Takagi–Sugeno–Kang Fuzzy Classifier Research Articles

Residual Sketch Learning for a Feature-Importance-Based and Linguistically Interpretable Ensemble Classifier.

Motivated by both the commonly used "from wholly coarse to locally fine" cognitive behavior and the recent finding that simple yet interpretable linear regression model should be a basic component of a classifier, a novel hybrid ensemble classifier called hybrid Takagi-Sugeno-Kang fuzzy classifier (H-TSK-FC) and its residual sketch learning (RSL) method are proposed. H-TSK-FC essentially shares the virtues of both deep and wide interpretable fuzzy classifiers and simultaneously has both feature-importance-based and linguistic-based interpretabilities. RSL method is featured as follows: 1) a global linear regression subclassifier on all original features of all training samples is generated quickly by the sparse representation-based linear regression subclassifier training procedure to identify/understand the importance of each feature and partition the output residuals of the incorrectly classified training samples into several residual sketches; 2) by using both the enhanced soft subspace clustering method (ESSC) for the linguistically interpretable antecedents of fuzzy rules and the least learning machine (LLM) for the consequents of fuzzy rules on residual sketches, several interpretable Takagi-Sugeno-Kang (TSK) fuzzy subclassifiers are stacked in parallel through residual sketches and accordingly generated to achieve local refinements; and 3) the final predictions are made to further enhance H-TSK-FC's generalization capability and decide which interpretable prediction route should be used by taking the minimal-distance-based priority for all the constructed subclassifiers. In contrast to existing deep or wide interpretable TSK fuzzy classifiers, benefiting from the use of feature-importance-based interpretability, H-TSK-FC has been experimentally witnessed to have faster running speed and better linguistic interpretability (i.e., fewer rules and/or TSK fuzzy subclassifiers and smaller model complexities) yet keep at least comparable generalization capability.

Three-way decision-based Takagi–Sugeno–Kang fuzzy classifier for partially labeled data

The salient features of Takagi–Sugeno–Kang (TSK) fuzzy classifiers are their superior nonlinear fitting capability and better interpretability, rendering them widely applicable in the domains of data mining and machine learning. However, using TSK fuzzy classifiers for partially labeled data has received little attention. Based on the three-way decision (TWD) theory, this study proposed a TSK fuzzy model to learn from partially labeled data. First, an adaptive sample weight strategy is introduced for the fuzzy partition of the antecedent part and the cross-entropy loss of the consequent part, respectively. Subsequently, a prototype-based firing strength loss mechanism is proposed to constrain the optimization of the model in the fuzzy representation space. It employs a TWD strategy based on the entropy criterion to classify samples as useful, useless, and uncertain, where the proposed model enhances the performance by iteratively utilizing a certain number of useful pseudo-labeled samples. Finally, the validity of the model is theoretically analyzed based on the principle of noise learning. The experimental results on UCI datasets demonstrate that the proposed model exhibits superior performance compared with classical semi-supervised methods, even attaining a performance comparable to that of the model trained on all data with ground-truth labels.

A dynamic broad TSK fuzzy classifier based on iterative learning on progressively rebalanced data

Most of the existing class imbalanced classification methods are weak in interpretability, which is necessary for models to be convincing in some specific scenarios. In this study, we propose a dynamic broad Takagi-Sugeno-Kang (TSK) fuzzy classifier based on iterative learning on progressively expanded imbalanced dataset (DB-TSK-IL) to enhance interpretability. This method begins with a zero-order TSK fuzzy sub-classifier and constructs a TSK fuzzy classifier with a broad ensemble structure through an iterative and progressive process that repeatedly integrates the misclassified instance set of the previous broad model with the training set to train the next zero-order TSK fuzzy sub-classifier. Despite its simple structure, the proposed DB-TSK-IL provides advantageous over the comparative class-imbalanced classification methods with mostly static structures in three aspects: (1) generalization performance, (2) dynamic method with different fuzzy rules activated for different instances, and (3) significantly fewer fuzzy rules, which provide DB-TSK-IL with superior interpretability. Both the theoretical analysis and experimental results validate the efficiency of this method.

Transferable Takagi-Sugeno-Kang Fuzzy Classifier With Multi-Views for EEG-Based Driving Fatigue Recognition in Intelligent Transportation

The safety monitoring system of intelligent transportation provides driving fatigue warning and risk control. Electroencephalogram (EEG) signals can directly reflect the neuronal activity of the brain. The detection and early warning of driving fatigue using EEG signals has important practical significance. However, because of the non-stationarity and timeliness of EEG signals, the single feature detection method is significantly impacted by data distribution differences. In this paper, in the framework of multi-input multi-output (MIMO) Takagi-Sugeno-Kang (TSK) fuzzy system, transferable TSK fuzzy classifier with multi-views (T-TSK-MV) is developed for EEG-based driving fatigue recognition in intelligent transportation. First, in view-specific consequent parameter learning, the view-specific consequent regularizer is designed based on technologies of ridge regression, maximum mean discrepancy (MMD), and manifold regularization, which becomes the bridge to transfer the discriminative information from the related domain to the target domain. In addition, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell_{2,1} $</tex-math> </inline-formula> -norm sparse constraint on consequent parameters is used to simplify fuzzy rules. Then multi-view learning is integrated into the consequent parameter learning, in which T-TSK-MV explores the view-shared consequent regularizer and adaptively assigns weights to each view. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell_{2,1} $</tex-math> </inline-formula> -norm sparse constraint on view-shared consequent regularizer can effectively exploit the local structure of multi-view data. Finally, the fuzzy classifier is constructed on view-specific regularizers and view weights. The experiment on real-word datasets shows that the proposed fuzzy classifier can significantly improve the driving fatigue recognition performance.

A CNN-Based Born-Again TSK Fuzzy Classifier Integrating Soft Label Information and Knowledge Distillation

This paper proposes a CNN-based born-again Takagi-Sugeno-Kang (TSK) fuzzy classifier denoted as CNNBaTSK. CNNBaTSK achieves the following distinctive characteristics: 1) CNNBaTSK provides a new perspective of knowledge distillation with a non-iterative learning method (least learning machine with knowledge distillation, LLM-KD) to solve the consequent parameters of fuzzy rule, where consequent parameters are trained jointly on the ground-truth label loss, knowledge distillation loss, and regularization term; 2) with the inherent advantage of the fuzzy rule, CNNBaTSK has the capability to express the dark knowledge acquired from the CNN in an interpretable manner. Specifically, the dark knowledge (soft label information) is partitioned into five fixed antecedent fuzzy spaces. The centers of each soft label information in different fuzzy rules are {0, 0.25, 0.5, 0.75, 1}, which may have corresponding linguistic explanations: { <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">very low, low, medium, high, very high</i> }. For the consequent part of the fuzzy rule, the original features are employed to train the consequent parameters that ensure the direct interpretability in the original feature space. The experimental results on the benchmark datasets and the CHB-MIT EEG dataset demonstrate that CNNBaTSK can simultaneously improve the classification performance and model interpretability.

Hybrid-ensemble-based interpretable TSK fuzzy classifier for imbalanced data

Owing to its distinguished nonlinear mapping capability and interpretability, a Takagi–Sugeno–Kang (TSK) fuzzy classifier is always employed to achieve both enhanced generalization and better interpretability on imbalanced datasets. In this study, inspired by ensemble learning, a novel hybrid-ensemble-based imbalanced interpretable TSK fuzzy classifier (HI-TSK-FC) is proposed to integrate an imbalanced global linear regression sub-classifier (IGLRc) and several imbalanced TSK fuzzy sub-classifiers (I-TSK-FCs). According to both human's “wholly coarse to locally fine” cognitive behavior and the stacked generalization principle, the training method of HI-TSK-FC, called imbalanced residual sketch learning (IRSL), is further devised to share the virtues of both deep and wide learning. Concretely, IRSL firstly generates IGLRc by calling a newly proposed imbalanced global-sparse-representation-based regression method (IGSR) on all training samples to achieve a wholly coarse result and identifies the nonlinearly distributed training samples in imbalanced datasets. Subsequently, the nonlinearly distributed training samples can be partitioned into several imbalanced residual sketches with much imbalanced likely by calling the proposed residual-based partition method (RPM). After that, several I-TSK-FCs are generated to achieve locally fine results in a parallel way on the corresponding imbalanced residual sketches. Finally, a new minimal-distance-based voting strategy is taken on the stacked outputs of both IGLRc and all I-TSK-FCs to obtain the final output of HI-TSK-FC. Besides, the proposed minimal-distance-based voting strategy also guarantees an interpretable and clear prediction route of HI-TSK-FC for each testing sample. Consequently, HI-TSK-FC owns both feature-importance-based and linguistic-based interpretabilities. Both experimental and statistical results confirm that except for feature-importance-based interpretability, HI-TSK-FC achieves at least comparable generalization capability, better linguistic interpretability (fewer adopted fuzzy rules and smaller model complexity) and faster running speed on all adopted imbalanced datasets.

Fuzzy rule dropout with dynamic compensation for wide learning algorithm of TSK fuzzy classifier

This paper extends our recent work about dropout for the design of Takagi–Sugeno–Kang(TSK) fuzzy classifiers, i.e., fuzzy-knowledge-out, to the generalized concept, i.e., fuzzy rule dropout with dynamic compensation. This extension is motivated by very complicated firing patterns of all pieces of knowledge in human brain, i.e., binary or continuous or both random ways for different situations. Our theoretical analysis indicates that this generalized concept can encapsulate various random dropouts of fuzzy rules with more match of human cognitive behavior, more capabilities of both generalization and co-adaptation avoidance. Based on this concept, we develop a wide learning algorithm of a TSK fuzzy classifier. Experimental results about the thirteen datasets demonstrate that with high interpretability guarantee, TSK fuzzy classifiers designed by means of fuzzy rule dropout with dynamic compensation outperform the comparative methods, especially in the sense of testing accuracy.

A wide interpretable Gaussian Takagi–Sugeno–Kang fuzzy classifier and its incremental learning

While wide fuzzy classifiers which combine several TSK fuzzy sub-classifiers with some aggregation strategy like weighting have been widely developed to achieve good classification performance and/or interpretability, the aggregation strategies inevitably deteriorate the interpretability of the whole ensemble and hinder them from developing the corresponding incremental algorithm easily yet efficiently for online learning. To avoid this weakness and ensure enhanced generalization capability and interpretability, this work attempts to develop a novel wide interpretable Gaussian Takagi–Sugeno–Kang (TSK) fuzzy classifier (WIG-TSK) by simultaneously training all the Gaussian TSK fuzzy sub-classifiers without any aggregation strategy, just like a single structure. Each fuzzy rule of WIG-TSK generates its Gaussian fuzzy antecedent on randomly chosen features by exerting the Gaussian random selection on the original features of data. WIG-TSK has four merits: (1) Gaussian random selection of features guarantees both its easy interpretability and the avoidance of rule-explosion curse, and hence WIG-TSK is suitable to deal with multi- and even high-dimensional data. (2) all the sub-classifiers of WIG-TSK can be simultaneously trained in parallel without any aggregation strategy, and hence the corresponding incremental learning can be developed to dynamically update the whole structure of WIG-TSK. (3) WIG-TSK has a solid theoretical guarantee to be structurally equivalent to a more complicated zero-order Gaussian TSK fuzzy classifier. (4) WIG-TSK theoretically has better generalization capability than the corresponding wide combination structure. The effectiveness of WIG-TSK is manifested by the experimental results on eighteen benchmarking datasets and a commonly-used UCI dataset in terms of classification accuracy, running speed and interpretability.

Prediction by Fuzzy Clustering and KNN on Validation Data With Parallel Ensemble of Interpretable TSK Fuzzy Classifiers

For many application scenarios where raw and even multidomain training data can be easily collected, and at the same time, validation data (as ground-truth data) are available, it becomes naturally desirable for us to perform an enhanced classification/prediction on only validation data with the appropriate leverage of training data. In this article, a novel ensemble framework EP-TSK-FK of Takagi–Sugeno–Kang (TSK) fuzzy subclassifiers, is proposed to achieve the following distinctive characteristics: 1) each interpretable TSK fuzzy subclassifier on each training subset can be quickly built in parallel such that its outputs provide the values of the corresponding augmented features of the original validation data space; 2) as a novel ensemble method of fuzzy subclassifiers, EP-TSK-FK trains all the interpretable TSK fuzzy subclassifiers only once and does not explicitly reuse them while predicting a testing sample, which thereby reduces the computational complexity of the ensemble process for prediction; 3) after running the proposed iterative fuzzy c-means clustering algorithm iterative fuzzy C-means clustering (IFCM) on the augmented validation data to obtain the representative centroids, the fast classification/prediction of EP-TSK-FK on the testing samples is realized by using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -nearest neighbor (KNN) method on the representative centroids with the original features; and 4) enhanced classification performance by the IFCM & KNN method is theoretically revealed, and the experimental results on the benchmarking datasets indicate the effectiveness of EP-TSK-FK and its parallel learning method in the sense of enhanced classification performance, running time, and interpretability.

Realizing Deep High-Order TSK Fuzzy Classifier by Ensembling Interpretable Zero-Order TSK Fuzzy Subclassifiers

Although high-order Takagi–Sugeno–Kang (TSK) fuzzy systems have demonstrated their computational advantages and simultaneously circumvent the weakness that the number of rules with the number of input variables and membership functions grows exponentially in both zero-order and first-order TSK fuzzy systems for complex modeling tasks, they still face two serious issues: incapability for a changing environment and no interpretability of the coefficients in high-order polynomial used in the consequent part of each fuzzy rule. In order to circumvent these two challenges, a novel stacked architecture of an interpretable deep higher order TSK fuzzy classifier called DHO-TSK and its deep learning method are proposed by proving the equivalence between a high-order TSK fuzzy classifier and a deep ensemble of interpretable zero-order TSK fuzzy classifiers in this article. DHO-TSK can be built by assembling interpretable zero-order TSK fuzzy classifiers in a special stacked way. Each zero-order TSK fuzzy classifier can be learnt by randomly selecting input features, randomly assigning an antecedent fuzzy subset from a fixed fuzzy partition to each of the selected input features, and then multiplying the output of each TSK fuzzy classifier by a randomly selected feature. Except for the abovementioned solid theoretical equivalence, DHO-TSK is featured in the following aspects: first, the consequent part of each fuzzy rule in DHO-TSK becomes interpretable and the output expression of each layer in DHO-TSK becomes comprehensible due to the adopted stacked ensemble; second, its enhanced classification performance can be achieved in a stacked deep learning way; third, DHO-TSK has its adoptability for changing environments owing to random selection of both features and fuzzy membership functions. Our experimental results on the benchmarking UCI and KEEL datasets and a real dataset indicate the effectiveness of DHO-TSK and its learning method in the sense of both classification performance and interpretability.

Interpretable Recognition for Dementia Using Brain Images

Machine learning-based models are widely used for neuroimage-based dementia recognition and achieve great success. However, most models omit the interpretability that is a very important factor regarding the confidence of a model. Takagi–Sugeno–Kang (TSK) fuzzy classifiers as the high interpretability and promising classification performance have widely used in many scenarios. TSK fuzzy classifier can generate interpretable fuzzy rules showing the reasoning process. However, when facing high-dimensional data, the antecedent become complex which may reduce the interpretability. In this study, to keep the antecedent of fuzzy rule concise, we introduce the subspace clustering technique and use it for antecedent learning. Experimental results show that the used model can generate promising recognition performance as well as concise fuzzy rules.

Quantitative-integration-based TSK fuzzy classification through improving the consistency of multi-hierarchical structure

In traditional hierarchical fuzzy classifiers, there exist some main problems. These issues include the output of the previous training layer influencing with the input of the next layers, the inconsistency between the intra-layer and inter-layer, and the improvement of consequent parameters. Based on the above troubles, a novel quantitative-integration-based hierarchical Takagi–Sugeno–Kang (TSK) is proposed to handle the challenges in existing hierarchical fuzzy classifiers. As a novel hierarchical structure, the proposed classifier is built in a stacked manner. Each base building unit consists of an optimized zero-order TSK fuzzy classifier. For good interpretability of each base building unit, the antecedent parameters are solved by random selections of input features, random combinations of fuzzy rules, divisions of fuzzy partitions and generations of cluster centers. In addition, an improved method based on classical ridge regression is proposed to solve the problem of the consistency between intra-layer and inter-layer. In order to enhance the classification performance of the fuzzy classifier, the input of each layer is optimized to effectively resolve the problem that the output of the previous layer affects the input of the next base building unit. Moreover, a method that randomly selects a part of the sample from the original training set is adopted to open the manifold structure of input set. Furthermore, the experimental results indicate that this method can indeed make the QI-TSK-FC fuzzy classifier obtain good or comparative classification performance. To improve the generalization ability of the fuzzy classifier, a method that quantitatively solves the integrated output is considered so that the QI-TSK-FC model can quickly obtain the satisfactory optimal solution. Finally, the classification performance and interpretability of the proposed fuzzy classifier are verified through the MIT-BIH sleep datasets.

A Deep-Ensemble-Level-Based Interpretable Takagi-Sugeno-Kang Fuzzy Classifier for Imbalanced Data.

Existing research reveals that the misclassification rate for imbalanced data depends heavily on the problematic areas due to the existence of small disjoints, class overlap, borderline, and rare data samples. In this study, by stacking zero-order Takagi-Sugeno-Kang (TSK) fuzzy subclassifiers on the minority class and its problematic areas in the deep ensemble, a novel deep-ensemble-level-based TSK fuzzy classifier (IDE-TSK-FC) for imbalanced data classification tasks is presented to achieve both promising classification performance and high interpretability of zero-order TSK fuzzy classifiers. Simultaneously, according to the stacked generalization principle, the proposed classifier lifts up oversampling from the data level to the deep ensemble level with a guarantee of enhanced generalization capability for class imbalance learning. In the structure of IDE-TSK-FC, the first interpretable zero-order TSK fuzzy subclassifier is built on the original training dataset. After that, several successive zero-order TSK fuzzy subclassifiers are stacked layer by layer on the newly identified problematic areas from the original training dataset plus the corresponding interpretable predictions obtained by the averaging strategy on all previous layers. IDE-TSK-FC simply takes the classical K -nearest neighboring algorithm at each layer to identify its problematic area that consists of the minority samples and its surrounding K majority neighbors. After randomly neglecting certain input features and randomly selecting the five Gaussian membership functions for all the chosen input features and the augmented feature in the premise of each fuzzy rule, each subclassifier can be quickly obtained by using the least learning machine to determine the consequent part of each fuzzy rule. The experimental results on both the public datasets and a real-world healthcare dataset demonstrate IDE-TSK-FC's superiority in class imbalanced learning.

Identification of Alzheimer's EEG With a WVG Network-Based Fuzzy Learning Approach.

A novel analytical framework combined fuzzy learning and complex network approaches is proposed for the identification of Alzheimer's disease (AD) with multichannel scalp-recorded electroencephalograph (EEG) signals. Weighted visibility graph (WVG) algorithm is first applied to transform each channel EEG into network and its topological parameters were further extracted. Statistical analysis indicates that AD and normal subjects show significant difference in the structure of WVG network and thus can be used to identify Alzheimer's disease. Taking network parameters as input features, a Takagi-Sugeno-Kang (TSK) fuzzy model is established to identify AD's EEG signal. Three feature sets—single parameter from multi-networks, multi-parameters from single network, and multi-parameters from multi-networks—are considered as input vectors. The number and order of input features in each set is optimized with various feature selection methods. Classification results demonstrate the ability of network-based TSK fuzzy classifiers and the feasibility of three input feature sets. The highest accuracy that can be achieved is 95.28% for single parameter from four networks, 93.41% for three parameters from single network. In particular, multi-parameters from the multi-networks set obtained the best result. The highest accuracy, 97.12%, is achieved with five features selected from four networks. The combination of network and fuzzy learning can highly improve the efficiency of AD's EEG identification.

A Parallel Ensemble Fuzzy Classifier for Diabetes Diagnosis

Diabetes is one of the deadliest disease on the planet. It isn't just an ailment yet additionally a maker of various types of maladies like heart assault, blurred vision, nephropathy and dyspnea. When decision-making process by traditional machine learning methods for a patient is made, it often face the following challenges: (1) some uncertain factors exist in the patient or the decision-making process which often result in misdiagnosis; (2) the decision-making process with traditional machine learning methods are block-box which are not interpretable. In this paper, a parallel-based fuzzy partition and fuzzy weighted ensemble TSK (Takagi-Sugeno-Kang) fuzzy classifier called FP-TSK-FW is proposed for diabetes diagnosis by utilizing its strong uncertainty-handling capability and interpretability so as to achieve promising classification performance. In FP-TSK-FW, the training dataset firstly is partitioned into several subsets by fuzzy clustering algorithm FCM on certain attributes, each interpretable TSK fuzzy subclassifier on each training subset can be quickly built in parallel, and with different structures. Finally, the final prediction of FP-TSK-FW is realized by fuzzy weighted for the results of each classifier. The experimental results on Pima Indians Diabetes dataset indicate the effectiveness of the proposed methods in the sense of both enhanced classification performance and interpretability.

Optimize TSK Fuzzy Systems for Classification Problems: Minibatch Gradient Descent With Uniform Regularization and Batch Normalization

Takagi-Sugeno-Kang (TSK) fuzzy systems are flexible and interpretable machine learning models; however, they may not be easily optimized when the data size is large, and/or the data dimensionality is high. This paper proposes a mini-batch gradient descent (MBGD) based algorithm to efficiently and effectively train TSK fuzzy classifiers. It integrates two novel techniques: 1) uniform regularization (UR), which forces the rules to have similar average contributions to the output, and hence to increase the generalization performance of the TSK classifier; and, 2) batch normalization (BN), which extends BN from deep neural networks to TSK fuzzy classifiers to expedite the convergence and improve the generalization performance. Experiments on 12 UCI datasets from various application domains, with varying size and dimensionality, demonstrated that UR and BN are effective individually, and integrating them can further improve the classification performance.

Biologically Plausible Fuzzy-Knowledge-Out and Its Induced Wide Learning of Interpretable TSK Fuzzy Classifiers

As an alternative to existing construction methods of Takagi–Sugeno–Kang (TSK) fuzzy classifiers, this paper presents a novel design methodology formulated by a new concept called fuzzy-knowledge-out and its induced wide learning way. Analogous to the “ dropout ” concept in deep learning, the concept of fuzzy-knowledge-out in TSK fuzzy classifiers is motivated by the firing pattern of knowledge in biological neural networks. Our theoretical analysis reveals that a fuzzy classifier built after fuzzy-knowledge-out from a complete set of highly interpretable fuzzy rules is distinctive in generalization and coadaption avoidance. As such, an ensemble called wide learning based TSK (WL-TSK), of highly interpretable zero-order TSK fuzzy subclassifiers constructed quickly by means of fuzzy-knowledge-out operations in a wide learning manner is proposed to achieve enhanced classification performance and high interpretability. With the use of the proposed halving or averaging operations, WL-TSK essentially behaves like only one zero-order TSK fuzzy classifier. Thus, the proposed method can be considered as a new design methodology of TSK fuzzy classifiers. Our experimental results on 15 datasets indicate the effectiveness of WL-TSK in terms of both enhanced classification performance and high interpretability.

Stacked Blockwise Combination of Interpretable TSK Fuzzy Classifiers by Negative Correlation Learning

In this paper, we propose a blockwise combination of interpretable Takagi–Sugeno–Kang (TSK) fuzzy classifiers to simultaneously achieve high accuracy and concise interpretability. As a special hierarchical fuzzy classifier, the proposed classifier is built in a stacked block-by-block way. Each base building block consists of multiple zero-order TSK fuzzy classifiers, which are simultaneously trained in an analytical manner by using negative correlation learning to enhance the generalization ability of the base building block. For utilizing the stacked generalization principle, a random projection of the outputs from the current base building block is presented to the next base building block together with the current training sample in order to enhance the generalization ability of our hierarchical fuzzy classifier. The purpose of such a special hierarchical structure is that all base building blocks can be trained in the same input–output space with the current training sample and the randomly projected output from the previous building block. In the input layer, the target output for the current training sample is used instead of the randomly projected output from the previous building block. Each TSK fuzzy classifier in base building blocks consists of interpretable TSK fuzzy rules, which are generated by randomly selecting input features and randomly assigning an antecedent fuzzy subset from a fixed fuzzy partition to each of the selected input features. Merits of the proposed classifier are demonstrated through comparative studies on benchmark datasets.

Deep Takagi–Sugeno–Kang Fuzzy Classifier With Shared Linguistic Fuzzy Rules

In many practical applications of classifiers, not only high accuracy but also high interpretability is required. Among a wide variety of existing classifiers, Takagi–Sugeno–Kang (TSK) fuzzy classifiers may be one of the best choices for achieving a good balance between interpretability and accuracy. In order to further improve their accuracy without losing their interpretability, we propose a highly interpretable deep TSK fuzzy classifier HID-TSK-FC (deep shared-linguistic-rule-based TSK fuzzy classifier) based on the concept of shared linguistic fuzzy rules. The proposed classifier has two characteristics: One is a stacked hierarchical structure of component TSK fuzzy classifiers for high accuracy, and the other is the use of interpretable linguistic rules with the same set of linguistic labels for all inputs. High interpretability is achieved at each layer by using the same set of linguistic values for all inputs, including the outputs from the previous layers in the stacked hierarchical structure. We show that a linguistic rule with the outputs from the previous layers as its inputs is equivalent to a fuzzy rule with a nonlinear consequent or a linear consequent with a certainty factor. We also show that HID-TSK-FC is mathematically equivalent to a novel TSK fuzzy classifier with shared interpretable linguistic fuzzy rules. Promising performance of HID-TSK-FC is demonstrated through extensive computational experiments on benchmark datasets and a real-world application case.

Bayesian Takagi–Sugeno–Kang Fuzzy Classifier

In this paper, the Takagi–Sugeno–Kang (TSK) fuzzy classifier is casted into the Bayesian inference framework and a new fuzzy classifier called Bayesian TSK fuzzy classifier (B-TSK-FC) is proposed accordingly. The proposed classifier can be constructed by learning both the antecedent and consequent parameters of the involved fuzzy rules simultaneously. As a result of the introduction of Bayesian inference, the proposed B-TSK-FC can be distinguished as follows. 1) Unlike most existing TSK fuzzy classifiers where the antecedent and consequent parameters of fuzzy rules are learnt in a decoupled manner and the antecedent parameters are learnt only in the input space, the antecedent parameters of the fuzzy rules in B-TSK-FC are learnt by developing a fuzzy clustering method in the input–output space, and the consequent parameters of fuzzy rules are learnt in accordance with the maximum margin of separation principle, thereby resulting to form an intrinsic link between the input and output spaces to achieve improved classification performance and better interpretability. 2) With a Dirichlet prior assumption about fuzzy memberships in fuzzy clustering, a Markov-Chain Monte-Carlo technique is employed to estimate the parameters of the proposed classifier from a sampling perspective. 3) Rather than being rivals, fuzziness and probability in B-TSK-FC are collaboratively modeled to enhance the performance of TSK fuzzy classifier, in terms of classification and interpretability. Our experimental results in synthetic datasets as well as several real-world datasets confirm such merits of the proposed fuzzy classifier.