In data analysis, the arrangement of data in a hierarchical structure is an important technique for describing the relationships between data items. Formal concept analysis has been established as a mathematical tool for organising data into a hierarchical lattice-based structure, and the use of fuzzy formal concept analysis to produce a fuzzy lattice has been proposed as a way to model the imprecision and the vagueness inherent in many data sets. In a dynamic environment the relationship between data items may shift over time, and consequently the lattice generated from the new data may differ from the original. This thesis will be concerned with development of a metric measure that gauges the edit-distance between two fuzzy concepts and thereby two fuzzy lattices. Whilst it is possible to deal with a fuzzy context directly, a simpler approach is to discretise objects membership along the unit interval based on fuzzy entries for each attribute. We shall present a method to transform a fuzzy context to an equivalent crisp context that produces a lattice which is isomorphic to the lattice that emerges from the original fuzzy context. Fuzzy formal concept analysis can generate a large number of concepts some of which are very similar. This thesis will present an approach to factor out some of these smaller concepts utilising the edit-distance measure between the concepts. For a coarse classification of data, often a distance based clustering such as k-means clustering is used, we shall use formal fuzzy concept analysis along with the notion of the edit-distance to find the nearest concept to each cluster and thereby find the semantic definition of each cluster based on their attributes.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:683402 |
| Date | January 2015 |
| Creators | Majidian, Andrei |
| Publisher | University of Bristol |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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