A historical review of evolutionary learning methods for Mamdani-type fuzzy rule-based systems: Designing interpretable genetic fuzzy systems

Autonomous learning for fuzzy systems: a review

As one of the three pillars in computational intelligence, fuzzy systems are a powerful mathematical tool widely used for modelling nonlinear problems with uncertainties. Fuzzy systems take the form of linguistic IF-THEN fuzzy rules that are easy to understand for human. In this sense, fuzzy inference mechanisms have been developed to mimic human reasoning and decision-making. From a data analytic perspective, fuzzy systems provide an effective solution to build precise predictive models from imprecise data with great transparency and interpretability, thus facilitating a wide range of real-world applications. This paper presents a systematic review of modern methods for autonomously learning fuzzy systems from data, with an emphasis on the structure and parameter learning schemes of mainstream evolving, evolutionary, reinforcement learning-based fuzzy systems. The main purpose of this paper is to introduce the underlying concepts, underpinning methodologies, as well as outstanding performances of the state-of-the-art methods. It serves as a one-stop guide for readers learning the representative methodologies and foundations of fuzzy systems or who desire to apply fuzzy-based autonomous learning in other scientific disciplines and applied fields.

Fuzzy Pattern Tree Evolution Using Grammatical Evolution

A novel approach to induce Fuzzy Pattern Trees using Grammatical Evolution is presented in this paper. This new method, called Fuzzy Grammatical Evolution, is applied to a set of benchmark classification problems. Experimental results show that Fuzzy Grammatical Evolution attains similar and oftentimes better results when compared with state-of-the-art Fuzzy Pattern Tree composing methods, namely Fuzzy Pattern Trees evolved using Cartesian Genetic Programming, on a set of benchmark problems. We show that, although Cartesian Genetic Programming produces smaller trees, Fuzzy Grammatical Evolution produces better performing trees. Fuzzy Grammatical Evolution also benefits from a reduction in the number of necessary user-selectable parameters, while Cartesian Genetic Programming requires the selection of three crucial graph parameters before each experiment. To address the issue of bloat, an additional version of Fuzzy Grammatical Evolution using parsimony pressure was tested. The experimental results show that Fuzzy Grammatical Evolution with this extension routinely finds smaller trees than those using Cartesian Genetic Programming without any compromise in performance. To improve the performance of Fuzzy Grammatical Evolution, various ensemble methods were investigated. Boosting was seen to find the best individuals on half the benchmarks investigated.

Social Sustainability and Resilience in Supply Chains of Latin America on COVID-19 Times: Classification Using Evolutionary Fuzzy Knowledge

The number of research papers interested in studying the social dimension of supply chain sustainability and resilience is increasing in the literature. However, the social dimension is complex, with several uncertainty variables that cannot be expressed with a traditional Boolean logic of totally true or false. To cope with uncertainty, Fuzzy Logic allows the development of models to obtain crisp values from the concept of fuzzy linguistic variables. Using the Structural Equation Model by Partial Least Squares (SEM-PLS) and Evolutionary Fuzzy Knowledge, this research aims to analyze the predictive power of social sustainability characteristics on supply chain resilience performance in the context of the COVID-19 pandemic with representative cases from Mexico and Chile. We validate our approach using the Chile database for training our model and the Mexico database for testing. The fuzzy knowledge database has a predictive power of more than 80%, using social sustainability features as inputs regarding supply chain resilience in the context of the COVID-19 pandemic disruption. To our knowledge, no works in the literature use fuzzy evolutionary knowledge to study social sustainability in correlation with resilience. Moreover, our proposed approach is the only one that does not require a priori expert knowledge or a systematic mathematical setup.

A Granular Approach to Interval Output Estimation for Rule-Based Fuzzy Models

Rule-based fuzzy models play a dominant role in fuzzy modeling and come with extensive applications in the system modeling area. Due to the presence of system modeling error, it is impossible to construct a model that fits exactly the experimental evidence and, at the same time, exhibits high generalization capabilities. To alleviate these problems, in this study, we elaborate on a realization of granular outputs for rule-based fuzzy models with the aim of effectively quantifying the associated modeling errors. Through analyzing the characteristics of modeling errors, an error model is constructed to characterize deviations among the estimated outputs and the expected ones. The resulting granular model comes into play as an aggregation of the regression model and the error model. Information granularity plays a central role in the construction of granular outputs (intervals). The quality of the produced interval estimates is quantified in terms of the coverage and specificity criteria. The optimal allocation of information granularity is determined through a combined index involving these two criteria pertinent to the evaluation of interval outputs. A series of experimental studies is provided to demonstrate the effectiveness of the proposed approach and show its superiority over the traditional statistical-based method.

Dissolved oxygen modelling of the Yamuna River using different ANFIS models

Dissolved oxygen (DO) is one of the prime parameters for assessing the water quality of any stream. Thus, the accurate estimation of DO is necessary to evolve measures for maintaining the riverine ecosystem and designing appropriate water quality improvement plans. Machine learning techniques are becoming valuable tools for the prediction and simulation of water quality parameters. A study has been performed in the Delhi stretch of the Yamuna River, India, and physiochemical parameters were examined for 5 years to simulate the DO using various machine learning techniques. Simulation and prediction competencies of adaptive neuro fuzzy inference system-grid partitioning (ANFIS-GP) and subtractive clustering (ANFIS-SC) were performed on high dimensional river characteristics. Four different models (M1, M2, M3 and M4) were developed using different combination of input parameters to predict DO. Results obtained from the models were evaluated using root mean square error and coefficient of determination (R²) to identify the appropriate combination of parameters to simulate the DO. Results suggest that both types of ANFIS models work adequately and accurately predict the DO; however, ANFIS-GP outperforms the ANFIS-SC. M4 generated R² of 0.953 from ANFIS-GP compared to 0.911 from ANFIS-SC.

Intelligent rail lubrication system based on fuzzy group analysis

The security of a train becomes a more critical issue as the train’s speed and the complexity of the railway conditions increases. It is especially true when the train runs on a curved radius rail when the lateral force between the train and the rail is less stable. The rail’s side grinding is a significant problem that affects the train’s safety, especially when the train passes through small radial sections in mountainous areas. The intelligent rail lubrication system is critical to enhancing rails’ safety and efficiency and reducing grease pollution along rail lines. This system is modeled with a force analysis of train curve motion and numerical simulation of wear power. The lubrication system is constructed with hardware and software. Based on fuzzy group analysis, this system and the adaptive Proportional Integration Differential (PID) controller is presented to improve the lubricative effects. The system test results show that the quality of lubrication control using this system is efficacious; the control convergence is more reliable than the conventional PID controller.

A Decision Tree-Initialised Neuro-fuzzy Approach for Clinical Decision Support

Apart from the need for superior accuracy, healthcare applications of intelligent systems also demand the deployment of interpretable machine learning models which allow clinicians to interrogate and validate extracted medical knowledge. Fuzzy rule-based models are generally considered interpretable that are able to reflect the associations between medical conditions and associated symptoms, through the use of linguistic if-then statements. Systems built on top of fuzzy sets are of particular appealing to medical applications since they enable the tolerance of vague and imprecise concepts that are often embedded in medical entities such as symptom description and test results. They facilitate an approximate reasoning framework which mimics human reasoning and supports the linguistic delivery of medical expertise often expressed in statements such as 'weight low' or 'glucose level high' while describing symptoms. This paper proposes an approach by performing data-driven learning of accurate and interpretable fuzzy rule bases for clinical decision support. The approach starts with the generation of a crisp rule base through a decision tree learning mechanism, capable of capturing simple rule structures. The crisp rule base is then transformed into a fuzzy rule base, which forms the input to the framework of adaptive network-based fuzzy inference system (ANFIS), thereby further optimising the parameters of both rule antecedents and consequents. Experimental studies on popular medical data benchmarks demonstrate that the proposed work is able to learn compact rule bases involving simple rule antecedents, with statistically better or comparable performance to those achieved by state-of-the-art fuzzy classifiers.

A Survey of Fuzzy Algorithms Used in Multi-Motor Systems Control

Multi-motor systems are strong coupled multiple-input–multiple-output systems. The main objective in multi-motor drive control is to achieve synchronized operation of all motors in the system. In this paper, multi-motor systems are classified in accordance with their control demands. This paper also provides a systematic categorization of multi-motor synchronization techniques. The review of recent research literature indicates that fuzzy algorithms are widely used in multi-motor control. Finally, in this paper, a review of fuzzy logic controllers and their functionalities in multi-motor control is given.

Differential diagnosis of asthma and restrictive respiratory diseases by combining forced oscillation measurements, machine learning and neuro-fuzzy classifiers

To design machine learning classifiers to facilitate the clinical use and increase the accuracy of the forced oscillation technique (FOT) in the differential diagnosis of patients with asthma and restrictive respiratory diseases. FOT and spirometric exams were performed in 97 individuals, including controls (n = 20), asthmatic patients (n = 38), and restrictive (n = 39) patients. The first experiment of this study showed that the best FOT parameter was the resonance frequency, providing moderate accuracy (AUC = 0.87). In the second experiment, a neuro-fuzzy classifier and different supervised machine learning techniques were investigated, including k-nearest neighbors, random forests, AdaBoost with decision trees, and support vector machines with a radial basis kernel. All classifiers achieved high accuracy (AUC ≥ 0.9) in the differentiation between patient groups. In the third and fourth experiments, the use of different feature selection techniques allowed us to achieve high accuracy with only three FOT parameters. In addition, the neuro-fuzzy classifier also provided rules to explain the classification. Neuro-fuzzy and machine learning classifiers can aid in the differential diagnosis of patients with asthma and restrictive respiratory diseases. They can assist clinicians as a support system providing accurate diagnostic options.

Demand Prediction Using a Soft-Computing Approach: A Case Study of Automotive Industry

According to the literature review performed, there are few methods focused on the study of qualitative and quantitative variables when making demand projections by using fuzzy logic and artificial neural networks. The purpose of this research is to build a hybrid method for integrating demand forecasts generated from expert judgements and historical data and application in the automotive industry. Demand forecasts through the integration of variables; expert judgements and historical data using fuzzy logic and neural network. The methodology includes the integration of expert and historical data applying the Delphi method as a means of collecting fuzzy date. The result according to proposed methodology shows how fuzzy logic and neural networks is an alternative for demand planning activity. Machine learning techniques are techniques that generate alternatives for the tools development for demand forecasting. In this study, qualitative and quantitative variables are integrated through the implementation of fuzzy logic and time series artificial neural networks. The study aims to focus in manufacturing industry factors in conjunction time series data.

Versatile Internet of Things for Agriculture: An eXplainable AI Approach

The increase of the adoption of IoT devices and the contemporary problem of food production have given rise to numerous applications of IoT in agriculture. These applications typically comprise a set of sensors that are installed in open fields and measure metrics, such as temperature or humidity, which are used for irrigation control systems. Though useful, most contemporary systems have high installation and maintenance costs, and they do not offer automated control or, if they do, they are usually not interpretable, and thus cannot be trusted for such critical applications. In this work, we design Vital, a system that incorporates a set of low-cost sensors, a robust data store, and most importantly an explainable AI decision support system. Our system outputs a fuzzy rule-base, which is interpretable and allows fully automating the irrigation of the fields. Upon evaluating Vital in two pilot cases, we conclude that it can be effective for monitoring open-field installations.

Efficient Image Retrieval by Fuzzy Rules from Boosting and Metaheuristic

Fast content-based image retrieval is still a challenge for computer systems. We present a novel method aimed at classifying images by fuzzy rules and local image features. The fuzzy rule base is generated in the first stage by a boosting procedure. Boosting meta-learning is used to find the most representative local features. We briefly explore the utilization of metaheuristic algorithms for the various tasks of fuzzy systems optimization. We also provide a comprehensive description of the current best-performing DISH algorithm, which represents a powerful version of the differential evolution algorithm with effective embedded mechanisms for stronger exploration and preservation of the population diversity, designed for higher dimensional and complex optimization tasks. The algorithm is used to fine-tune the fuzzy rule base. The fuzzy rules can also be used to create a database index to retrieve images similar to the query image fast. The proposed approach is tested on a state-of-the-art image dataset and compared with the bag-of-features image representation model combined with the Support Vector Machine classification. The novel method gives a better classification accuracy, and the time of the training and testing process is significantly shorter.

Fuzzy-multidimensional deep learning for efficient prediction of patient response to antiretroviral therapy

Drug component interactions are most likely to trigger unexpected pharmacological effects with unknown causal mechanisms, hence, demanding the discovery of patterns to establish suitable and effective regimens. This paper proposes a novel framework that embeds machine learning (ML) and multidimensional scaling (MDS) techniques, for efficient prediction of patient response to antiretroviral therapy (ART). To achieve this, experiment databases were created from two independent sources: a publicly available HIV domain datasets of patients with failed treatment – hosted by the Stanford University, hereinafter referred to as the Stanford HIV database, and locally sourced datasets gathered from 13 prominent healthcare facilities treating HIV patients in Akwa Ibom State of Nigeria, hereinafter referred to as the Akwa-Ibom HIV database: with 5,780 and 3,168 individual treatment change episodes (TCEs) of HIV treatment indicators (baseline CD4 count (BCD4), followup CD4 count (FCD4), baseline viral load (BRNA), followup viral load (FRNA), and drug type combination (DType)), observed from 1,521 and 1,301 unique patient records, respectively. A hybridised (two-stage) classification system consuming the Interval Type-2 Fuzzy Logic (IT2FL) and Deep Neural Network (DNN) was employed to model and optimise patients’ response to ART with appreciable error pruning achieved through MDS. Visualisation of the experiment databases showed remarkable immunological changes in the Akwa-Ibom HIV database, as the FCD4 of TCEs clustered far above the BCD4, compared to the Stanford HIV database, where over 40% of FCD4 clustered below the BCD4. Similar changes were noticed for the RNA, as more FRNA copies clustered below the BRNA for the Akwa-Ibom datasets, compared to the Stamford datasets. DNN classification results for both databases showed best performance metrics for the Levenberg-Marquardt algorithm when compared with the resilient backpropagation algorithm, with improved drug pattern predictions for experiment with MDS. This paper is most likely to evolve an avenue that triggers interesting combination(s) for optimum patient response, while ensuring minimal side effects, as further findings revealed the superiority of the proposed approach over existing approaches.

Fuzzy Union to Assess Climate Suitability of Annual Ryegrass (Lolium multiflorum), Alfalfa (Medicago sativa) and Sorghum (Sorghum bicolor)

The Law of the Minimum is often implemented using t-norm or fuzzy intersection. We propose the use of t-conorm or fuzzy union for climate suitability assessment of a grass species using annual ryegrass (Lolium multiflorum Lam.) as an example and evaluate the performance for alfalfa (Medicago sativa L.) and sorghum (Sorghum bicolor L.). The ORF and ANDF models, which are fuzzy logic systems based on t-conorm and t-norm between temperature and moisture conditions, respectively, were developed to assess the quality of climate conditions for crops. The parameter values for both models were obtained from existing knowledge, e.g., the EcoCrop database. These models were then compared with the EcoCrop model, which is based on the t-norm. The ORF model explained greater variation (54%) in the yield of annual ryegrass at 84 site-years than the ANDF model (43%) and the EcoCrop model (5%). The climate suitability index of the ORF model had the greatest likelihood of occurrence of annual ryegrass compared to the other models. The ORF model also had similar results for alfalfa and sorghum. We emphasize that the fuzzy logic system for climate suitability assessment can be developed using knowledge rather than presence-only data, which can facilitate more complex approaches such as the incorporation of biotic interaction into species distribution modeling.

A hybrid Q-learning sine-cosine-based strategy for addressing the combinatorial test suite minimization problem

The sine-cosine algorithm (SCA) is a new population-based meta-heuristic algorithm. In addition to exploiting sine and cosine functions to perform local and global searches (hence the name sine-cosine), the SCA introduces several random and adaptive parameters to facilitate the search process. Although it shows promising results, the search process of the SCA is vulnerable to local minima/maxima due to the adoption of a fixed switch probability and the bounded magnitude of the sine and cosine functions (from -1 to 1). In this paper, we propose a new hybrid Q-learning sine-cosine- based strategy, called the Q-learning sine-cosine algorithm (QLSCA). Within the QLSCA, we eliminate the switching probability. Instead, we rely on the Q-learning algorithm (based on the penalty and reward mechanism) to dynamically identify the best operation during runtime. Additionally, we integrate two new operations (Lévy flight motion and crossover) into the QLSCA to facilitate jumping out of local minima/maxima and enhance the solution diversity. To assess its performance, we adopt the QLSCA for the combinatorial test suite minimization problem. Experimental results reveal that the QLSCA is statistically superior with regard to test suite size reduction compared to recent state-of-the-art strategies, including the original SCA, the particle swarm test generator (PSTG), adaptive particle swarm optimization (APSO) and the cuckoo search strategy (CS) at the 95% confidence level. However, concerning the comparison with discrete particle swarm optimization (DPSO), there is no significant difference in performance at the 95% confidence level. On a positive note, the QLSCA statistically outperforms the DPSO in certain configurations at the 90% confidence level.

Fuzzy-Logic Based Distributed Energy-Efficient Clustering Algorithm for Wireless Sensor Networks

Due to the high-energy efficiency and scalability, the clustering routing algorithm has been widely used in wireless sensor networks (WSNs). In order to gather information more efficiently, each sensor node transmits data to its Cluster Head (CH) to which it belongs, by multi-hop communication. However, the multi-hop communication in the cluster brings the problem of excessive energy consumption of the relay nodes which are closer to the CH. These nodes' energy will be consumed more quickly than the farther nodes, which brings the negative influence on load balance for the whole networks. Therefore, we propose an energy-efficient distributed clustering algorithm based on fuzzy approach with non-uniform distribution (EEDCF). During CHs' election, we take nodes' energies, nodes' degree and neighbor nodes' residual energies into consideration as the input parameters. In addition, we take advantage of Takagi, Sugeno and Kang (TSK) fuzzy model instead of traditional method as our inference system to guarantee the quantitative analysis more reasonable. In our scheme, each sensor node calculates the probability of being as CH with the help of fuzzy inference system in a distributed way. The experimental results indicate EEDCF algorithm is better than some current representative methods in aspects of data transmission, energy consumption and lifetime of networks.

Evolution of Collective Behaviour in an Artificial World Using Linguistic Fuzzy Rule-Based Systems

Collective behaviour is a fascinating and easily observable phenomenon, attractive to a wide range of researchers. In biology, computational models have been extensively used to investigate various properties of collective behaviour, such as: transfer of information across the group, benefits of grouping (defence against predation, foraging), group decision-making process, and group behaviour types. The question ‘why,’ however remains largely unanswered. Here the interest goes into which pressures led to the evolution of such behaviour, and evolutionary computational models have already been used to test various biological hypotheses. Most of these models use genetic algorithms to tune the parameters of previously presented non-evolutionary models, but very few attempt to evolve collective behaviour from scratch. Of these last, the successful attempts display clumping or swarming behaviour. Empirical evidence suggests that in fish schools there exist three classes of behaviour; swarming, milling and polarized. In this paper we present a novel, artificial life-like evolutionary model, where individual agents are governed by linguistic fuzzy rule-based systems, which is capable of evolving all three classes of behaviour.