STUDY OF FUZZY MULTISETS AND THEIR ALGEBRA

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Date
2015-03
Authors
ALKALI, Alhaji Jibril
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Abstract
In this dissertation, fundamentals of the theory of fuzzy sets, multisets and fuzzy multisets were studied, and some properties of -cuts, specifically two decomposition theorems for fuzzy sets, were extended to fuzzy multisets. Also, properties of inverse -cuts for fuzzy sets were strengthened and extended to fuzzy multisets. Moreover, some new operations were introduced which helped developing certain monoids of multiset partitions and fuzzy partitions. Finally, fuzzy groups, multigroups and fuzzy multigroups were studied and abelian fuzzy multigroup was introduced.
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A DISSERTATION SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA-NIGERIA. IN PARTIAL FULFILMENT FOR THE AWARD OF DOCTOR OF PHILOSOPHY IN MATHEMATICS DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE AHMADU BELLO UNIVERSITY, ZARIA March, 2015
Keywords
STUDY,, FUZZY,, MULTISETS,, ALGEBRA.
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