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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:rhodes/vital:5399 |
| Date | January 1992 |
| Creators | Lubczonok, Pawel |
| Publisher | Rhodes University, Faculty of Science, Mathematics |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis, Doctoral, PhD |
| Format | 107 leaves, pdf |
| Rights | Lubczonok, Pawel |
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