A STUDY OF MULTISET ALGEBRAS
A STUDY OF MULTISET ALGEBRAS
| dc.contributor.author | IBRAHIM, ADEKU MUSA | |
| dc.date.accessioned | 2014-02-24T12:05:50Z | |
| dc.date.available | 2014-02-24T12:05:50Z | |
| dc.date.issued | 2010-05 | |
| dc.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 | en_US |
| dc.description.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. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/2416 | |
| dc.language.iso | en | en_US |
| dc.subject | STUDY, | en_US |
| dc.subject | MULTISET, | en_US |
| dc.subject | ALGEBRAS | en_US |
| dc.title | A STUDY OF MULTISET ALGEBRAS | en_US |
| dc.type | Thesis | en_US |
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