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https://ptsldigital.ukm.my/jspui/handle/123456789/499874Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | Abdul Razak Salleh, Dato' Dr. | - |
| dc.contributor.author | Abdallah Mohammad Fadel Alhusban (P70499) | - |
| dc.date.accessioned | 2023-10-13T09:35:41Z | - |
| dc.date.available | 2023-10-13T09:35:41Z | - |
| dc.date.issued | 2017-02 | - |
| dc.identifier.other | ukmvital:85345 | - |
| dc.identifier.uri | https://ptsldigital.ukm.my/jspui/handle/123456789/499874 | - |
| dc.description | Several mathematicians followed the Rosenfeld and Anthony-Sherwood's approach in investigating fuzzy group theory. One of the modifications is Dib's approach which introduced fuzzy space as the universal set. In this research, the fuzzy space is generalised to complex fuzzy space by extending the membership function from the closed unit interval [0, 1] to unit disc in the complex plane. The thesis is divided into two parts, complex fuzzy algebra and complex fuzzy hyperalgebra. Firstly, the properties of the basic operations, namely union, intersection, difference and containment on complex fuzzy spaces are defined and derived. Then the concept of complex fuzzy subspace, complex fuzzy function and complex fuzzy binary operation are introduced. In addition, the algebra of complex fuzzy spaces and complex fuzzy subspaces is studied. Using the concept of complex fuzzy spaces and complex fuzzybinary operations, the complex fuzzy group theory are developed by defining complex fuzzy group, complex fuzzy subgroup, complex fuzzy normal subgroup, complex fuzzy quotient group and complex fuzzy group homomorphism. New results are derived and giving consequences in fuzzy group theory and ordinary group theory. Furthermore, using the concept of complex fuzzy space and complex fuzzy binary operation, the structure of complex fuzzy ring theory is developed by defining complex fuzzy ring, complex fuzzy subring, complex fuzzy integral domain, complex fuzzy ideal, complex fuzzy quotient ring, complex fuzzy ring homomorphism and complex fuzzy field. The second part of the thesis deals with complex fuzzy hyperalgebra. Based on the notion of complex fuzzy spaces, complex fuzzy hyperstructure and complex fuzzy hyperoperation are introduced and studied. This includes complex fuzzy hypergroup (complex fuzzy Hv-group), complex fuzzy hyperring (complex fuzzy Hv-ring), complex fuzzy subhypergroup, complex fuzzy subhyperring and complex fuzzy hyperideal. New results are derived and as a consequence some results in fuzzy hyperalgebra and ordinary hyperalgebra have been obtained.,Certification of Master's/Doctoral Thesis" is not available | - |
| dc.language.iso | eng | - |
| dc.publisher | UKM, Bangi | - |
| dc.relation | Faculty of Science and Technology / Fakulti Sains dan Teknologi | - |
| dc.rights | UKM | - |
| dc.subject | Fuzzy algebra | - |
| dc.subject | Fuzzy hyperalgebra | - |
| dc.subject | Dissertations, Academic -- Malaysia | - |
| dc.title | Complex fuzzy algebra and complex fuzzy hyperalgebra | - |
| dc.type | Theses | - |
| dc.format.pages | 116 | - |
| dc.identifier.barcode | 002592(2017) | - |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| ukmvital_85345+SOURCE1+SOURCE1.0.PDF Restricted Access | 407.6 kB | Adobe PDF |  View/Open |
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