Fuzzy Theory Research Articles

On Connectivity of Multidimensional Fuzzy Graphs and its Applications

Connectivity, average connectivity, and its related concepts are prominent notions in fuzzy graph theory that have applications in various areas, including neural networks, transportation problems, cluster analysis, and telecommunication. This work introduces the concepts of connectivity index, average connectivity index, type 2 connectivity index, etc. to a more generalized variant of a fuzzy graph, namely the multidimensional fuzzy graph. Basic results such as the relation of these parameters to vertices and edges, their bounds in some particular multidimensional fuzzy graphs, etc. are studied with proper illustrations. Theorems on the connectivity index of multidimensional fuzzy graphs are obtained after performing operations like direct product, tensor product, composition, join, and so on. Finally, a decision-making problem that can be effectively handled using the connectivity index is demonstrated and compared with others and similar models.

On Domination and Related Concepts of Multidimensional Fuzzy Graphs and Their Applications

Domination and its associated concepts are significant ideas in fuzzy graph theory that have applications in diverse fields such as neural networks, game theory, and telecommunication. This study presents the notions of dominance and its associated research in a broader form of fuzzy graph called the multidimensional fuzzy graph. Basic results, such as the relationship between these parameters and vertices, edges, minimal sets, and so forth, are identified and illustrated with appropriate examples. The dominance number of multidimensional fuzzy graphs is determined after undergoing operations such as direct product, tensor product, composition, join, and others. Ultimately, this study displays a decision-making problem that can be efficiently addressed by utilizing the concept of the dominance number. The effectiveness of this approach is then compared to various models, like [Formula: see text]-polar fuzzy sets.

Application and Empirical Analysis of Fuzzy Neural Networks in Mining Social Media Users’ Behavioral Characteristics and Formulating Accurate Online Marketing Strategies

In the current digital social environment, social media platforms have become an important position for user behavior insights and precision marketing. User behavioral data on social media contain rich information, but they are often fuzzy, uncertain and highly complex. Fuzzy neural network (FNN), as an advanced model combining fuzzy logic and neural network theory, provides a powerful tool for processing and analyzing social media user behavioral features. This study is dedicated to exploring the application of fuzzy neural networks in social media user behavior analysis and their key role in the design of accurate online marketing strategies. We construct and optimize a fuzzy neural network model by meticulously classifying and quantifying user behavioral features, including behavioral frequency features, content topic features, social interaction features, and time series features, as well as applying fuzzy set theory to deal with fuzzy features such as emotional states. Through empirical analysis, we will show how fuzzy neural networks can reveal the intrinsic laws behind user behaviors, and how these insights can be used to design and implement precise online marketing strategies to improve advertising effectiveness, user engagement, and brand loyalty.

Clustering based fuzzy classification with a noise cluster in detecting fraud in insurance

Fraud detection is one of the main issues in reducing the unsystematic risks in insurance business as its costs might reach to catastrophic amounts leading to higher loadings on reserves and premiums. Due to its cause of nature in diversity, fraud detection may require a wide range of factors and variables to be considered. To make logical relations between many factors and reveal their differences, estimate odds (or probabilities), and predict the fraud risk, scoring systems become an important aid. In this paper, we introduce a clustering-based fuzzy classification with a noise cluster (CBFCN) to identify the true state of a fraud. The approach proposed in this paper is based on fuzzy k-means clustering having a noise cluster (FKMN) and is a novel method for identifying outliers by achieving robust clustering. We integrate fuzzy theory to boost the prediction ability of machine learning (ML) approaches for a proper determination of the contributing features. The two critical features of the CBFCN method which are the membership values obtained from the FKMN clustering algorithm are implemented to capture the behavior of an existing structure better and detect the noise (extremes) in the dataset. Extensive analyses are made on two real datasets exposing different characteristics in their variables to demonstrate how CBFCN performs in detecting the fraud compared to the conventional approaches. Additionally, employing fuzzy approach to improve the ML performance is elaborated through the inclusion of noise clusters. The findings indicate that the suggested CBFCN models produce promising classification results in fraud detection in insurance claims occurrences.

Full robustness-based decision-making computational approach for RC structures subjected to multiple hazards

Existing RC structures show accidental loadings vulnerabilities because of inadequate design detailing causing in premature failure. The installation of a certain reinforcement measure on the susceptible structure is a common option to mitigate these fragility. At this time, reinforcement measures aided by the participation of stakeholders are crucial to combat multiple hazards. However, previous studies did not necessarily dealt with the integration multi-hazard loss, multi-uncertainty, and dependence configuration in a performance-based engineering decision-making framework, to retrofit selection from the robustness of structures perspective. In this paper, an efficient fuzzy full robustness-based decision-making framework is proposed to tackle the challenge of integration of multi-uncertainty and dependence, and further to avoid biased strategies. This framework contained Probabilistic Multi-hazards Fuzzy Global Vulnerability (PMFGV), Loss (PMFGL), and Robustness Assessment (PMFRA) for structures, by incorporating the fuzzy theory and Vine-Copula tree structure. The mentioned robustness index can be used as a reference indicator in the rehabilitation and retrofitting planning. The PMFRA-based making-decision methodology is applied to RC structures with three design schemes, which were established the platform OpenSEEsPy. Results confirm that the established assessment framework is effective in evaluating actual RC structures’ robustness. The fuzzy full robustness index for the frame S-RC, SS-RC, and RS-RC, was < 0.327, 0.421, 0.470 > , < 0.400, 0.503, 0.523 > , < 0.356, 0.453, 0.507 > , respectively. Whether the robustness-cost-based or the Cumulative Prospect Theory-based, the robustness of the reinforcement strategy with the installation of secondary beam (SS-RC) outdistance that of the additional reinforcement ratio (RS-RC). Such parameters are suggested as reasonable and meaningful making-decision index for selecting the optimal retrofitting schemes for structures subjected to multiple hazards, which leads to a balance between the enhancement of full robustness and reduction of life cost.

An operational risk assessment method for petrochemical plants based on deep learning

The petrochemical industry is an important guarantee for the development of people’s lives, and the operational risk assessment method of personnel in the operation of petrochemical enterprises is the most important. Based on a deep learning algorithm, a new method based on the micro-Doppler effect and fuzzy analytic hierarchy process is proposed to evaluate the operational risk of personnel in petrochemical enterprises. The original monitoring image of petrochemical equipment is invoked, and micro-Doppler analysis is performed based on the original image to identify the activity target of the personnel on the job site and generate the activity map of the petrochemical plant operators. Based on the analysis data of the micro-Doppler effect, the fuzzy function and hierarchical analysis method are combined. The fuzzy theory is introduced into the analytic hierarchy process, and the inherent expert evaluation scores are transformed into fuzzy numbers. It makes the expert evaluation of petrochemical plants more accurate in the subsequent coupling and improves the objectivity of the traditional analytic hierarchy process. The scheme proposed in this paper can monitor real-time operation safety and provide a guarantee for the personal safety of field operators. This method plays an important role in improving the safety of petrochemical plants.

A novel hybrid forecasting system for crude oil futures prices: A dual perspective of deterministic forecasting and uncertainty analysis

The crude oil market occupies a crucial place in the composition of the global economy, however, the high level of uncertainty in crude oil prices makes it a challenging task to construct reliable forecasting techniques to obtain reliable expected results. Therefore, to effectively cope with the high uncertainty and the technical limitations of existing forecasting studies, this study constructs a hybrid forecasting system from the dual perspectives of deterministic forecasting and uncertainty analysis. With the concept of “denoising-integration” as the core, the system integrates several denoising techniques, econometric methods, and artificial intelligence methods, and establishes a hybrid forecasting model with high accuracy and robustness with the assistance of multi-objective optimization theory. Furthermore, by introducing fuzzy theory onto the basis of deterministic prediction results, an interval forecasting model with a narrower interval width and better comprehensive performance is constructed under the premise of ensuring that the coverage of prediction intervals meets the requirements of the confidence level. In this study, the forecasting system is applied to four global core crude oil futures markets, and the empirical study finds that the performance is improved by more than 50 % compared with the benchmark model, which has an impressive performance advantage.

An Analysis of and Improvements in the Gear Conditions of the Automated Mechanical Transmission of a Battery Electric Vehicle Considering Energy Consumption and Power Performance

The design of the gear quantity and transmission parameters of a vehicle has large effects on its economical and power performance. This paper mainly researches the gear conditions (including the gear quantity and each gear’s transmission parameters) of two-gear and three-gear AMT (Automated Mechanical Transmission). This research uses Cruise software to build a multi-gear simulation model of a BEV (Battery Electric Vehicle) and adopts the LHS (Latin hypercube sampling) method to design an experiment plan and conduct a simulation experiment. This paper proposes a systematic method for influencing factor analyses and the optimization of transmission parameters, combining fuzzy theory, multiple regression, and particle swarm optimization. The research results show that the gear quantity allowing for optimal overall performance is three. The highest score obtained in the results of the simulation experiment for three-gear AMT is 11.15% higher than that of the two-gear AMT. The optimal design plan for the two-gear AMT is a small ig1 with a big k1, in which case the highest score of the regression model increases by 2.67% compared with that before modeling. The optimal design plan for the three-gear AMT is a big k1 with a big k2, in which case the highest score of the regression model increases by 12.78% compared with that before modeling. Then, this research uses PSO (particle swarm optimization) to further optimize the regression models and compares the difference between the highest scores in the results of the simulation experiment. The difference between the highest scores of the three-gear and two-gear AMT further increases to 21.95% after optimization. As shown in the results, the key factor influencing the performance of two-gear and three-gear AMT is gear quantity.

Adaptive Variable Universe Fuzzy Droop Control Based on a Novel Multi-Strategy Harris Hawk Optimization Algorithm for a Direct Current Microgrid with Hybrid Energy Storage

In the off-grid photovoltaic DC microgrid, traditional droop control encounters challenges in effectively adjusting the droop coefficient in response to varying power fluctuation frequencies, which can be influenced by factors such as line impedance. This paper introduces a novel Multi-strategy Harris Hawk Optimization Algorithm (MHHO) that integrates variable universe fuzzy control theory with droop control to develop an adaptive variable universe fuzzy droop control strategy. The algorithm employs Fuch mapping to evenly distribute the initial population across the solution space and incorporates logarithmic spiral and improved adaptive weight strategies during both the exploration and exploitation phases, enhancing its ability to escape local optima. A comparative analysis against five classical meta-heuristic algorithms on the CEC2017 benchmarks demonstrates the superior performance of the proposed algorithm. Ultimately, the adaptive variable universe fuzzy droop control based on MHHO dynamically optimizes the droop coefficient to mitigate the negative impact of internal system factors and achieve a balanced power distribution between the battery and super-capacitor in the DC microgrid. Through MATLAB/Simulink simulations, it is demonstrated that the proposed adaptive variable universe fuzzy droop control strategy based on MHHO can limit the fluctuation range of bus voltage within ±0.75%, enhance the robustness and stability of the system, and optimize the charge and discharge performance of the energy storage unit.

Optimizing Multi-Tier Scheduling and Secure Routing in Edge-Assisted Software-Defined Wireless Sensor Network Environment Using Moving Target Defense and AI Techniques

Software Defined Wireless Sensor Networks (SDWSN) enable flexibility in Wireless Sensor Network (WSN) environments by defining the controllable functions to WSN nodes by the Software Defined Network (SDN) controller. Due to the rapid evolution of SDWSNs, adverse effects also have occurred in terms of interference, energy consumption, and security issues. Several state-of-the-art works lend their utmost best to the SDWSN environment. However, the complete picture (i.e., relatability and security in SDWSN) poses severe challenges. The state-of-the-art issues is addressed in this research by proposing interference-aware Multi-Tier Scheduling for the SDWSN environment (MTS-SDWSN). First, we perform network construction in which the proposed network is constructed in a 2D hexagonal grid structure to resolve the connectivity issue. Upon constructing the network, the SDWSN nodes are clustered and managed to reduce the energy consumption using the Divide Well To Merge Better (DWTMB) algorithm in which the optimal Cluster Leader (CL) is selected based on adequate constraint. The data from the clustered nodes are sent to the Local Base Station (LBS) via CL in which they are scheduled in multi-tier format to diminish the complexity and interference issues. The first tier involved in scheduling among Cluster Members (CMs) and CL using adequate metrics, whereas the successive tiers (i.e., second and third) involved in scheduling among CLs to LBSs and LBSs to Sink Node (SN) are done using the Non-Cooperative Fuzzy Theory (NCFT) method. Last, the scheduled nodes are routed to appropriate destinations using Secure and Optimal Routing Protocol (SORP). The proposed SORP includes the Alibaba and Forty Thieves (AFT) and Multi Criteria Decision Making (MCDM) algorithms for selecting and ranking the optimal routes. Further, the security of the routes is enabled by adopting trust and Moving Target Defense (MTD) mechanisms. The MTD includes route switching among the SDWSN devices and active switch handling using Cycle Generative Adversarial Networks (CGAN) among the switches. The proposed work is implemented using a NS-3.26 simulation tool, and performance of the proposed model and existing works shows that the proposed work outperforms the existing works.

Fixed Point Results for Fuzzy Enriched Contraction in Fuzzy Banach Spaces with Applications to Fractals and Dynamic Market Equillibrium

We introduce fuzzy enriched contraction, which extends the classical notion of fuzzy Banach contraction and encompasses specific fuzzy non-expansive mappings. Our investigation establishes both the presence and uniqueness of fixed points considering this broad category of operators using a Krasnoselskij iterative scheme for their approximation. We also show the graphical representation of fuzzy enriched contraction and analyze its graph for different values of beta. The implications of these findings extend to significant results within fuzzy fixed-point theory, enriching the understanding of iterative processes in fuzzy metric spaces. To demonstrate the versatility of our innovative concepts and the associated fixed-point theorems, we provide illustrative examples that showcase their applicability across diverse domains, including the generation of fractals. This demonstrates the relevance of fuzzy enriched contraction to iterated function systems, enabling the study of fractal structures under various contractive conditions. Additionally, we explore practical applications of fuzzy enriched contraction in dynamic market equilibrium, offering new insights into stability and convergence in economic models. Through this unified framework, we open new avenues for both theoretical advancements and real world applications in fuzzy systems.

A Fractional-Order Model Predictive Control Strategy with Takagi–Sugeno Fuzzy Optimization for Vehicle Active Suspension System

Aiming at the problem of system controller performance failure caused by improperly setting the value of each weighting coefficient of the model predictive control (MPC), a fractional-order MPC strategy with Takagi–Sugeno fuzzy optimization (T–SFO MPC) is proposed for a vehicle active suspension system. Firstly, the fractional-order model predictive control framework for active suspension systems is designed based on a 1/4 vehicle model. Then, we analyze the influence of different weighting coefficients on the suspension performance and introduce the Takagi–Sugeno fuzzy optimization theory to adaptively adjust the weighting coefficients of the fractional-order MPC controller. Finally, the system responses of the T–SFO MPC, traditional MPC, linear quadratic regulator (LQR), and passive suspension control are numerically analyzed under various road conditions. Simulation results show that suspension response with the T–SFO MPC is significantly improved compared with passive suspension control, traditional MPC control, and LQR control, and the weight coefficients of the T–SFO MPC can be adaptively adjusted according to the dynamic changes of suspension response. Compared with passive suspension, the root mean square (RMS) value of the vertical acceleration of the T–SFO MPC under various roads decreased by a maximum of 37.97%, and the RMS value of suspension dynamic deflection and tire dynamic load decreased by a maximum of 32.94% and 37.8%, respectively. These results validate that the proposed control method can achieve coordinated optimization of vehicle comfort and handling stability.

Design of a Robust Controller for Induction Motor Drive Systems Based on Extendable Fuzzy Theory

In this paper, an extendable fuzzy robust speed controller suitable for induction motor drive systems was proposed. Firstly, the two-degrees-of-freedom (2DOF) robust control technology with feedforward control and disturbance elimination method was adopted. Upon parameter variation and load disturbance, the motor drive system could utilize a robust controller to generate compensation signals and reduce the impact on the controlling performance of the motor drive system. The magnitude of the compensation signal was adjusted via the weighting factor. However, should a fixed weighting factor be adopted, system instability might be generated easily when time delay and saturation of control force occur. Based on the above, the smart method of extendable fuzzy theory (EFT) was adopted in this paper to adjust adequate weighting factors, where the controlling performance of the induction motor drive system could be improved accordingly. Lastly, the simulation software Matlab/Simulink (R2023b version) was applied to simulate the utilization of the controlling method proposed for the induction motor drive system. The simulation results proved that the extendable fuzzy robust speed controller proposed provided better speed tracking and load regulation-controlling performance than the conventional robust controller.

Optimization of ore pillar recovery based on weighting combined with uncertainty measurement theory

Abstract Given the multi-objective nature and inherent uncertainty in evaluating ore pillar mining schemes, the analytic hierarchy process (AHP) and entropy method were applied to determine factor weights. A new combined weighting method was proposed to obtain more objective and accurate results. Seven quantitative and four qualitative indicators were selected based on various mining performance factors and grading standards. A combined weighting–uncertainty measurement theory evaluation model was then constructed, integrating weight values and confidence levels from the recognition criteria. This model was applied to evaluate three proposed schemes, determining their relative merits and ranking. The evaluation demonstrated that the combined weighting–uncertainty measurement model outperformed both the fuzzy theory and the TOPSIS method in delivering comprehensive, objectivity and reliable results for assessing ore pillar mining schemes.

Urban Emergency Evacuation Path Optimization Based on Uncertain Environments to Enhance Response for Symmetric and Asymmetric Evacuation Problems

Background: Serious secondary disasters caused by extreme natural weather conditions occur frequently, making it essential to establish a scientific and efficient modern emergency management system to maximize life-saving efforts. Methods: This study focuses on the uncertain environment of urban road networks and employs fuzzy theory to construct a 0–1 integer programming model for emergency evacuation paths that minimizes the average expected travel time. Results: We enhanced the neighborhood search strategy of the traditional ACO_time by incorporating the 2-opt and 3-opt perturbation mechanisms from the SA algorithm. Additionally, we utilized improved ant-volume and ant-perimeter models, along with their combinations, in the pheromone-updating mechanism of the basic ACO. The heuristic principles of the A* algorithm were integrated, introducing the joint influence of path and time into the heuristic function of the ACO algorithm. Conclusions: The IACO3 algorithm was tested on the Sioux Falls network and the Berlin Heisenheimer Center network. The computation time of the improved IACO3 algorithm was reduced by up to 20% compared to the original IACO3 algorithm in relation to the SA algorithm, with only a 4–5% increase in computation time compared to the ACO_time algorithm, which translates to an increase of merely 4–5 s. This demonstrates the superior solution efficiency of the IACO3 algorithm.

Consumer Behavior in the Digital Marketplace: A Fuzzy Evaluation Approach

With the growing prevalence of the internet and the development of logistics, consumers face increasingly complex choices when shopping online. Therefore, this article introduces fuzzy comprehensive evaluation to address these shopping issues. In analyzing consumers' purchase decision-making problems for online shopping, it is essential to subjectively evaluate products, such as price, quality, and reputation. By constructing fuzzy relationships and assigning weights, this method effectively handles the ambiguity and uncertainty of evaluation information, reflecting consumers' subjective preferences in actual shopping decisions. This study concludes that quality is the dominant factor among numerous commodity factors,and it also established a shopping decision model, which aids consumers in making the best decisions during their shopping, thereby enhancing shopping efficiency and satisfaction. The results indicate that compared to traditional methods, this method can more accurately focus on consumer purchase intention and improve the understanding of shopping decisions. The paper summarizes the fuzzy comprehensive evaluation of its application value in shopping problems, pointing out that it can better simulate human fuzzy decision-making processes and provide a more practical shopping decision assistance tool. This study not only enriches the application of fuzzy comprehensive evaluation theory in consumer behavior research, but also provides consumers with a scientific and practical shopping decision support method.

Method of intelligent agricultural pest image recognition based on machine vision algorithm

In recent years, people have paid increasing attention to smart agriculture. Its core technology is to combine information technology such as computer vision with agricultural production. In agricultural production, the occurrence of pests and diseases can seriously affect agricultural production. Therefore, in agricultural production, the diagnosis and identification of agricultural pests and diseases is the key to improve crop yield. Traditional machine vision methods often rely on feature extraction and classifier design, lack of strong learning and generalization ability, and can not effectively control crop diseases and pests in a timely manner. In order to solve this problem, this paper designs an agricultural pest recognition system based on machine vision algorithm of fuzzy recognition theory, and applies it to agricultural pest recognition. Compared with the traditional machine vision method, this method has obvious advantages, and can effectively improve the monitoring and early warning ability of crop diseases and pests. The experimental results show that the highest recognition rate of the machine vision optimization algorithm based on fuzzy recognition theory is 98.06%, and the lowest recognition error rate is 5.83%. It can be seen that the machine vision recognition algorithm based on fuzzy recognition theory has good recognition effect and can be used in agricultural pest recognition system to help farmers carry out agricultural production and reduce economic losses caused by diseases and pests.

Finite‐time lag bipartite synchronization of double‐layer networks with non‐linear coupling strength and random coupling delays via T‐S fuzzy logic theory

AbstractThis article discusses finite‐time lag bipartite (FETLB) synchronization of double‐layer networks with non‐linear coupling strength and multiple time delays. The cooperative and competitive interactions between nodes are considered based on signed graphs. To address the non‐linear couplings strength, the T‐S fuzzy logic theory is used. An intermittent control approach is introduced to achieve FETLB synchronization, effectively minimizing control costs. Moreover, by the Lyapunov functional method, we derive criteria for achieving FETLB synchronization and provide estimations for the synchronization settling time. In addition, numerical simulation affirms the validity of the theoretical findings, showcasing the practical application of the synchronization results in secure communication.

A distributionally robust optimization approach of multi-park integrated energy systems considering shared energy storage and Uncertainty of Demand Response

To enhance the economic efficiency and renewable energy integration capacity of multi-park integrated energy systems (MPIES) and address the issue of insufficient consideration of demand response uncertainty in existing studies, this paper proposes a distributionally robust optimization approach for multi-park integrated energy systems, considering shared energy storage and the uncertainty of demand response. First, models of the shared energy system and demand response are established. Based on these models, a deterministic optimization scheduling model for MPIES is developed, aiming to minimize system costs while considering constraints such as grid power balance. To address uncertainty in demand response, this paper employs Interval Type-2 Fuzzy Theory to construct uncertainty sets and considers system reliability constraints. The original optimization problem is then transformed into an equivalent robust counterpart model, and the optimal distributionally robust solution is obtained through parameter domain decomposition methods. Finally, the proposed method is validated using the IEEE 33-bus system. The results show that considering shared energy storage and demand response individually can reduce total system costs by 4.86 % and 26.46 %, respectively. After accounting for the uncertainty in demand response, the total system cost increases only slightly by 4.36 %, but this improves the system's robustness.

Solving the Problem of Fuzzy Partition-Distribution with Determination of the Location of Subset Centers

A large number of real-world problems from various fields of human activity can be reduced to optimal partitioning-allocation problems with the purpose of minimizing the partitioning quality criterion. A typical representative of such problem is an infinite-dimensional transportation problem and more generalized problems—infinite-dimensional problems of production centers placement along with the partitioning of the area of continuously distributed consumers with the purpose of minimizing transportation and production costs. The relevant problems are characterized by some kind of uncertainty level of a not-probabilistic nature. A method is proposed to solve an optimal fuzzy partitioning-allocation problem with the subsets centers placement for sets of n-dimensional Euclidean space. The method is based on the synthesis of the methods of fuzzy theory and optimal partitioning-allocation theory, which is a new science field in infinite-dimensional mathematical programming with Boolean variables. A theorem was proved that determines the form of the optimal solution of the corresponding optimal fuzzy partitioning-allocation problem with the subsets centers placement for sets of n-dimensional Euclidean space. An algorithm for solving fuzzy partitioning-allocation problems is proposed, which is based on the proved theorem and on a variant of Shor’s r-algorithm—a non-differential optimization method. The application of the proposed method is demonstrated on model tasks, where the coefficient of mistrust is integrated to interpret the obtained result—the minimum value of the membership function, which allows each point of the set partition to be assigned to a specific fuzzy subset.