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Search Results (2,143)

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16 pages, 1419 KB  
Article
Study on Risk Analysis of a Rotary Kiln-Based Activated Carbon Manufacturing Process Using Fuzzy-FMEA
by Jong Gu Kim and Byong Chol Bai
Processes 2026, 14(7), 1071; https://doi.org/10.3390/pr14071071 - 27 Mar 2026
Abstract
Rotary kiln-based activated carbon production combines high-temperature operation with flammable/reducing gases, carbonaceous dust, and downstream off-gas treatment and acid/base washing, creating complex escalation pathways. This study prioritizes safety improvements by applying classical failure modes and effects analysis (FMEA) and a transparent Fuzzy-FMEA framework [...] Read more.
Rotary kiln-based activated carbon production combines high-temperature operation with flammable/reducing gases, carbonaceous dust, and downstream off-gas treatment and acid/base washing, creating complex escalation pathways. This study prioritizes safety improvements by applying classical failure modes and effects analysis (FMEA) and a transparent Fuzzy-FMEA framework to 18 representative failure modes (six each for kiln/activation, acid/base handling, and atmosphere/control). Five experts evaluated Severity, Occurrence, and Detection on a 10-point scale. The fuzzy model used triangular membership functions (L/M/H), a monotonic 27-rule base, Mamdani max–min inference, and centroid defuzzification to compute a continuous fuzzy risk priority number (FRPN, 0–10). Classical FMEA identified dust explosion (RPN = 405), temperature control failure (RPN = 378), and off-gas leakage (RPN = 324) as the highest-ranked risks. Fuzzy-FMEA preserved the top-risk group while more strongly highlighting barrier-related risks, placing off-gas leakage, instrumentation/interlock failure, and electrostatic ignition control alongside dust explosion (FRPN 9.221–9.332). The rankings were strongly correlated (Spearman ρ = 0.871; Kendall τ = 0.752), yet mid-risk items were rearranged (mean |Δrank| = 2.06; max = 5), improving discrimination within tied RPN clusters. The five highest-priority scenarios were reconstructed into actionable engineering packages, including dust and ignition control, off-gas integrity linked to shutdown logic, interlock proof testing and bypass management, and independent protection layers for kiln temperature control. Full article
(This article belongs to the Special Issue Optimization and Analysis of Energy System)
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18 pages, 2328 KB  
Article
Advancing Path Choice in Transport Systems: Insights from Fuzzy Logic Models
by Antonino Vitetta
Sustainability 2026, 18(7), 3236; https://doi.org/10.3390/su18073236 - 26 Mar 2026
Abstract
This paper presents a comprehensive formulation of fuzzy path choice, based on representing utilities through fuzzy numbers. This approach advances the modelling of path choice problems in transportation systems. This model improves the ability to capture the uncertainty of travellers’ perceptions and behaviours, [...] Read more.
This paper presents a comprehensive formulation of fuzzy path choice, based on representing utilities through fuzzy numbers. This approach advances the modelling of path choice problems in transportation systems. This model improves the ability to capture the uncertainty of travellers’ perceptions and behaviours, providing an alternative to traditional probabilistic frameworks. These models are the core of the assignment models used to simulate transport systems and calculate sustainability indicators. To support its use in assignment procedures, the paper set out the mathematical operations required for manipulating fuzzy quantities, ensuring internal consistency and operational feasibility. A key contribution is the combined use of normalised and non-normalised fuzzy numbers, which increases modelling flexibility and provides a novel way to simulate path overlap. The model is based on two approaches: the introduction of a factor that modifies the core of the fuzzy number, and an approach that modifies the confidence of the fuzzy number. The two approaches are specified and applied in a test network. Numerical applications demonstrate that the proposed method effectively accounts for path dependencies where traditional fuzzy operators fail. Full article
(This article belongs to the Special Issue Sustainable and Smart Transportation Systems)
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20 pages, 375 KB  
Article
Higher-Order Fuzzy Difference Equations: Existence, Stability, and Illustrative Numerical Examples
by Hashem Althagafi and Ahmed Ghezal
Mathematics 2026, 14(6), 1051; https://doi.org/10.3390/math14061051 - 20 Mar 2026
Viewed by 117
Abstract
This paper examines the dynamics of positive solutions to a system of fuzzy difference equations, which provide effective tools for modeling dynamical systems with uncertain or imprecise parameters. The main objective is to establish the existence, uniqueness, and qualitative properties of positive solutions [...] Read more.
This paper examines the dynamics of positive solutions to a system of fuzzy difference equations, which provide effective tools for modeling dynamical systems with uncertain or imprecise parameters. The main objective is to establish the existence, uniqueness, and qualitative properties of positive solutions within a fuzzy framework. After recalling some fundamental notions from fuzzy set theory, we analyze the dynamics of the proposed system. The main results prove the existence of a unique positive fuzzy solution under suitable conditions and establish the boundedness, continuity, and convergence of the solutions. In particular, all solutions converge to a unique positive equilibrium point. Numerical experiments for (l1,l2)=(2,3) and (l1,l2)=(4,1) with uncertainty levels γ=0.2 and γ=0.8 illustrate the theoretical results and confirm the convergence toward the unique positive equilibrium. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Chaos, and Mathematical Physics)
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29 pages, 2311 KB  
Review
Trust Assessment Methods for Blockchain-Empowered Internet of Things Systems: A Comprehensive Review
by Mostafa E. A. Ibrahim, Yassine Daadaa and Alaa E. S. Ahmed
Appl. Sci. 2026, 16(6), 2949; https://doi.org/10.3390/app16062949 - 18 Mar 2026
Viewed by 185
Abstract
The Internet of things (IoT) is rapidly pervading daily life and linking everything. Although higher connectivity offers many benefits, including higher productivity, robotic processes, and decision-making guided by data, it also poses a number of security dangers. Modern risks to data authenticity and [...] Read more.
The Internet of things (IoT) is rapidly pervading daily life and linking everything. Although higher connectivity offers many benefits, including higher productivity, robotic processes, and decision-making guided by data, it also poses a number of security dangers. Modern risks to data authenticity and confidence are getting harder to handle through typical central safety solutions. In this paper, we present a detailed investigation of the latest innovations and approaches for assessing reputation and confidence in the blockchain-empowered Internet of Things (BIoT) area. A comprehensive literature search was conducted across major electronic databases, including IEEE, Springer, Elsevier, Wiley, MDPI, and top indexed conference proceedings. The publication year was restricted to the period from 2018 to 2025. The methodological quality of a total of 122 studies met the inclusion criteria assessed using predefined quality measures. We figure out existing flaws at each layer of IoT architecture, illustrating how autonomous, transparent, and impenetrable blockchain ledgers address these flaws. Plus, we analytically compare public, private, consortium, and hybrid blockchain networking architectures to emphasize the underlying compromises among security, reliability, and decentralization. We also assess how reputation evaluation techniques evolved over time, moving from classical fuzzy logic and weighted average models to modern mature game theory and machine learning (ML) models, addressing their limitations in terms of computational overhead, scalability, adaptability, and deployment feasibility in IoT systems. Additionally, we outline future directions for BIoT system trust assessment and identify research limitations and potential solutions. Our research indicates that although ML-driven models offer more accurate predictions for identifying illicit node activities, they are still constrained by limited unbalanced data and high processing overhead. Full article
(This article belongs to the Special Issue Advanced Blockchain Technologies and Their Applications)
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26 pages, 1106 KB  
Article
An Improved Intuitionistic Fuzzy Set TOPSIS Method Based on a New Distance Measure with an Application to Marine Aquaculture Water Quality Evaluation
by Shanshan Ge, Hui Lin, Yizhi Wang, Fengyuan Ma and Lixin Zhai
Water 2026, 18(6), 712; https://doi.org/10.3390/w18060712 - 18 Mar 2026
Viewed by 105
Abstract
With the rapid development of intensive marine aquaculture, water quality has become a key factor affecting both economic benefits and ecological safety in marine aquaculture. In the process of actual water quality evaluation, due to the great uncertainty and ambiguity of evaluation indicators, [...] Read more.
With the rapid development of intensive marine aquaculture, water quality has become a key factor affecting both economic benefits and ecological safety in marine aquaculture. In the process of actual water quality evaluation, due to the great uncertainty and ambiguity of evaluation indicators, experts find it difficult to evaluate in real number form and are more inclined to use linguistic variables to evaluate indicators, which poses challenges for the construction of water quality evaluation models. An intuitionistic fuzzy set (IFS) is an effective tool for dealing with uncertainty and fuzziness in complex problems. Based on a detailed analysis of existing distance measures for IFS, this study proposes a new distance measure that not only considers membership and non-membership information, but also constructs an allocation function for membership and non-membership, introducing hesitation information into distance metrics. We proposed the definitions and proved the properties. The comparative experiments show that the new distance measure can overcome the shortcomings of existing distance measures. Furthermore, based on the newly proposed distance measure, the IFS TOPSIS method is improved in multi-attribute decision-making applications. Finally, a practical application of marine aquaculture water quality evaluation is used. The results illustrate that when α = 1 the closeness declines from 0.741 to 0.432, when =2 the closeness declines from 0.662 to 0.46, and when =6 the closeness declines from 0.566 to 0.82. The convenience and effectiveness of the new method is demonstrated. Full article
(This article belongs to the Section Water, Agriculture and Aquaculture)
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22 pages, 1016 KB  
Article
Critical Resilience Factors for Post-Disaster Tourism Recovery: Evidence from Baños de Agua Santa via Fuzzy Multi Criteria Analysis
by Giovanni Herrera-Enríquez, Eddy Castillo-Montesdeoca, Luis Simbaña-Taipe and Juan Gabriel Martínez-Navalón
Tour. Hosp. 2026, 7(3), 84; https://doi.org/10.3390/tourhosp7030084 - 17 Mar 2026
Viewed by 207
Abstract
Tourism destinations exposed to chronic natural hazards require robust analytical frameworks to understand and prioritize the factors that sustain post-disaster resilience. This study examines Baños de Agua Santa (Ecuador), a volcano-exposed destination whose long recovery trajectory illustrates the complexity of socio-ecological adaptation. Using [...] Read more.
Tourism destinations exposed to chronic natural hazards require robust analytical frameworks to understand and prioritize the factors that sustain post-disaster resilience. This study examines Baños de Agua Santa (Ecuador), a volcano-exposed destination whose long recovery trajectory illustrates the complexity of socio-ecological adaptation. Using a multidimensional FAHP model grounded in expert judgments, eight dimensions and fifty-six criteria were evaluated through fuzzy triangular numbers and the extended analysis method of Chang to capture uncertainty and ambiguity in decision-making. Results show a consistent and hierarchical structure of resilience, with experiential, economic-entrepreneurial, and socio-community dimensions emerging as the most influential drivers of post-disaster adaptability. Fifteen criteria—primarily perceptual, community-based, and endogenous—achieved “very high impact” status, including risk perception, basic education, individual resilience capacities, institutional coordination, and entrepreneurial environment. Conversely, limited healthcare infrastructure, low economic diversification, and national-level vulnerabilities were identified as critical weaknesses. The study concludes that post-disaster recovery in Baños is shaped by a bottom-up dynamic that emphasizes agency, learning and socio-ecological memory. It also proposes an evidence-based Action Matrix for adaptive governance to guide prioritized, time-phased interventions. The FAHP model proves effective for transparent, context-sensitive prioritization in highly uncertain tourism environments. Full article
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22 pages, 8220 KB  
Article
Waterlogging Risk Assessment of Airport Airfield Areas Using the Analytic Network Process with Triangular Fuzzy Numbers
by Jing Peng, Rui Li, Fuchang Tian and Shu Wang
Water 2026, 18(6), 701; https://doi.org/10.3390/w18060701 - 17 Mar 2026
Viewed by 195
Abstract
Risk assessment is an effective management tool for mitigating waterlogging disasters. In this study, a novel airport waterlogging risk assessment framework based on the analytic network process with triangular fuzzy numbers (TFN-ANP) was developed to evaluate hazard, exposure, vulnerability, and comprehensive risk under [...] Read more.
Risk assessment is an effective management tool for mitigating waterlogging disasters. In this study, a novel airport waterlogging risk assessment framework based on the analytic network process with triangular fuzzy numbers (TFN-ANP) was developed to evaluate hazard, exposure, vulnerability, and comprehensive risk under different return periods. The proposed framework was compared with the triangular fuzzy analytic hierarchy process (TFN-AHP). The results indicated that water depth, land cover type, and maintenance cost exerted dominant influences on hazard, exposure, and vulnerability, respectively. Compared with TFN-AHP, TFN-ANP produced different global weight distributions and a broader spatial extent of high-risk areas. Under the 50-year return period, TFN-ANP classified 31.65% of the study area as highest-risk, whereas TFN-AHP did not delineate any highest-risk zones and classified 40.05% of the study area as higher risk. A similar pattern was observed under the 100-year return period. TFN-ANP delineated 35.41% of the study area as being at the highest risk under the 100-year return period. By explicitly accounting for interdependencies among risk factors, TFN-ANP generated more differentiated spatial risk patterns. The proposed framework provides an effective decision-support tool for waterlogging risk management in data-scarce airport environments. Full article
(This article belongs to the Section Hydrology)
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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 167
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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22 pages, 967 KB  
Article
Solutions of a Fuzzy Difference Equation with Maximum
by Lirong Ma, Changyou Wang and Yue Sun
Axioms 2026, 15(3), 202; https://doi.org/10.3390/axioms15030202 - 9 Mar 2026
Viewed by 183
Abstract
This paper systematically investigates the dynamical properties of a class of max-type fuzzy difference equation. The study first establishes the existence and uniqueness of the solution sequence under given initial conditions with positive fuzzy numbers. Subsequently, by applying the cut-set theory, the fuzzy [...] Read more.
This paper systematically investigates the dynamical properties of a class of max-type fuzzy difference equation. The study first establishes the existence and uniqueness of the solution sequence under given initial conditions with positive fuzzy numbers. Subsequently, by applying the cut-set theory, the fuzzy equation is transformed into a system coupled by two ordinary difference equations. Through a combination of case analysis and mathematical induction, the study rigorously demonstrates that the solutions of this system exhibit global periodicity with a period of 4, while also deriving the exact closed-form expressions of the periodic solutions. Based on the periodic solutions obtained from the ordinary difference system, the research successfully reveals the periodic characteristics of the solutions to the original fuzzy difference equation and rigorously analyzes their boundedness and persistence. Finally, numerical simulations conducted with Matlab 2016 provide robust data support for the theoretical conclusions and the effectiveness of the methodology. Full article
(This article belongs to the Special Issue Delay Differential Equations: Theory, Control and Applications)
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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 204
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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25 pages, 1774 KB  
Article
An Agentic Digital Twin Framework for Fuzzy Multi-Objective Optimization in Dynamic Humanitarian Logistics
by Zornitsa Yordanova and Hamed Nozari
Algorithms 2026, 19(3), 198; https://doi.org/10.3390/a19030198 - 6 Mar 2026
Viewed by 352
Abstract
Humanitarian logistics faces challenges such as conflicting objectives, severe uncertainty, temporal dynamics, and the need for interpretable decisions. This research presents an integrated decision-making framework that simultaneously considers fuzzy uncertainty, system dynamics, and adaptive decision logic. Operational uncertainties are modeled using triangular fuzzy [...] Read more.
Humanitarian logistics faces challenges such as conflicting objectives, severe uncertainty, temporal dynamics, and the need for interpretable decisions. This research presents an integrated decision-making framework that simultaneously considers fuzzy uncertainty, system dynamics, and adaptive decision logic. Operational uncertainties are modeled using triangular fuzzy numbers and a dynamic representation of the system allows for continuous updating of decisions over time. Computational results based on simulated data show that the proposed framework is capable of generating stable, diverse, and interpretable solutions. An improvement in the average quality of the Pareto front of more than 5% and a reduction in the distance from the reference front of about 30% are observed compared to non-adaptive approaches. Also, stability and dynamic behavior analyses show that the decisions are robust to changing environmental conditions and parameters and have high adaptability. These features make the proposed framework a reliable tool for decision support in relief operations. Full article
(This article belongs to the Special Issue Optimizing Logistics Activities: Models and Applications)
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22 pages, 405 KB  
Article
A Fermatean Fuzzy SWARA-TOPSIS Based Approach for Sustainable Packaging Selection in Logistics Operations
by Sedat Belbağ
Sustainability 2026, 18(5), 2522; https://doi.org/10.3390/su18052522 - 4 Mar 2026
Viewed by 251
Abstract
This study presents an integrated Multi-Criteria Decision-Making (MCDM) approach to select the most suitable sustainable packaging for logistics operations under uncertainty. The aim of this study is to identify the most suitable eco-friendly packaging options for reducing packaging waste, by considering several criteria. [...] Read more.
This study presents an integrated Multi-Criteria Decision-Making (MCDM) approach to select the most suitable sustainable packaging for logistics operations under uncertainty. The aim of this study is to identify the most suitable eco-friendly packaging options for reducing packaging waste, by considering several criteria. The methodology combines the SWARA and TOPSIS methods within a Fermatean Fuzzy Set (FFS) framework to address the ambiguity in expert evaluations and the qualitative nature of decision-making criteria. The research considers various sustainable packaging alternatives, including recycled cardboard, recycled plastic, biodegradable plastic, and compostable plastic, while incorporating criteria such as production cost, environmental impact, reusability, and material specifications. The approach offers a robust and comprehensive decision-making tool for companies aiming to improve sustainability in their logistics operations while mitigating the environmental impact of packaging waste. The results demonstrate that the direct incorporation of fuzzy numbers notably influences the ranking outcomes compared to traditional methods, and comparing the considered approach with different MCDM methods yields various recommendations for sustainable packaging selection. Full article
(This article belongs to the Section Sustainable Products and Services)
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20 pages, 390 KB  
Article
Selection of Urban Overtourism Management Strategies in Croatia: The Case of Zadar County
by Jurica Bosna, Anđelka Štilić and Adis Puška
Urban Sci. 2026, 10(3), 139; https://doi.org/10.3390/urbansci10030139 - 4 Mar 2026
Viewed by 330
Abstract
This research assessed management strategies for overtourism in Zadar County. Overtourism has become apparent in both city and seaside destinations, affecting residents’ quality of life. This study defines overtourism as a challenge for urban management, emphasizing that exploring strategies to address overtourism also [...] Read more.
This research assessed management strategies for overtourism in Zadar County. Overtourism has become apparent in both city and seaside destinations, affecting residents’ quality of life. This study defines overtourism as a challenge for urban management, emphasizing that exploring strategies to address overtourism also influences the management of sustainability and quality of life in urban areas. Here, a methodological framework was created with five strategies, each evaluated against seven criteria. The evaluation was carried out by the directors of the county’s tourist boards. Since these strategies have not yet been implemented, the directors had to rate them with some uncertainty, as they lacked complete information about the criteria and potential effects. To handle this uncertainty, the intuitionistic fuzzy set (IFS) approach was used. Additionally, the SiWeC method determined the importance of the criteria, and the TOPSIS method ranked the strategies. Results, based on ratings from 12 directors, indicated that Digital Support and Environmental Sustainability are the most important criteria. Strategy C, which aims to redirect tourists to lesser-known locations within the county, performed best, maintaining visitor numbers while helping preserve the region’s natural resources. This research has shown that strategies for managing overtourism help reduce the pressure tourists place on urban environments, thereby improving the quality of life and sustainable development of these environments. Full article
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24 pages, 384 KB  
Article
Evaluation of Strategic Management Strategies for Reducing Household Municipal Waste Using Symmetric Fuzzy Numbers
by Adis Puška, Dejan Antanasković, Vladica Ristić, Vladimir Tomašević, Danijela Despotović, Anđelka Štilić and Radivoj Prodanović
Symmetry 2026, 18(3), 428; https://doi.org/10.3390/sym18030428 - 28 Feb 2026
Viewed by 248
Abstract
This research aimed to examine which of the selected strategies can most effectively influence households to reduce their total municipal waste and thus protect the environment. To achieve this goal, a sample of 202 households from the Brčko District of BiH was used. [...] Read more.
This research aimed to examine which of the selected strategies can most effectively influence households to reduce their total municipal waste and thus protect the environment. To achieve this goal, a sample of 202 households from the Brčko District of BiH was used. Respondents evaluated six strategies against ten criteria, expressing their assessments through linguistic values. These linguistic inputs were modeled using symmetric fuzzy numbers, ensuring a consistent and mathematically robust representation of uncertainty and subjective judgment. The research used the fuzzy SiWeC (Simple Weight Calculation) method to determine the importance of the criteria, and the fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), ARAS (Additive Ratio Assessment), and SAW (Simple Additive Weighted) methods to rank the strategies. The application of several methods in decision-making helps validate results and verify the robustness of strategy selection. These methods identified “waste reduction efficiency” as the most important criterion and “Strategy 3—Packaging return machines” as the most effective overall. Furthermore, analysis of demographic subgroups revealed significant variations in the perceived value of alternative strategies. Consequently, this study concludes that to optimize municipal waste management, strategies should be tailored to specific demographic profiles. This targeted approach would enhance waste reduction at the source, divert more waste from landfills, and promote the broader implementation of circular economy principles. The use of symmetric fuzzy numbers provided a reliable and stable foundation for this multi-criteria decision-making analysis. Full article
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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 361
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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