Search Results (147)

Traditional fuzzy decision-making often relies on manual expert calibration, which is labor-intensive and susceptible to subjective bias. This study addresses these limitations by proposing a novel framework that transforms the intrinsic probabilistic outputs of Large Language Models (LLMs) into Triangular Fuzzy Numbers (TFNs). We introduce a multi-temperature sampling strategy coupled with weighted quantile aggregation and an adaptive interval adjustment mechanism to systematically map model stochasticity to fuzzy possibility distributions. Empirical validation on a structured prototype dataset demonstrates that the proposed method achieves high consistency with expert consensus, with GPT-4.2 exhibiting superior central accuracy and Gemini-2.5 excelling in uncertainty coverage. Furthermore, in complex unstructured scenarios involving business public opinion, the integration of Model Context Protocol (MCP) and Retrieval-Augmented Generation (RAG) significantly corrects cognitive biases and converges uncertainty boundaries. This research establishes a rigorous pathway from generative AI probabilities to fuzzy decision theory, offering a robust automated solution for quantitative risk assessment and intelligent decision support. Full article

In this study, we introduce new versions of fuzzy fractional integral operators for both one- and two-variable cases. Using these operators, several Hermite–Hadamard-type ($H$-type) inclusions are established for fuzzy-number-valued convex functions ($F$·$N\cdot V$-functions) and $F$·$N\cdot V$-coordinated convex functions. These results are obtained by employing $F$·$N\cdot V$-weighted functions within the framework of the newly defined Hadamard and generalized fractional integrals in one- and two-dimensional settings. The use of generalized fractional integral operators provides a unified approach that encompasses a wide class of classical and modern fractional integrals, including the fuzzy Riemann–Liouville and Hadamard types. This unified setting enables the derivation of more comprehensive and flexible inequality results in the fuzzy-number context. The inclusions obtained in this work significantly extend and generalize several known $H\cdot H$-type inequalities previously established for real-valued and interval-valued functions ($I\cdot V$-functions). Furthermore, the proposed results yield a variety of meaningful special cases by specifying suitable kernel functions and parameters of the generalized fractional integrals. In particular, we derive new weighted $H\cdot H$-type inclusions involving logarithmic functions in the fuzzy-number framework. These findings underscore the effectiveness of generalized fractional integrals in capturing nonlocal behavior and uncertainty, and they provide new tools for further investigations in fuzzy analysis, fractional calculus, and generalized convexity. Full article

Geological storage of carbon dioxide in faulted sedimentary basins requires suitability evaluation methods that can address uncertainty, indicator interaction, and limited data availability. This study develops an integrated evaluation framework that combines the Analytic Hierarchy Process, triangular fuzzy numbers, and the Choquet fuzzy integral to assess basin-scale geological carbon dioxide storage suitability. The framework enables structured weight determination, explicit representation of expert uncertainty, and non-additive aggregation of interacting indicators. The evaluation focuses on deep saline aquifers in the Jianghan Basin and is based on seventeen indicators covering geological, structural, hydrogeological, and socio-economic conditions. The assessment integrates seismic interpretation, geological mapping, logging data, and published datasets, and is conducted at the level of tectonic units to support basin-scale screening. The method is applied to the Jianghan Basin using seventeen geological, structural, hydrogeological, and socio-economic indicators. The results indicate that burial depth primarily acts as a threshold condition, whereas caprock sealing capacity, fault system development, and hydrogeological stability dominate suitability differentiation. Interaction analysis reveals pronounced substitution effects among geological indicators, indicating that strong performance in key safety-related factors can compensate for less favorable secondary constraints during early-stage screening. The Qianjiang Sag and Jiangling Sag are identified as the most suitable storage units. The proposed framework provides a transparent and robust tool for basin-scale screening in structurally complex, data-limited sedimentary basins. Full article

Fuzzy Cognitive Maps (FCMs) are a type of recurrent neural network with built-in meaning in their architecture, originally devoted to modeling and scenario simulation tasks. These knowledge-based neural systems support feedback loops that handle static and temporal data. Over the last decade, there has been a noticeable increase in the number of contributions dedicated to developing FCM-based models and algorithms for structured pattern classification and time series forecasting. These models are attractive since they have proven competitive compared to black boxes while providing highly desirable interpretability features. Equally important are the theoretical studies that have significantly advanced our understanding of the convergence behavior and approximation capabilities of FCM-based models. These studies can challenge individuals who are not experts in Mathematics or Computer Science. As a result, we can occasionally find flawed FCM studies that fail to benefit from the theoretical progress experienced by the field. To address all these challenges, this survey paper aims to cover relevant theoretical and algorithmic advances in the field, while providing clear interpretations and practical pointers for both practitioners and researchers. Additionally, we will survey existing tools and software implementations, highlighting their strengths and limitations towards developing FCM-based solutions. Full article

Airborne magnetic particles (AMPs) are associated with potentially toxic elements, and their size, mineralogy, and concentration can significantly impact both the environment and human health. However, their spatial analysis is often limited by small datasets, non-normality, and pronounced local variability. In this work, two sites with distinct demographic and geographic characteristics, the city of Mar del Plata (Argentina) and the Aburrá Valley region (Colombia), were analyzed using the fuzzy Magnetic Pollution Index (IMC) as an indicator of the concentration of AMPs. Moreover, an original methodological framework that explicitly incorporates measurement uncertainty through fuzzy numbers, combined with an approach modeling fuzzy semivariances via α-cuts, performs spatial prediction via ordinary kriging. This study produces maps that simultaneously reflect the magnitude of IMC and its associated uncertainty. Unlike classical geostatistics, the fuzzy-based model captures the inherent imprecision of magnetic measurements and reveals spatial patterns where uncertainty becomes informative about the type and origin of pollution. In particular, this approach demonstrates that areas with higher IMC levels are associated with high anthropic activity (near industrial zones, main avenues, slow traffic). In contrast, lower values were found in residential areas. Overall, the fuzzy-driven approach provides an additional layer of information not accessible through traditional methods, improving spatial interpretation and supporting the identification of priority areas for environmental monitoring. Full article

Maximum power point tracking (MPPT) under partial shading is a nonconvex, rapidly varying control problem that challenges multi-agent policies deployed on photovoltaic modules. We present Fuzzy–MAT3D, a fuzzy-augmented multi-agent TD3 (Twin-Delayed Deep Deterministic Policy Gradient) controller trained under centralized training/decentralized execution (CTDE). On the theory side, we prove that differentiable fuzzy partitions of unity endow the actor–critic maps with global Lipschitz regularity, reduce temporal-difference target variance, enlarge the input-to-state stability (ISS) margin, and yield a global $L_{\infty }$$\gamma$-contraction of fixed-policy evaluation (hence, non-expansive with $\kappa =\gamma <1$). We further state a two-time-scale convergence theorem for CTDE-TD3 with fuzzy features; a PL/last-layer-linear corollary implies point convergence and uniqueness of critics. We bound the projected Bellman residual with the correct contraction factor (for $L^{\infty }$ and $L^2\left(\rho \right)$ under measure invariance) and quantified the negative bias induced by $min\{Q_1,Q_2\}$; an N-agent extension is provided. Empirically, a balanced common-random-numbers design across seven scenarios and 20 seeds, analyzed by ANOVA and CRN-paired tests, shows that Fuzzy–MAT3D attains the highest mean MPPT efficiency (92.0% ± 4.0%), outperforming MAT3D and Multi-Agent Deep Deterministic Policy Gradient controller (MADDPG). Overall, fuzzy regularization yields higher efficiency, suppresses steady-state oscillations, and stabilizes learning dynamics, supporting the use of structured, physics-compatible features in multi-agent MPPT controllers. At the level of PV plants, such gains under partial shading translate into higher effective capacity factors and smoother renewable generation without additional hardware. Full article

As a foundational analytical tool, the discernibility matrix plays a pivotal role in the systematic reduction of knowledge in rough set-based systems. Recent advancements in rough set theory have witnessed the proliferation of discernibility matrix-based knowledge reduction algorithms, with notable applications in classical, neighborhood, covering, and fuzzy rough set models. However, the quadratic growth of the discernibility matrix’s complexity (relative to domain size) imposes fundamental scalability limits, rendering it inefficient for real-world applications with massive datasets. To address this issue, we introduced a discernibility hashing strategy to limit the growth scale of the discernibility attributes and proposed a feature selection algorithm via discernibility hash based on rough set theory. First, on the premise of keeping the information of the original discernibility matrix unchanged, the method maps the discernibility attribute set of all objects to the storage unit through a hash function and records the number of collisions to construct a discernibility hash. By using this mapping, the two-dimensional matrix space can be reduced to a one-dimensional hash space, which greatly removes invalid and redundant elements. Secondly, based on the discernibility hash, an efficient knowledge reduction algorithm is proposed. The algorithm avoids invalid and redundant element attribute sets to participate in the knowledge reduction process and improves the efficiency of the algorithm. Finally, the experimental results show that the method is superior to the discernibility matrix method in terms of storage space and running time. Full article

We address information fusion and spatial structure modeling in high-dimensional fuzzy multi-attribute decision-making by proposing a novel framework that couples Triangular Intuitionistic Fuzzy Numbers (TIFNs) with the Plant Growth Simulation Algorithm (PGSA). The method first maps the triangular intuitionistic fuzzy information of experts on each evaluation scheme into high-dimensional spatial points to realize the structured expression of decision-making information. Subsequently, the PGSA is used to perform dynamic global optimization search on the high-dimensional point cloud to determine the optimal set point and realize the intelligent aggregation of heterogeneous fuzzy data from multiple sources. The algorithm breaks through the limitation of traditional linear aggregation on the portrayal of information spatial distribution and is able to improve the accuracy and consistency of decision-making results in high-dimensional complex environments. The experimental results show that the method in this paper outperforms the mainstream aggregation methods in a number of evaluation indexes such as weighted Hamming distance, correlation, information energy and correlation coefficient. The proposed model provides a new technical path for intelligent solution and theory expansion of high-dimensional fuzzy decision-making problems. Full article

We consider finite B-fuzzy topologies, that is, collections of mappings from a finite set to the Boolean algebra B, satisfying analogous conditions of classical topologies. We establish a one-to-one correspondence between the class of B-fuzzy topologies and the corresponding class of classical ones. Then many consequences follow. For example, we deduce the number of B-fuzzy topologies of small size. Full article

The quality of groundwater, a crucial freshwater resource in cold regions, directly affects human health. This study used groundwater quality monitoring data collected in the central Songnen Plain in 2014 and 2022 as a case study. The improved DRASTICL model was used to assess the vulnerability index, while water quality indicators were selected using a random forest algorithm and combined with the entropy-weighted groundwater quality index (E-GQI) approach to realize water quality assessment. Furthermore, self-organizing maps (SOM) were used for pollutant source analysis. Finally, the study identified the synergistic migration mechanism of NH₄⁺ and Cl⁻, as well as the activation trend of As in reducing environments. The uncertainty inherent to health risk assessment was considered by developing a kernel density estimation–trapezoidal fuzzy number–Monte Carlo simulation (KDE-TFN-MCSS) model that reduced the distribution mis-specification risks and high-risk misjudgment rates associated with conventional assessment methods. The results indicated that: (1) The water chemistry type in the study area was predominantly HCO₃⁻–Ca²⁺ with moderately to weakly alkaline water, and the primary and nitrogen pollution indicators were elevated, with the average NH₄⁺ concentration significantly increasing from 0.06 mg/L in 2014 to 1.26 mg/L in 2022, exceeding the Class III limit of 1.0 mg/L. (2) The groundwater quality in the central Songnen Plain was poor in 2014, comprising predominantly Classes IV and V; by 2022, it comprised mostly Classes I–IV following a banded distribution, but declined in some central and northern areas. (3) The results of the SOM analysis revealed that the principal hardness component shifted from Ca²⁺ in 2014 to Ca²⁺–Mg²⁺ synergy in 2022. Local high values of As and NH₄⁺ were determined to reflect geogenic origin and diffuse agricultural pollution, whereas the Cl⁻ distribution reflected the influence of de-icing agents and urbanization. (4) Through drinking water exposure, a deterministic evaluation conducted using the conventional four-step method indicated that the non-carcinogenic risk (HI) in the central and eastern areas significantly exceeded the threshold (HI > 1) in 2014, with the high-HI area expanding westward to the central and western regions in 2022; local areas in the north also exhibited carcinogenic risk (CR) values exceeding the threshold (CR > 0.0001). The results of a probabilistic evaluation conducted using the proposed simulation model indicated that, except for children’s CR in 2022, both HI and CR exceeded acceptable thresholds with 95% probability. Therefore, the proposed assessment method can provide a basis for improved groundwater pollution zoning and control decisions in cold regions. Full article

Classifying study objects into groups is facilitated by fuzzy classifiers based on a set of rules and membership functions. Typically, the characteristics of the study objects are used to establish the criteria for classification. This work arises from the need to design fuzzy classifiers in contexts where real data is scarce or highly random, proposing a design based on statistics and chaotic maps that simplifies the design process. This study introduces the development of a fuzzy classifier, assuming that three features of the population to be classified are random variables. A Mamdani fuzzy inference system and three pseudorandom number generators based on one-dimensional chaotic maps are utilized to achieve this. The logistic, Bernoulli, and tent chaotic maps are implemented to emulate the random features of the target population, and their statistical distribution functions serve as input to the fuzzy inference system. Four experimental tests were conducted to demonstrate the functionality of the proposed classifier. The results show that it is possible to achieve a symmetric and robust classification through simple adjustments to membership functions, without the need for supervised training, which represents a significant methodological contribution, especially because this indicates that designers with minimal experience can build effective classifiers in just a few steps. Real applications of the proposed design may focus on the classification of biomedical signals (sEMG), network traffic, and personalized medical assistance systems, where data exhibits high variability and randomness. Full article

To enhance the safety risk management and control capabilities for TBM (Tunnel Boring Machine) construction in hydraulic tunnels, this study conducts a correlation analysis and dynamic evolution study of safety risks. Data were collected through multiple channels, including a literature review, on-site records, and expert interviews. Grounded theory was employed for three-level coding to initially identify risk factors, and gray relational analysis was used for indicator optimization, ultimately establishing a safety risk system comprising 5 categories and 21 indicators. A multi-level hierarchical structure of risk correlation was established using fuzzy DEMATEL and ISM, which was then mapped into a Bayesian network (BN). The degree of correlation was quantified based on probabilistic information, leading to the construction of a risk correlation analysis model based on fuzzy DEMATEL–ISM–BN. Furthermore, considering the risk correlations, a safety risk evolution model for TBM construction in hydraulic tunnels was developed based on system dynamics. The validity of the model was verified using the AY project as a case study. The results indicate that the safety risk correlation structure for TBM construction in hydraulic tunnels consists of 7 levels, with the closest correlation found between “inadequate management systems” and “failure to implement safety training and technical disclosure”. As the number of interacting risk factors increases, the trend of risk level evolution also rises, with the interrelations within the management subsystem being the key targets for prevention and control. The most sensitive factors within each subsystem were further identified as adverse geological conditions, improper construction parameter settings, inappropriate equipment selection and configuration, weak safety awareness, and inadequate management systems. The control measures proposed based on these findings can provide a basis for project risk prevention and control. The main limitations of this study are that some probability parameters rely on expert experience, which could be optimized in the future by incorporating more actual monitoring data. Additionally, the applicability of the established model under extreme geological conditions requires further verification. Full article

Robots play a crucial role in experimental smart cities and are ubiquitous in daily life, especially in complex environments where multiple robots are often needed to solve problems collaboratively. Researchers have found that the swarm intelligence optimization algorithm has a better performance in planning robot paths, but the traditional swarm intelligence algorithm cannot be targeted to solve the robot path planning problem in difficult problem. Therefore, this paper aims to introduce a fuzzy controller, mutation factor, exponential noise, and other strategies on the basis of particle swarm optimization to solve this problem. By judging the moving speed of different particles at different periods of the algorithm, the individual learning factor and social learning factor of the particles are obtained by fuzzy controller, and using the leader particle and random particle, designing a new dynamic balance of mutation factor, with the iterative process of the adaptation value of continuous non-updating counter and continuous updating counter to control the proportion of the elite individuals and random individuals. Finally, using exponential noise to update the matrix of the population every 50 iterations is a way to balance the local search ability and global exploration ability of the algorithm. In order to test the proposed algorithm, the main method of this paper is simulated on simple scenarios, complex scenarios, and random maps consisting of different numbers of static obstacles and dynamic obstacles, and the algorithm proposed in this paper is compared with eight other algorithms. The average path deviation error of the planned paths is smaller; the average distance of untraveled target is shorter; the number of steps of the robot movements is smaller, and the path is shorter, which is superior to the other eight algorithms. This superiority in solving multi-robot cooperative path planning has good practicality in many fields such as logistics and distribution, industrial automation operation, and so on. Full article

Real-time coordination of heterogeneous multi-agent systems in dynamic and partially observable environments poses significant challenges. To address this, we propose a framework that integrates fuzzy inference systems with real-valued genetic algorithms to optimize decision-making under strict time constraints and sensory uncertainty. We evaluate the proposed method in the RoboCup Soccer Simulation 2D League, where 22 autonomous agents coordinate through a fuzzy-evaluated action sequence search. Spatial heuristics are encoded as fuzzy rules, and optimization based on genetic algorithms refines evaluation function parameters according to performance metrics such as number of shots, goal area entries, and scoring rates. The resulting control strategy remains interpretable; spatial heat maps reveal emergent behaviors such as coordinated positioning and ridgeline passing patterns near the penalty area. The experiments against established RoboCup teams, serving as benchmarks, demonstrate the competitive performance of our trained agents while enabling analyses of evolving decision structures and agent behaviors. Our method provides a transparent and adaptable framework for controlling heterogeneous agents in uncertain real-time environments, with broad applicability to robotics, autonomous systems, and distributed control systems. Full article

This study is organized to introduce the concept of center–radius $\left(cr\right)$-ordered fuzzy number-valued convex mappings. Based on this class of mappings, we have initiated the idea of fuzzy number-valued extended $cr$-ℏ convex mappings incorporating control mapping ℏ. Furthermore, several potential new classes of convexity will be provided to discuss its generic nature. Also, some essential properties, criteria, and detailed characterizations through Jensen’s and Hermite–Hadamard-like inequalities are provided, incorporating Riemann–Liouville fractional operators, which are defined by $\rho$-level mappings. To validate the proposed fractional bounds through simulations, we consider both triangular and trapezoidal fuzzy numbers. Our results are based on totally ordered fuzzy-valued mappings, which are new and generic. The under-consideration class also includes a blend of new classes of convexity, which are controlled by non-negative mapping ℏ. In previous studies, the researchers have focused on different partially ordered relations. Full article