Density-Based Dynamic Fuzzy Rule Interpolation

Abstract

Sparse fuzzy rule bases often leave input observations unmatched, preventing classical fuzzy inference from producing meaningful outputs and leading to failed inference. Fuzzy Rule Interpolation (FRI) addresses this limitation by generating temporary interpolated rules; however, these rules are conventionally discarded, which restricts knowledge coverage and reduces efficiency. The core problem examined in this thesis is how interpolation outcomes can be exploited to construct a dynamic, self-improving rule base that increases coverage and sustains predictive performance.

To address this problem, a novel framework of Dynamic Fuzzy Rule Interpolation(D-FRI) is developed to promote frequently recurring interpolated rules back into the sparse rule base. Three density-oriented mechanisms of Dynamic Fuzzy Rule Interpolation are introduced in combination with Transformation-based FRI (T-FRI). The first employs Harmony Search to guide candidate rule promotion (HS-D-FRI). The second applies DBSCAN to exploit density connectivity in order to identify promotion regions (DBSCAN-D-FRI). The third incorporates OPTICS clustering, utilising reachability ordering together with a generalized membership frequency weighting and rule-uniqueness measure to rank promotion candidates (OPTICS-DFRI). In all cases, interpolation, density evaluation, and promotion can be integrated into an iterative pipeline, producing an enriched rule base while preserving the underlying semantics of FRI reasoning.

The proposed methods are systematically evaluated on benchmark datasets including Iris, Yeast, Banana, Glass, and Tae. Performance is assessed in terms of accuracy, rule-base coverage, and additional diagnostic indicators. The results demonstrate that the Density-Based-D-FRI mechanisms substantially improve coverage and enhance accuracy relative to conventional FRI baselines, with OPTICS-D-FRI providing particularly robust density-ordering for promotion
decisions. The framework is further applied to mammography abnormality detection using the INbreast dataset, where texture and shape features are extracted to drive the iterative D-FRI process. In this real-world application, the promoted rules demonstrate reusability for subsequent observations and contribute to sustained improvements across iterations.

The contributions of this thesis lie in the formalisation of a general Density-Based D-FRI framework that transforms temporary interpolation outcomes into valuable rule-base updates, the development of three density-based promotion mechanisms integrated with T-FRI, the introduction of a generalized membership frequency weighting and uniqueness criterion for rule promotion, and the delivery of comprehensive evaluations on both benchmark datasets and a
medical imaging application.

Date of Award	2025
Original language	English
Awarding Institution	Aberystwyth University
Supervisor	Qiang Shen (Supervisor) & Reyer Zwiggelaar (Supervisor)