-criteria decision-making (MCDM) problems in complex evaluation systems are often characterized by high uncertainty in expert judgments and dynamic variations in indicator importance. Traditional analytic hierarchy process (AHP) and entropy-based weighting methods typically suffer from two inherent limitations: the inability to explicitly quantify expert hesitation and the rigidity of static weight assignment under evolving data distributions. To address these challenges, this paper proposes a dynamic hybrid weighting framework that integrates an interval-valued intuitionistic fuzzy analytic hierarchy process (IVIF-AHP) with an entropy-triggered correction mechanism. First, interval-valued intuitionistic fuzzy numbers are employed to simultaneously model membership, non-membership, and hesitation degrees in pairwise comparisons, enabling a more comprehensive representation of expert uncertainty. Second, an entropy-triggered dynamic fusion strategy is developed by jointly incorporating information entropy and coefficient of variation, allowing adaptive adjustment between subjective expert weights and objective data-driven weights. This mechanism effectively enhances sensitivity to high-dispersion criteria while preserving expert knowledge in low-variability indicators. The proposed framework is formulated in a hierarchical fuzzy decision structure and implemented through a fuzzy comprehensive evaluation process. Its feasibility and robustness are validated through a concrete case study on teaching effectiveness evaluation for a university engineering course, leveraging multi-source data. Comparative analysis demonstrates that the proposed approach effectively mitigates the weight rigidity and evaluation inflation observed in conventional methods. Furthermore, it improves diagnostic resolution and decision stability across different evaluation periods. The results indicate that the proposed entropy-triggered IVIF-AHP framework provides a mathematically sound and practically applicable solution for dynamic MCDM problems under uncertainty, with strong potential for extension to other complex evaluation and decision-support systems. Full article
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