A STUDY OF MULTISET ALGEBRAS
A STUDY OF MULTISET ALGEBRAS
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Date
2010-05
Authors
IBRAHIM, ADEKU MUSA
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Abstract
This dissertation presents a concise history of the uses of multisets in various disguised
forms which eventually led to a formalization of multiset theory. We present a
comprehensive study of fundamentals of multisets and their applications which
appeared in two of our publications (Singh et al., 2007 and 2008). We study max–plus
algebra and by exploiting the notion of compatibility relation (reflexive and symmetric),
we develop a truncated symmetrized max–plus algebra called minimal max or ≈ max,
and discuss its application which appeared in our publication (Singh et al., 2010). We
extend our study on application of compatibility relation to multisets and outline a
theory of “Tolerance multiset and its topological perspective”. We explicate the notion
of multiset space, introduce two new operations on the multiset space and show that it
shares properties of many algebraic structures. We also develop the concept of relations
and functions on multiset spaces and show that the multiset space can be metrized
thereby defining topology on a multiset. Finally, we delineate the problem related to
difference and complementation in multiset theory. We show that none of the existing
approaches succeeds in resolving the attendant difficulties without assuming some
contrived stipulations.
Description
A DISSERTATION SUBMITTED TO THE POSTGRADUATE
SCHOOL, AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA IN
PARTIAL FULFILLMENT FOR THE AWARD OF DOCTOR OF
PHILOSOPHY IN MATHEMATICS
DEPARTMENT OF MATHEMATICS
AHMADU BELLO UNIVERSITY, ZARIA
NIGERIA
Keywords
STUDY,, MULTISET,, ALGEBRAS