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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. [ABSTRACT FROM AUTHOR]

Many practical scenarios have demanded that we should classify unlabeled data more accurately based on both physical features (e.g., color, distance, or similarity) and implicit style features of data. As most extant classification algorithms classify unlabeled data based only on their physical features, they become weak in achieving expected classification results for many scenarios. To work around this drawback in this paper, a novel classification method (FuCM) from the perspective of fuzzy social network based on both physical and implicit style features of data is proposed. Based on the proposed fuzzy social network and its dynamics about fuzzy influences of nodes, FuCM comprises two stages. In its training stage, after the fuzzy social network has been built, it learns the topological structure, reflecting physical features and implicit style features of data by carrying out fuzzy influence dynamics in the built network. In its prediction stage, both physical and implicit style features of data are effectively integrated to yield the double structure efficiency characterized by fuzzy influences of nodes. FuCM classifies unlabeled data according to the strongest connection measure based on the proposed double structure efficiency. FuCM does not assume that both data distribution and the classification by physical features or by both physical and implicit style features of data must be known in advance. Thus, it is a novel unified classification framework in this sense. In contrast to all the nine comparative methods, FuCM experimentally demonstrates its comparable classification performance on most synthetic, UCI and KEEL datasets, which can be well classified based only on physical features of data. Furthermore, it displays distinctive superiority on five case studies where satisfactory classification certainly depends on both physical and implicit style features. [ABSTRACT FROM AUTHOR]

In data science applications, it is very often to require predictive models satisfying monotonicity with respect to the explanatory variables involved in the dataset. In ordinal classification or regression, this occurs when the output variable or class label do not decrease when input variables increase, or vice versa. This problem is commonly known as monotonic classification, and most existing classification techniques are not able to manage this kind of constraints or they require first to monotonize the data. In the literature, the monotonicity has been considered in linguistic fuzzy models, fuzzy-inference methods, and fuzzy rule-based control systems. However, to the best of our knowledge, there is no fuzzy rule-based system designed to produce monotonic fuzzy rule-based models for classification problems. In this paper, we propose to incorporate some mechanisms based on monotonicity indexes for addressing such problems in two popular and competitive evolutionary fuzzy systems algorithms for classification and regression tasks: FARC-HD and FSmogfs$^e$ +Tun$^e$. In addition, the proposals are able to handle any kind of classification dataset without the necessity of preprocessing. The quality of our approaches is analyzed using statistical analysis and comparing with well-known monotonic classifiers. [ABSTRACT FROM AUTHOR]

Recently, evolutionary multiobjective optimization (EMO) algorithms have been utilized for the design of accurate and interpretable fuzzy rule-based systems. This research area is often referred to as multiobjective genetic fuzzy systems (MoGFS), where EMO algorithms are used to search for non-dominated fuzzy rule-based systems with respect to their accuracy and interpretability. In this paper, we examine the ability of EMO algorithms to efficiently search for Pareto optimal or near Pareto optimal fuzzy rule-based systems for classification problems. We use NSGA-II (elitist non-dominated sorting genetic algorithm), its variants, and MOEA/D (multiobjective evolutionary algorithm based on decomposition) in our multiobjective fuzzy genetics-based machine learning (MoFGBML) algorithm. Classification performance of obtained fuzzy rule-based systems by each EMO algorithm is evaluated for training data and test data under various settings of the available computation load and the granularity of fuzzy partitions. Experimental results in this paper suggest that reported classification performance of MoGFS in the literature can be further improved using more computation load, more efficient EMO algorithms, and/or more antecedent fuzzy sets from finer fuzzy partitions. [ABSTRACT FROM AUTHOR]

An introduction to the journal is presented in which the editor discusses an article on genetic fuzzy data mining, an article on Mamdani fuzzy systems, and the application of subgroup discovery methods for analysis of patients and the arrival time in Psychiatric Emergency Department.