ALGEBRAICSTUDYOFSOFTLATTICETHEORY ANDITSAPPLICATIONSTODISTRIBUTED COMPUTINGSYSTEM
ALGEBRAICSTUDYOFSOFTLATTICETHEORY ANDITSAPPLICATIONSTODISTRIBUTED COMPUTINGSYSTEM
| dc.contributor.author | YUSUF, AHMEDOMEIZA | |
| dc.date.accessioned | 2017-01-24T11:33:27Z | |
| dc.date.available | 2017-01-24T11:33:27Z | |
| dc.date.issued | 2016-03 | |
| dc.description | A THESIS SUBMITTED TO THE SCHOOL OF POST GRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA-NIGERIA, IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF DOCTOR OF PHILOSOPHY IN MATHEMATICS DEPARTMENT OF MATHEMATICS AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA | en_US |
| dc.description.abstract | In this thesis, we crisply present the fundamentals of soft set theory to emphasize that soft set has enough developed basic supporting tools through which various algebraic structures in theoretical point of view could be developed. The concepts of conjunction and disjunction are redefined as binary operations on soft sets and their properties are presented. A perception named soft Boolean algebra is introduced where some related results were established. It is shown that if SB is a collection of all soft sets under a common universe U, then (SB,∧,∨,∅, ˜U) is a Boolean algebra. For any two soft sets (F,A), (G,B)∈ (SB), domination, idempotents, absorption and complement laws are satisfied, where ∅ and ˜U are unique. We define soft lattice in terms of the redefined conjunction and disjunction and present some examples. Upper bound and least upper bound, lower bound and greatest lower bound were defined in soft set context. Soft lattice is redefine in terms of supremum and infimumanditisshownthatthetwodefinitionsareequivalent. Givenanysoft semilattice (Γ,E), where Γ(e1)⊆ Γ(e2) if and only if Γ(e1)∧ Γ(e2) = Γ(e1), ∀ e1,e2∈ E, we show that ((Γ,E),⊆) is an ordered soft set in which every pair of elements has greatest lower bound. The idea of soft lattice is extended to distributed soft lattice, modular soft lattice and isomorphic soft lattice and their properties are presented with some related results. We established that if (Γ,E) is an ordered soft set and A,B⊆ E, such that θ : (F,A)→ (G,B) is defined by θ(F(e1)) ={F(e2)∈ (F,A) : F(e1)⊆ F(e2),∀F(e1)∈ (F,A)}, then (F,A) is isomorphic to the range of θ ordered by containment ⊆. Finally, some applications of soft lattice theory to distributed computing system are presented where it is shown that, a predicate is linear if and only if it is meetclosed. If B is a linear predicate with the efficient advancement property, then there exists an efficient algorithm to determine the least consistent cut that satisfy B (if any). We presented an algorithm to detect a linear predicate of a consistentcutandshowedthatthesliceofadistributedcomputingisuniquely defined for all predicate. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/8523 | |
| dc.language.iso | en | en_US |
| dc.subject | ALGEBRAICSTUDY, | en_US |
| dc.subject | SOFT LATTICE THEORY, | en_US |
| dc.subject | APPLICATIONS, | en_US |
| dc.subject | DISTRIBUTED COMPUTING SYSTEM, | en_US |
| dc.title | ALGEBRAICSTUDYOFSOFTLATTICETHEORY ANDITSAPPLICATIONSTODISTRIBUTED COMPUTINGSYSTEM | en_US |
| dc.type | Thesis | en_US |
Files
Original bundle
1 - 1 of 1
No Thumbnail Available
- Name:
- ALGEBRAIC STUDY OF SOFT LATTICE THEORY.pdf
- Size:
- 592.24 KB
- Format:
- Adobe Portable Document Format
- Description:
License bundle
1 - 1 of 1
No Thumbnail Available
- Name:
- license.txt
- Size:
- 1.62 KB
- Format:
- Item-specific license agreed upon to submission
- Description: