Typescript. Includes vita and abstract. Includes bibliographical references (leaves 53-54) Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2001. / Includes bibliographical references (p. 112).

Thesis (Ph. D.)--University of Chicago. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Chicago, Department of Mathematics, August 2002. / Includes bibliographical references. Also available on the Internet.

Thesis (Doctoral)--Universität Bonn, 1991. / Includes bibliographical references.

Revised version of the author's Ph. D. thesis, Free University, Amsterdam. / Includes bibliographical references (p. 236-245) and index.

Thesis (D. Min.)--Southwestern Baptist Theological Seminary, 2004. / Includes prospectus. Includes abstract. Includes bibliographical references (leaves 223-234).

No description available.

An important trend in fuzzy group theory in recent years has been the notion of classification of fuzzy subgroups using a suitable equivalence relation. In this dissertation, we have successfully used the natural equivalence relation defined by Murali and Makamba in [81] and a natural fuzzy isomorphism to classify fuzzy subgroups of some finite abelian p-groups of rank three of the form Zpn + Zp + Zp for any fixed prime integer p and any positive integer n. This was achieved through the usage of a suitable technique of enumerating distinct fuzzy subgroups and non-isomorphic fuzzy subgroups of G. We commence by giving a brief discussion on the theory of fuzzy sets and fuzzy subgroups from the perspective of group theory through to the theory of sets, leading us to establish a linkage among these theories. We have also shown in this dissertation that the converse of theorem 3.1 proposed by Das in [24] is incorrect by giving a counter example and restate the theorem. We have then reviewed and enriched the study conducted by Ngcibi in [94] by characterising the non-isomorphic fuzzy subgroups in that study. We have also developed a formula to compute the crisp subgroups of the under-studied group and provide its proof. Furthermore, we have compared the equivalence relation under which the classification problem is based with various versions of equivalence studied in the literature. We managed to use this counting technique to obtain explicit formulae for the number of maximal chains, distinct fuzzy subgroups, non-isomorphic maximal chains and non-isomorphic fuzzy subgroups of these groups and their proofs are provided.

A dissertation submitted in fulfillment of the requirements for the degree of Master of Science in the school of Mathematics , University of the Witwatersrand, Johannesburg, 2018 / MT 2018