Formal Taxon Concept and Rough Set Approximation
Nozomi Ytow1, Akira Sato2, David R. Morse3, David McL Roberts4
1 Gene Reserch Center, University of Tsukuba, Tsukuba, Ibaraki, 305-8572 Japan. 2 Academic Computing and Communication Center, University of Tsukuba,
Tsukuba, Ibaraki, 305-8571 Japan. 3 Faculty of Mathematics and Computing, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom. 4 Department of Zoology, The Natural History Museum, Cromwell Road, London SW7 5BD, United KingdomTaxon concepts can be implicit (undefined) or defined as sets either of individuals or character states. Multiple taxonomy databases and taxonomic data from multiple data sources require an appropriate method to manage these alternative representations. Formal concept analysis, FCA, (Ganter and Wille, 1996, 1999) allows the handling of
taxon concepts as a pair of sets called extension (character states, a circumscription) and intension (specimens, ostensive definition). Although FCA has an affinity with taxonomy, it inherits a restriction from set theory, that a set is a definite list of elements. In reality, a taxon consists of an indefinite collection of individuals, specimens and character states as knowledge about the taxa and its relatives increases. Rough set approximation separates the including and excluding boundaries, defining a zone of uncertainty, which mathematically relaxes the problem of indefinite sets and facilitates the detection of incompatible concepts.