Document Details
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Document Type |
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Thesis |
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Document Title |
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HESITANT FUZZY SET AND SOME OF ITS APPLICATIONS المجموعة الفازية الترددية وبعض تطبيقاتها |
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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 hesitant fuzzy sets and hesitant fuzzy soft sets on BCK-algebras and investigate their properties.
In Chapter1, we provided the previous concepts of BCK-algebra, ideals of BCK-algebras, fuzzy sets, fuzzy ideals of BCK-algebras, anti fuzzy subalgebra, anti fuzzy ideals, soft set, fuzzy soft sets of BCK-algebras. Also, some of the properties and theories were reviewed in order to take advantage of them in the coming chapters of the thesis.
In Chapter2, the notion of hesitant fuzzy sets are introduced, and the concepts of hesitant fuzzy subalgebra/ideal of a BCK-algebras are presented. However, we introduce the new types of ideals of BCK-algebras and discuss some properties of them. In addition, we defined the notions of hesitant anti fuzzy on subalgebra/ideals of BCK-algebras and investigated relationship between of these concepts. In last chapter, we introduced some applications on hesitant fuzzy sets.
In Chapter3, we introduced the concepts of hesitant fuzzy soft sets, hesitant fuzzy soft subalgebras and hesitant fuzzy soft ideals of BCK-algebras. Also, presented some of different properties. The notions of hesitant fuzzy soft implicative ideal, hesitant fuzzy soft positive implicative ideal and hesitant fuzzy soft commutative ideal of BCK-algebras were discussed and some related result. However, the notions of hesitant anti fuzzy soft of subalgebras/ideals of BCK-algebras were defined some of the properties of the above concepts were investigated. Also, we define the concepts of hesitant anti fuzzy soft for (implicative, positive
Implicative and commutative) ideals of BCK-algebras. As we discuss some of the properties associated with them. Finally, we presented some applications on hesitant fuzzy soft set in last chapter. All results have submitted as articles to scientific journals. We have been three articles published and one has obtained accepted to publish.
The outcomes of this dissertation are the following papers:
1. New types of hesitant fuzzy ideals in BCK-algebras[4].
2. New types of hesitant fuzzy soft ideals in BCK-algebras [8].
3. Hesitant anti fuzzy set in BCK-algebras [6].
4. Hesitant anti fuzzy soft set in BCK-algebras [3].
5. Trapezoidal interval type-2 hesitant fuzzy sets associated with new operation[5].
6. Trapezoidal Interval type-2 hesitant fuzzy soft set and its application[7]. |
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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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1439 AH
2018 AD |
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Co-Supervisor |
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Prof. Hamza A. Abujabal |
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Added Date |
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Thursday, February 22, 2018 |
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Researchers
| حليمة عبد الرحمن الشهري | Alshehri, Halimah Abdulrahman | Researcher | Doctorate | |
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