Lubczonok, Pawel (1992) Aspects of fuzzy spaces with special reference to cardinality, dimension, and order-homomorphisms. PhD thesis, Rhodes University.
Aspects of fuzzy vector spaces and fuzzy groups are investigated, including linear independence, basis, dimension, group order, finitely generated groups and cyclic groups. It was necessary to consider cardinality of fuzzy sets and related issues, which included a question of ways in which to define functions between fuzzy sets. Among the results proved, are the additivity property of dimension for fuzzy vector spaces, Lagrange's Theorem for fuzzy groups ( the existing version of this theorem does not take fuzziness into account at all), a compactness property of finitely generated fuzzy groups and an extension of an earlier result on the order-homomorphisms. An open question is posed with regard to the existence of a basis for an arbitrary fuzzy vector space.
|Item Type:||Thesis (PhD)|
|Uncontrolled Keywords:||Mathematics, Fuzzy sets, Fuzzy groups, Linear independence, Basis, Dimension, Group order, Finitely generated groups, Cyclic groups, Dimension|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty > Faculty of Science > Mathematics (Pure & Applied)|
|Deposited By:||Philip Clarke|
|Deposited On:||10 Dec 2012 07:36|
|Last Modified:||10 Dec 2012 07:36|
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