Aspects of fuzzy spaces with special reference to cardinality, dimension, and order-homomorphisms

Title: Aspects of fuzzy spaces with special reference to cardinality, dimension, and order-homomorphisms
Creator: Lubczonok, Pawel
Subject: Fuzzy sets Topological spaces
Date Issued: 1992
Date: 1992
Type: Thesis
Type: Doctoral
Type: PhD
Identifier: vital:5399
Identifier: http://hdl.handle.net/10962/d1005213
Description: 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.
Format: 107 leaves
Format: pdf
Publisher: Rhodes University
Publisher: Faculty of Science, Mathematics
Language: English
Rights: Lubczonok, Pawel

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RU Department of Mathematics (Pure and Applied)

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