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This work applies Evolutionary Computation to achieve completely self-adapting Evolving Fuzzy Neural Networks (EFuNNs) for operating in both incremental (on-line) and batch (off-line) modes. EFuNNs belong to a class of Evolving Connectionist Systems (ECOS), capable of performing clustering-based, on-line, local area learning and rule extraction. Through Evolutionary Computation, its parameters such as learning rates and membership functions are continuously adjusted to reflect the changes in the dynamics of incoming data. The proposed methods are tested on the Mackey–Glass series and the results demonstrate a substantial improvement in EFuNN's performance.

Our plenary panel focused on issues of mathematics education reform that have gained increasing significance since the start of the pandemic in 2020. Our panelists contributions provoked conversation about directions for mathematics education reform post 2020 with a view towards building towards ‘better’ quality and equitable mathematics teaching and learning for the future. Our topic cohered well with the 2021 International Day of Mathematics theme which was “Mathematics for a Better World”. The panel engaged with equity issues relating to two interrelated aspects of ‘building back better’ as we emerge from the crippling challenges of the pandemic. The first issue related to transitions towards remote and online teaching and learning in mathematics education which gained speed due to the massive closure of, and disruption to, schools due to Covid across the globe. The second related to the 2015 United Nations Sustainable Development Goals (SDGs), aimed at building ‘a better future’. We shared insights into emerging issues and research from across the globe and raised questions about the role of mathematics education in providing a better footing to achieve the SDGs and so build towards a more equitable future and a better world. Our paper is based on our panel contributions with voices and perspectives from diverse geographical backgrounds, research interests and expertise. The aim of the paper is to further provoke conversation about emerging and increasingly urgent issues our mathematics education community must grapple with.

We have applied the extended Kalman filter to the parameter, state and structure estimation of a recurrent radial basis function network. The architecture of a recurrent radial basis function network implements a nonlinear autoregresive model with exogenous inputs. The on-line structure adaptation of the network is achieved by combining growing and pruning of the hidden units and connections of the network. Statistical criteria for growing and pruning were derived using the Kalman filter's innovation statistics and state estimation error. Examples of non-stationary dynamic system modeling are given to illustrate the proposed algorithm.

The paper discusses some biological principles of the human brain that would be useful to implement in intelligent information systems (IS). These principles are used to formulate seven major requirements to the current and the future IS. These requirements are met in a new connectionist architecture called evolving connectionist systems (ECOS). ECOS are designed to facilitate building on-line, adaptive, knowledge-based IS. ECOS evolve through incremental, hybrid (supervised/unsupervised), on-line learning. They can accommodate new input data, including new features, new classes, etc. through local element tuning. New connections and new neurons are created during the operation of the system. The ECOS framework is presented and illustrated on a particular type of evolving neural networks - evolving fuzzy neural networks (EFuNNs). EFuNNs can learn spatial-temporal sequences in an adaptive way, through one pass learning. Rules can be inserted and extracted at any time of the system operation. ECOS and EFuNNs are suitable for adaptive pattern classification; adaptive, phoneme-based spoken language recognition; adaptive dynamic time-series prediction; intelligent agents.