Robust Fuzzy Model Research Articles

Fuzzy robust regression based on exponential-type kernel functions

The least squares method is a frequently used technique in fuzzy regression analysis. However, it is highly sensitive to outliers in the dataset. To address this challenge, we propose a novel robust fuzzy regression model based on exponential-type kernel functions. This approach effectively mitigates the influence of poorly fitted observations on the predicted results by reducing their weights. Furthermore, we use the gh-transformation to guarantee the nonnegativity of the spreads of the predicted response variable. In order to evaluate the performance of our method, a simulation study and three real data sets were considered. The experimental results demonstrate that the proposed method outperforms several popular robust methods in almost all cases. Furthermore, a sensitivity analysis of the estimated parameters provides further evidence of the superior efficiency of the proposed method.

A Robust Fuzzy Model for Evaluating Defects in Building Elements

A Robust Fuzzy Model for Evaluating Defects in Building Elements

Decision-Making Approach to Design a Sustainable Photovoltaic Closed-Loop Supply Chain Considering Market Share for Electric Vehicle Energy

This study aims to develop a model for the closed-loop supply chain of photovoltaic (PV) systems. The primary objective addresses strategic and tactical decision-making using a two-stage approach. To pinpoint suitable locations for solar power plants, the PROMETHEE II method is utilized, which is a component of multi-attribute decision making (MADM) approaches. Next, a multi-objective modeling of the closed-loop PV supply chain is conducted. This model aims to minimize total supply chain costs, reduce environmental impacts, mitigate adverse social effects, maximize the on-time delivery (OTD) of manufactured products, and maximize market share. Additionally, a robust fuzzy mathematical model is introduced to examine the model’s sustainability under various uncertainties. An evaluation of the effectiveness and utility of this model is conducted in Tehran city. Furthermore, a comprehensive analysis of various supply chain costs indicates that production centers have the highest costs, while separation centers have the lowest costs.

Data-driven ensemble optimal compensation control for partially known delayed and persistently disturbed nonlinear systems

In almost all industrial processes, the development of an accurate mathematical model that comprehensively characterizes the regulated system poses a substantial obstacle. Diverse factors, such as unidentified system components and time-varying external disturbances, contribute to this phenomenon. This can result in a disparity between the model and the plant and thereby compromising the performance of the designed controller. In this study, a novel data-driven ensemble optimal compensation control framework is proposed for partially known nonlinear systems with state delays and structural disturbances. Initially, the estimated system model is leveraged to construct a robust fuzzy model predictive controller (RFMPC) based on the Lyapunov–Krasovskii functional (LKF), ensuring the input-to-state stability (ISS) of the plant. Then, a reinforcement learning (RL)-based compensator is assembled to gradually minimize the model-plant mismatch across the entire state space. To streamline the training process of the compensator and facilitate its stability, a dynamic network update scheme is devised, incorporating a moving average gradient calculation method and a learning rate tuning strategy. Furthermore, comparative discussions with some prevalent methods are demonstrated. With the established control framework, the performance of the RFMPC can be securely enhanced, and convergence is ensured within a narrow proximity to equilibrium, despite time-varying perturbation dynamics. By integrating this approach with deep learning (DL) methods, the efficacy of numerous industrial processes could be significantly improved. A numerical simulation and a discretized continuous-time stirring tank reactor (CSTR) example validate the effectiveness and benefits of the proposed control strategy.

Ideal Parameter Estimation of Photocatalysis Process to Boost Amoxicillin Degradation Efficiency Using Marine Predators Optimization Algorithm

This paper presents a methodology for determining the optimal parameters of a photocatalysis process for treating pharmaceutical wastewater. Three parameters are considered: pH value, catalyst dosages, and reaction time to boost the amoxicillin degradation efficiency (ADE). The proposed methodology contains two stages: fuzzy modelling and a parameter determination process using the marine predators algorithm (MPA). Firstly, based on the experimental dataset of ADE in terms of pH value, catalyst dosages, and reaction time, a robust fuzzy model is produced to model the photocatalysis/ozonation process. The target is reducing the root mean square error (RMSE) between the actual data and the experimental dataset. Using fuzzy, the RMSE decreased from 2.0248 using ANOVA to 0.3148 using fuzzy (decreased by 84%). Next, using the MPA, the optimal parameters of pH value, catalyst dosages, and reaction time corresponding to maximum ADE are determined. The suggested strategy boosted the ADE from 88.23% to a rate of 11.68% compared with the experimental and RSM approaches. Under this condition, the optimal solutions are 11, 384 mg/L, and 33.615 min, respectively, for pH, catalyst dosages, and reaction time.

Robust fuzzy model predictive control for nonlinear discrete‐time systems

SummaryThis paper studies the issue of Robust Fuzzy Model Predictive Control (RFMPC) of nonlinear discrete‐time systems in the presence of disturbance. To this end, Takagi‐Sugeno (T‐S) fuzzy model is adopted in order to characterize uncertain nonlinear systems and facilitate providing controller for such systems. Non‐parallel distributed compensation (non‐PDC) technique is applied to design improved RFPMC with better performance. The optimization problem of RFMPC is represented in terms of linear matrix inequalities (LMIs) so as to decrease online computational burden. Besides, feasibility and stability which are decisive factors in MPC theory are investigated for the proposed method. Ultimately, two examples including cart‐damper‐spring system are simulated to evaluate the results of this research work.

Boosting Biodiesel Production from Dairy-Washed Scum Oil Using Beetle Antennae Search Algorithm and Fuzzy Modelling

The major goal of this study was to develop a robust fuzzy model to mimic the generation of biodiesel from the transesterification of dairy-washed milk scum (DWMS) oil. Four process parameters were considered: the molar ratio of methanol to oil, the concentration of KOH, the reaction temperature, and the reaction time. The proposed technique was divided into two steps: fuzzy modelling and optimum parameter identification. The capability of fuzzy tools to capture and make use of linguistic variables and fuzzy sets is one of their main benefits. This means that fuzzy logic allows for the representation and manipulation of values that fall across a continuum rather than merely relying on crisp values or binary categories. When dealing with non-linear relationships, this is especially helpful since it gives a more accurate and nuanced depiction of the underlying data. As a result, an accurate fuzzy model was initially built based on collected data to simulate the biodiesel production in terms of the molar ratio of methanol to oil, the concentration of KOH, the temperature of the reaction, and the reaction duration. In the second phase, the beetle antennae search (BAS) algorithm was applied to identify the optimal values of the process parameters to boost the production of biodiesel. The BAS algorithm draws inspiration from beetle behavior, particularly how they navigate using their antennae. It employs a swarm-intelligence method by deploying virtual beetles that swarm over the problem area in search of the best solution. One of its main features is the BAS algorithm’s capacity to balance exploration and exploitation. This is accomplished through the algorithm’s adaptable step-size mechanism during the search phase. As a result, the algorithm can first investigate a large portion of the problem space before gradually moving closer to the ideal answer. Compared with ANOVA, and thanks to fuzzy, the RMSE decreased from 7 using ANOVA to 0.73 using fuzzy (a decrease of 89%). The predicted R2 increased from 0.8934 using ANOVA to 0.9614 using fuzzy (an increase of 7.6). Also, the optimisation results confirmed the superiority of the BAS algorithm. Biodiesel production increased from 92% to 98.16%.

Dual-Mode Robust Fuzzy Model Predictive Control of Time-Varying Delayed Uncertain Nonlinear Systems With Perturbations

For time-varying delayed nonlinear systems with parameter uncertainties and persistent disturbances, an online and an offline robust fuzzy model predictive control (RFMPC) algorithms are proposed in this paper. Both methods guarantee the input-to-state stability (ISS) of the system. Furthermore, a novel alternative optimization (AOP) approach and a dual-mode OP/AOP strategy are proposed to prevent the performance deterioration of the online optimal control (OP) approach due to the challenges in addressing the bilinear matrix inequality (BMI) constraints. With the established AOP and dual-mode OP/AOP techniques, the optimization problem constrained by BMIs is transformed into convex, and a significantly more precise approximation of the ellipsoidal minimal robust positively invariant (EmRPI) set can be calculated. Besides, the system can eventually converge into a more compact ellipsoidal set. These two alternative optimization methods can be easily extended to various nonlinear systems. A numerical example and a continuous-time stirring tank (CSTR) example are provided to validate the effectiveness and advantages of the established methodologies.

Optimizing sustainable biomass–coal co-firing power plant location problem under ambiguous supply

Promoting biomass–coal co-firing power generation technology in existing coal-fired power plants is a practical and relatively low-cost short-run choice for the coal-fired power industry to reduce carbon emissions and develop sustainably. However, the uncertainty of biomass supply complicates the location of co-firing power plants among existing coal-fired plants. To address the challenge that only limited historical data of uncertain supply are available, this paper proposes a new ambiguity distribution set to characterize the uncertain supply capacity, supply price, and supply quality (i.e., energy conversion coefficient). Accordingly, a novel bi-objective distributionally robust fuzzy optimization model is developed for the sustainable co-firing power plant location (SCPPL) problem to balance conflicting objectives of minimizing total cost and maximizing carbon emission reduction. Subsequently, the computationally tractable counterpart of the proposed model is derived against the worst-case distribution by reformulating the distributionally robust credibility objective and constraints as their solvable equivalent forms. Furthermore, the Pareto optimal solutions of the proposed bi-objective model are generated using the augmented ϵ-constraint method. Finally, a realistic case study of Heilongjiang Province in China is conducted to verify the feasibility and effectiveness of the proposed optimization method. The experimental results demonstrate that the proposed model can hedge against the distributional ambiguity of uncertain parameters and provides a robust co-firing power plant location strategy. By comparison with the nominal distribution model and analysis of the sensitivity of selected parameters, management insights are summarized for decision-makers.

Fuzzy Modelling and Optimization to Decide Optimal Parameters of the PEMFC

The main target is the maximization of the output power of PEM “proton exchange membrane” fuel cell via fuzzy modelling and optimization. In the beginning, using the experimental data, a robust fuzzy model is designed for simulating the PEM fuel cell using the relative humidity (%) and stoichiometric ratio at the anode and cathode. Then, the artificial ecosystem optimiser (AEO) is applied to determine the best values of the controlling input parameters. During the optimization process, the four controlling input parameters of the PEMFC are used as the decision variables, whereas as the cost function is required to be at the maximum of the output power density of the PEMFC. For the fuzzy model of the power, the RMSE values are 1.5588 and 3.1906, respectively, for training and testing data. The coefficient of determination values are 0.9826 and 0.8743 for training and testing, respectively. This confirms a successful modelling phase. Finally, the integration between fuzzy and AEO boosted the power of the PEMFC from 57.95 W to 78.44 W (by around 35%). Under this optimal condition, the controlling input parameters values are 26.65%, 56.77%, 1.14, and 1.68, respectively, for anode relative humidity, cathode relative humidity, anode stoichiometric ratio and cathode stoichiometric ratio. The present study, however, intends to highlight the importance of fuzzy modelling and metaheuristic algorithms in the development of digital twins to accelerate the commercialization of fuel cells as well as its applicability in diverse global economic sectors where a higher power requirement is needed. It is also aimed at informing the fuel cell research community and policy makers on strategies that could be adopted in boosting fuel cell performance and therefore could be a good reference source in decision-making for fuel cell commercialization and its practical implementation.

Fuzzy rough feature selection using a robust non-linear vague quantifier for ordinal classification

Ordinal classification is a common classification problem, which widely exists in multi-attribute decision making problems. The dominance-based rough set approach (DRSA) is a knowledge acquisition tool for ordinal classification tasks. Nevertheless, the existence of noise information in the collected data greatly reduces the accuracy of the DRSA and some extended model. An effective way to solve this issue is to improve the robustness of these models. In addition, most existing feature selection strategies based on dominance rough sets mainly focus on the monotonic classification consistency between features and decision, but ignoring the classification information provided by features combination. Motivated by these two issues, this paper proposes a robust fuzzy dominance rough set model to combat noise interference and develop a feature selection approach based on the proposed model for ordinal classification tasks. First, a non-linear vague quantifier is adopted to construct the robust model, and related dependency function is introduced. Second, the rank entropy based uncertainty measures are explored to characterize the contribution of features combination for ordinal classification. Based on the proposed uncertainty measures, a new feature evaluation index is presented. Meanwhile, the corresponding feature selection algorithm is designed. Finally, numerical comparative experiments are performed to indicate that the proposed model and feature selection algorithm have good capability.

RETRACTED ARTICLE: Sustainable and optimal design of Chinese herbal medicine supply chain network based on risk dynamic regulation mechanism

We propose a robust fuzzy design model for a sustainable closed-loop supply chain network. The model is based on a risk dynamic regulation mechanism. In this way, we can solve the problem of sudden disruptions and uncertain demand in the supply chain of Chinese herbal medicines. We also develop a hybrid algorithm solution to solve the model and design a resilient supply chain network. The specific steps are as follows: (1) The risk dynamic regulation mechanism is created with strong risk resistance by considering the information sharing platform, facility defense, drying station scheduling, safety stock, and shared inventory. (2) Based on the dynamic risk regulation mechanism, we establish a sustainable Chinese herbal medicine supply chain network design model. Then, we use the robust fuzzy method and the epsilon constraint to deal with the uncertainty and integrate the model. (3) We introduce opposition-based learning, cosine convergence factor, and levy flight to the original Whale and Grey wolf algorithms to obtain the Hybrid algorithm, which is used to solve the processed model. The results show the model and algorithm proposed in this paper have strong applicability and advantages in designing closed-loop supply chain networks for Chinese herbal medicine and provide references for relevant decision-makers.

Bus Bridging for Rail Disruptions: A Distributionally Robust Fuzzy Optimization Approach

Dealing with uncertain rail disruptions effectively raises a significant challenge for computational intelligence research. This article studies the bus bridging problem under demand uncertainty, where the passenger demand is represented as parametric interval-valued fuzzy variables and their associated uncertainty distribution sets. A distributionally robust fuzzy optimization model is proposed to minimize the maximum travel time and to search for the optimal scheme for vehicle allocation, route selection, and frequency determination. To solve the proposed robust model, we discuss the computational issues concerning credibilistic constraints, turning the robust counterpart model into computationally tractable equivalent formulations. The proposed approach is verified, and the resulting method is validated with a report on uncertain parameters in a real-world disrupted event of Shanghai Rail Line 1. Experimental results show that the distributionally robust fuzzy optimization approach can provide a better uncertainty-immunized solution.

Robust interval type-2 kernel-based possibilistic fuzzy clustering algorithm incorporating local and non-local information

Type-2 fuzzy set theory has certain potential advantage in processing high-order uncertainty, and has been more and more widely applied in pattern recognition, image processing, and system modeling. Although it has been introduced into robust fuzzy clustering modeling, most clustering methods based on type-2 fuzzy set theory have many obvious shortcomings, such as weak robustness against noise and high sensitivity to initial value. Therefore, this paper presents a novel single fuzzifier interval type-2 kernel-based possibilistic fuzzy local and non-local information c-means clustering, and it is driven by deep neighborhood information for image segmentation in the presence of high noise. Firstly, we construct the novel deep neighborhood window structure, which consists of local neighborhood window around current pixel and deep neighborhood window around the pixel in local neighborhood window around current pixel. Secondly, using the structural similarity between local neighborhood window and deep neighborhood window around current pixel, we construct a novel fuzzy local information factor to tune the impact of local neighborhood information on current pixel clustering. Thirdly, possibility theory and fuzzy local information factor are introduced into interval type-2 kernel-based fuzzy c-means clustering, and a novel single fuzzifier type-2 possibilistic fuzzy clustering with richer local and non-local information and kernel metric is proposed. Experimental results indicate that the proposed algorithm outperforms existing state-of-the-art robust fuzzy clustering-related algorithms, and significantly improve the robustness of robust fuzzy clustering algorithms against noise.

Feature Selection Considering Multiple Correlations Based on Soft Fuzzy Dominance Rough Sets for Monotonic Classification

Monotonic classification is a common task in the field of multicriteria decision-making, in which features and decision obey a monotonic constraint. The dominance-based rough set theory is an important mathematical tool for knowledge acquisition in monotonic classification tasks (MCTs). However, existing dominance-based rough set models are very sensitive to noise information, and only a misclassified sample will lead to large errors in acquiring knowledge. This unstable phenomenon does not meet the requirements of practical applications. On the other hand, feature selection is supposedly an effective dimensionality reduction approach for classification tasks. In the real world, feature combinations with multiple correlations can often provide important classification information, where the multiple correlations include redundancy, complementarity, and interaction between features. To the best of our knowledge, most of the existing feature selection methods for MCTs only consider the relevance between features and decision, while ignoring the multiple correlations. To overcome these two drawbacks, in this article, we propose a robust fuzzy dominance rough set model, and develop a feature selection method that considers multiple correlations based on the robust model for MCTs. First, a soft fuzzy dominance rough set (SFDRS) with robustness is proposed. Second, a feature evaluation index considering multiple correlations is presented. Finally, a feature selection algorithm based on SFDRS is designed to select an optimal feature subset. Extensive experiments are conducted on 12 public datasets, and the results show that the SFDRS model has good robustness and the proposed feature selection algorithm has excellent classification performance.

A food bank network design examining food nutritional value and freshness: A multi objective robust fuzzy model

One main reason for food scarcity is its improper and uneven distribution amongst those who require aid. To overcome this issue, charities and food banks serve as the connection between beneficiaries and donors. They are mostly nonprofit organizations but they incur operational costs for storage and delivery of the donated food items. The donated food items are either canned and cold, or hot meals from over production of businesses; and therefore their freshness, inventory and shelf-life bring about additional operational challenges in distribution and logistics. The uncertainty of demand and supply is another challenge to overcome, which necessitates a robust plan. This article proposes a multi-objective mathematical programming model for a food bank network design to optimize the cost, food freshness and its nutritional value. A robust fuzzy counterpart of the model is developed together with three solution methods including ϵ-constraint, MOGWO and NSGA II. The MOGWO algorithm shows a better performance in our numerical experiment with large instances. Its application on a case study resulted in a supply network with lower cost, smaller fleet size and higher food quality, although less fresh distributed foods compared to the benchmark network. The trade-off between the cost and freshness of food is depicted here by examining shelf-life of products and vehicle capacity. The long lasting products incur less transportation cost due to compactness of packaging, and similarly, higher capacity vehicles lead to more cost efficient dispatch with longer routes which decrease the freshness of food. According to our numerical results, higher uncertainty rate in the network increases total cost, but also overall nutritional value of the distributed food over the network due to greater supply of food.

State of Charge Estimation of Lithium-Ion Battery Using Robust Kernel Fuzzy Model and Multi-Innovation UKF Algorithm Under Noise

Accurate and robust state of charge (SOC) estimation of lithium-ion batteries is very important to prolong battery life and prevent catastrophic failures. However, the accuracy of SOC estimation is seriously affected by unknown noise, uncertain interference and temperature. In this article, a novel model fusion method is presented to achieve precise SOC estimation in the case of non-Gaussian noise and outliers. A state-space model of battery system is first developed to conduct SOC estimate. Then, a novel robust kernel Takagi–Sugeno fuzzy method to minimize the mean and variance of model error is developed to characterize the electrical performance of battery. This modeling strategy uses local nonlinear modeling mechanism, which the nonlinear relationship between data can be well represented, thus it can obtain a superior modeling performance. Finally, a multi-innovation unscented Kalman filter (UKF) algorithm considering the historical state information is designed to incorporate with the robust fuzzy model to filter out the noise in the observation and update the SOC estimation. Additional stability analysis shows the convergence of the proposed multi-innovation UKF algorithm. Experiments and verifications show that the presented estimation architecture is effective and has better modeling ability compared with several common methods.

Integration of sustainable closed-loop supply chain with reliability and possibility of new product development: a robust fuzzy optimisation model

ABSTRACT The development of a new product is an essential factor in changing the structure of supply chains. This paper proposes a sustainable closed-loop supply chain network with the possibility of new product development. Using a robust fuzzy optimisation model, the objectives are maximising profits, maximising the number of created jobs, and maximising reliability. The environmental emissions are considered a limitation in our optimisation model. Some parameters are uncertain to make our problem more realistic, and accordingly, a robust fuzzy optimisation method is used. To manage the complexity of the proposed model, a Multi-objective Grey Wolf Optimisation (MOGWO) algorithm was developed for solving the large-sized tests. The performance of the proposed multi-objective optimisation algorithm is shown against a traditional method called a Non-dominated Sorting Genetic Algorithm (NSGA-II). Accordingly, 15 large-scale test problems are solved, and multi-objective optimisation metrics are defined to compare the performance of the algorithms. The results showed how significantly the uncertainty reduction could affect the values of total net profit and reliability. The applicability of the proposed model is shown in a real case study in the lighting industry to approve the appropriate performance of the proposed MOGWO.

LMI-Based Robust Fuzzy Model Predictive Control of Discrete-Time Fuzzy Takagi-Sugeno Large-Scale Systems Based on Hierarchical Optimization and H∞ Performance

This paper studies robust fuzzy model predictive control of discrete-time fuzzy Takagi-Sugeno large-scale systems based on hierarchical optimization and H_[Formula: see text] Performance. The considered system in this paper is a large-scale system. So, the Takagi-Sugeno (T-S) fuzzy approach which uses nonlinear local models is applied to estimate the nonlinear system to reduce the burden of modeling. The model predictive control (MPC) is a practical application that is useful for all systems but the problem is the online computational cost. For large-scale systems, this problem is the online computational burden. Besides, it leads to conservative or even no solution. By the proposed method, more relaxed solutions are achieved. First, the T-S system with nonlinear local models is adopted. Second, the hierarchical optimization scheme is considered for the optimization part of the MPC. Third, by inspiring the [Formula: see text] performance, uncertainties and disturbances that are appeared are reduced. Moreover, the linear matrix inequalities (LMIs) are used to solve the proposed method that the computational burden significantly is reduced at the same time. Simulation results are finally presented to show the effectiveness of the proposed controller.

A robust fuzzy multi-objective location-routing problem for hazardous waste under uncertain conditions.

Industrialization and population growth have been accompanied by many problems such as waste management worldwide. Waste management and reduction have a vital role in national management. The presents study represents a multi-objective location-routing problem for hazardous wastes. The model was solved using Non dominated Sorting Genetic Algorithm-II, Multi-Objective Particle Swarm Optimization, Multi-Objective Invasive Weed Optimization, Pareto Envelope-based Selection Algorithm, Multi-Objective Evolutionary Algorithm Based on Decomposition and Multi-Objective Grey Wolf Optimizer algorithms. The findings revealed that the Multi-Objective Invasive Weed Optimization algorithm was the best and the most efficient among the algorithms used in this study. Obtaining income from the incineration of the wastes and reducing the risk of COVID-19 infection are the first innovation of the present study, which considered in the presented model. The second innovation is that uncertainty was considered for some of the crucial parameters of the model while the robust fuzzy optimization model was applied. Besides, the model was solved using several meta-heuristic algorithms such as Multi-Objective Invasive Weed Optimization, Multi-Objective Evolutionary Algorithm Based on Decomposition and Multi-Objective Grey Wolf Optimizer, which were rarely used in literature. Eventually, the most efficient algorithm was identified by comparing the considered algorithms.