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Document Type |
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Thesis |
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Document Title |
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Bipolar Fuzzy Sets Based on Algebraic Structure تطبيق مفهوم المجموعات الفازية ثنائية القطب على بنية جبرية |
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Subject |
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Faculty of Sciences |
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Document Language |
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Arabic |
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Abstract |
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The subject of this dissertation depends on the study of the properties of bipolar fuzzy sets based on BCK-modules.
BCK-algebras, ideals of BCK-algebras, BCK-modules, fuzzy sets and bipolar fuzzy sets based on BCK-algebras and ideals of BCK-algebras are basic concepts included in the first chapter of the dissertation. In Chapter two, the notion of bipolar fuzzy BCK-submodules is introduced, and some characterizations of bipolar fuzzy BCK-submodule are given. The concept of homomorphic images and preimages of bipolar fuzzy BCK-submodules are investigated. Normality and completely normality of bipolar fuzzy BCK-submodules are discussed. In Chapter three, translations and multiplications of bipolar fuzzy BCK-submodules are discussed, extensions of bipolar fuzzy BCK-submodules are introduced and relations between translations and multiplications of bipolar fuzzy BCK-submodules are presented. In Chapter four, we develop bipolar fuzzy TOPSIS method and bipolar fuzzy ELECTRE I method for solving MCDM problems that are equipped with bipolar-valued fuzzy information. Moreover, we apply a numerical example for both methods.
The outcomes of this dissertation are the following papers:
1- Maha Alghamdi, Najat Muthana and Noura Alshehri, "Novel concepts of bipolar fuzzy BCK-submodules", Discrete Dynamics in Nature and Society, 2017, 7 pages.
2- Maha Alghamdi, Noura Alshehri and Najat Muthana, "Bipolar fuzzy sets of BCK-modules", accepted for publication in Journal of Computational Analysis and application.
3- Maha Alghamdi and Noura Alshehri, "Some multi-criteria decision making methods based on bipolar-valued fuzzy sets", submitted. |
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Supervisor |
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Prof. Noura O. Alshehri |
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Thesis Type |
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Doctorate Thesis |
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Publishing Year |
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1438 AH
2017 AD |
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Added Date |
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Thursday, June 8, 2017 |
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Researchers
| مها عبدالله الغامدي | ALGHAMDI, MAHA ABDULLAH | Researcher | Doctorate | |
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