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Several methods have been studied in text categorization and mostly are inspired by the statistical distribution features in the texts, such as the implementation of Machine Learning (ML) methods. However, there is no work available that investigates the performance of ML-based methods against the text expression-based method, especially for incident and medical case categorization. Meanwhile, these two domains are becoming ever more popular, due to a growing interest of automation in security intelligence and health services. This paper presents a text expression-based method called Evolving Fuzzy Grammar (EFG) and evaluates its performance against the conventional ML methods of Naive Bayes, support vector machine, $$k$$k-nearest neighbor, adaptive booting, and decision tree. The incident dataset used is a real dataset that was taken from the World Incidents Tracking System, while ImageCLEF 2009 was used as the source for radiology case reports. The results suggested variations of strength and weakness of each method in both categorization tasks, where a standard evaluation technique (i.e., recall, precision, and $$F$$F-measure) was used. In both domains, the SMO and IBk methods were the best, while AdaBoost was the worst. It was also observed that the medical dataset was easier to categorize than the incident. Although EFG was ranked second lowest, it obtained the highest precision score in the bombing categorization, the highest score in armed attack recall, and was averagely ranked in the top three for the medical case categorization. It was also noted that the text expression-based method used in EFG was the most verbose and expressive, when compared to the ML methods. This indicates that EFG is a viable method in text categorization and may serve as an alternative approach to such a task.

Fuzzy sets are a good model of the flexible definitions used in human language, but do not always give results in accordance with human reasoning. One reason is that operations on fuzzy sets do not obey all identities from crisp set algebra, such as the law of the excluded middle. Additionally, when used to represent fuzzy numbers they lead to a generalised interval arithmetic rather than a fuzzy version of standard arithmetic. In this paper, we outline the $$X\hbox {-}\mu $$X-μ approach, a new method of representing, visualizing and calculating functions of fuzzy values. This fuzzy representation retains standard Boolean operations and leads to standard arithmetic when applied to numerical quantities. It includes the idea of strict fuzzy values, which do not incorporate set or interval-based uncertainty. Using simple examples, we illustrate the $$X\hbox {-}\mu $$X-μ approach and outline the notion of a strict fuzzy value.

The quantity of unstructured and semi-structured data available is growing rapidly. Adding structure to such data by grouping similar items into fuzzy categories (or granules) can be a productive approach, and can lead to additional knowledge (e.g. by monitoring association and other relations between classes). Formal concept analysis (and fuzzy formal concept analysis) enables us to identify hierarchical structure arising from similarities in attribute values. However, in an environment where source data is updated, this data-driven approach may lead to concept lattices whose structure varies over time (that is, the number of concepts and their relation to each other may change significantly as updates are processed). In this paper, we describe a novel way of measuring the distance between concept lattices. The method can be applied to comparison of lattices derived from the same set of objects using different attributes or to different sets of objects categorised by the same attributes. We prove that the proposed method is a distance metric and illustrate its use by means of examples.