STUDY OF FUZZY MULTISETS AND THEIR ALGEBRA
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.
Description
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.