Tolerance-based Granular Computing Methods in Learning: Foundations and Applications

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The primary significance of the proposed research accrues from a tolerance-based framework for different forms of knowledge representation and learning. This research bridges the gap between approximate and crisp forms of knowledge structures. Tolerance methods provide a formal foundation for almost solutions that are valid within some approximation, which is required for real world problems and applications. The utilization of various forms of set-based and graph-based approaches and nearness distance functionals of feature vectors make it possible to support approximate learning in three distinct areas: web information labelling, social networks and perception-based image and audio information. The proposed approach also explores computational challenges with big data in the three areas. A direct result of this research is its utility in a number of application areas. The novelty of the work is in: i) unifying theme of tolerance methods and nearness measures in distinct yet related areas, ii) establishing fundamental results of descriptive intersection based on regions and collections of regions and their interplay with classical spatial proximity, iii) unique approach to visual descriptive proximity leading to a broad spectrum of applications such as image analysis, iv) clustering based on Voronoi tessellations useful in efficient neighbourhood methods, v) change detection useful in visual surveillance, and vi) potential for technology transfer specifically with automated map production. This work will also help reveal that the representational structures viewed through the prism of tolerance have a great deal of fluidity and combined with a geometric view have the potential of integrating conceptual structures at different levels of granularity.