SEMIGRUP FUZZY SMARANDACHE
Smarandache semigroups is an expansion of semi group structure, by taking a proper subset of semigroups which is in form of group. But, a proper subset which is in form of group cannot always be found in semigroups. Therefore, we need necessary requirements and prosperous requirements in the Smarand...
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| Main Authors: | , |
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| Format: | Theses and Dissertations NonPeerReviewed |
| Published: |
[Yogyakarta] : Universitas Gadjah Mada
2012
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| Subjects: | |
| Online Access: | https://repository.ugm.ac.id/100981/ http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=57504 |
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| Institution: | Universitas Gadjah Mada |
| Summary: | Smarandache semigroups is an expansion of semi group structure, by taking
a proper subset of semigroups which is in form of group. But, a proper subset
which is in form of group cannot always be found in semigroups. Therefore, we
need necessary requirements and prosperous requirements in the Smarandache semigroups. Besides, this study also shows some kinds of Smarandache semigroups, which have specific characteristics, namely Smarandache commutative semigroups and Smarandache cyclic semi groups. Then, by the definitions, we will investigate the form of its Cartecius product.
In this thesis, fuzzification is also studied to generalize the structure of
Smarandache semigroups become Smarandache fuzzy semi groups. This
fuzzification is also done for the other two forms, Smarandache commutative semi groups and Smarandache cyclic semi groups. After obtaining the generalization in Smarandache fuzzy semigroups, then it is continued by finding the form of its cartecius product. In general, Cartecius product of Smarandache semigroups is Smarandache semigroups, and Cartecius product of Smarandache fuzzy semigroups is Smarandache fuzzy semigroups. Those results is also valid conversely by having specific requirements for Smarandache semigroups and Smarandache fuzzy semigroups. |
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