How best to Design Fuzzy Sets and Systems:In memory of Prof. Lotfi A. Zadeh

The fundamental shift in dealing with uncertainties [12] and computerised reasoning was made by the late Professor Lotfi Aliasker Zadeh (1921–2017) in 1965 in his seminal paper [1]. For the last over five decades the Fuzzy Sets theory has matured and was applied to a long list of applications spanning from engineering, social sciences, biology to transport, mathematics and many mor

Interpretable policies for reinforcement learning by empirical fuzzy sets

This paper proposes a method and an algorithm to implement interpretable fuzzy reinforcement learning (IFRL). It provides alternative solutions to common problems in RL, like function approximation and continuous action space. The learning process resembles that of human beings by clustering the encountered states, developing experiences for each of the typical cases, and making decisions fuzzily. The learned policy can be expressed as human-intelligible IF-THEN rules, which facilitates further investigation and improvement. It adopts the actor–critic architecture whereas being different from mainstream policy gradient methods. The value function is approximated through the fuzzy system AnYa. The state–action space is discretized into a static grid with nodes. Each node is treated as one prototype and corresponds to one fuzzy rule, with the value of the node being the consequent. Values of consequents are updated using the Sarsa() algorithm. Probability distribution of optimal actions regarding different states is estimated through Empirical Data Analytics (EDA), Autonomous Learning Multi-Model Systems (ALMMo), and Empirical Fuzzy Sets ( ε FS). The fuzzy kernel of IFRL avoids the lack of interpretability in other methods based on neural networks. Simulation results with four problems, namely Mountain Car, Continuous Gridworld, Pendulum Position, and Tank Level Control, are presented as a proof of the proposed concept

Parsimonious Random Vector Functional Link Network for Data Streams

The majority of the existing work on random vector functional link networks (RVFLNs) is not scalable for data stream analytics because they work under a batch learning scenario and lack a self-organizing property. A novel RVLFN, namely the parsimonious random vector functional link network (pRVFLN), is proposed in this paper. pRVFLN adopts a fully flexible and adaptive working principle where its network structure can be configured from scratch and can be automatically generated, pruned and recalled from data streams. pRVFLN is capable of selecting and deselecting input attributes on the fly as well as capable of extracting important training samples for model updates. In addition, pRVFLN introduces a non-parametric type of hidden node which completely reflects the real data distribution and is not constrained by a specific shape of the cluster. All learning procedures of pRVFLN follow a strictly single-pass learning mode, which is applicable for online time-critical applications. The advantage of pRVFLN is verified through numerous simulations with real-world data streams. It was benchmarked against recently published algorithms where it demonstrated comparable and even higher predictive accuracies while imposing the lowest complexities

Deep Rule-Based Aerial Scene Classifier using High-Level Ensemble Feature Descriptor

In this paper, a new deep rule-based approach using high-level ensemble feature descriptor is proposed for aerial scene classification. By creating an ensemble of three pre-trained deep convolutional neural networks for feature extraction, the proposed approach is able to extract more discriminative representations from the local regions of aerial images. With a set of massively parallel IF...THEN rules built upon the prototypes identified through a self-organizing, nonparametric, transparent and highly human-interpretable learning process, the proposed approach is able to produce the state-of-the-art classification results on the unlabeled images outperforming the alternatives. Numerical examples on benchmark datasets demonstrate the strong performance of the proposed approach

Semi-supervised deep rule-based approach for image classification

In this paper, a semi-supervised learning approach based on a deep rule-based (DRB) classifier is introduced. With its unique prototype-based nature, the semi-supervised DRB (SSDRB) classifier is able to generate human interpretable IF...THEN...rules through the semi-supervised learning process in a self-organising and highly transparent manner. It supports online learning on a sample-by-sample basis or on a chunk-by-chunk basis. It is also able to perform classification on out-of-sample images. Moreover, the SSDRB classifier can learn new classes from unlabelled images in an active way becoming dynamically self-evolving. Numerical examples based on large-scale benchmark image sets demonstrate the strong performance of the proposed SSDRB classifier as well as its distinctive features compared with the “state-of-the-art” approaches

Autonomous data-driven clustering for live data stream

In this paper, a novel autonomous data-driven clustering approach, called AD_clustering, is presented for live data streams processing. This newly proposed algorithm is a fully unsupervised approach and entirely based on the data samples and their ensemble properties, in the sense that there is no need for user-predefined or problem-specific assumptions and parameters, which is a problem most of the current clustering approaches suffer from. Moreover, the proposed approach automatically evolves its structure according to the experimentally observable streaming data and is able to recursively update its self-defined parameters using only the current data sample; meanwhile, it discards all the previously processed data samples. Experimental results based on benchmark datasets exhibit the higher performance of the proposed fully autonomous approach compared with the comparative approaches requiring user- and problem-specific parameters to be predefined. This new clustering algorithm is a promising tool for further applications in the field of real-time streaming data analytics

Self-organising fuzzy logic classifier

In this paper, we present a self-organising nonparametric fuzzy rule-based classifier. The proposed approach identifies prototypes from the observed data through an offline training process and uses them to build a 0-order AnYa type fuzzy rule-based system for classification. Once primed offline, it is able to continuously learn from the streaming data afterwards to follow the changing data pattern by updating the system structure and meta-parameters recursively. The meta-parameters of the proposed approach are derived from data directly. By changing the level of granularity, the proposed approach can make a trade-off between performance and computational efficiency, and, thus, the classifier is able to address a wide variety of problems with specific needs. The classifier also supports different types of distance measures. Numerical examples based on benchmark datasets demonstrate the high performance of the proposed approach and its ability of handling high-dimensional, complex, large-scale problems