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| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | Abd Ghafur Ahmad, Prof. Dr. | - |
| dc.contributor.author | Al-Masarwah Anas Mohammad Abdullah (P90674) | - |
| dc.date.accessioned | 2023-10-13T09:45:39Z | - |
| dc.date.available | 2023-10-13T09:45:39Z | - |
| dc.date.issued | 2020-07 | - |
| dc.identifier.other | ukmvital:128136 | - |
| dc.identifier.uri | https://ptsldigital.ukm.my/jspui/handle/123456789/500563 | - |
| dc.description | BCK-algebras are very important in many areas of mathematics and play a very significant rule in the development of mathematics. The concept of BCI-algebras was given as a generalization of BCK-algebras. Hybrid models of fuzzy sets are important and have a lot of applications in every field of life. Bipolar fuzzy sets and m-polar fuzzy sets are two hybrid models of fuzzy sets play a significant rule in several fields of applied mathematics, computer sciences and information systems. The idea of m-polar fuzzy set theory, advanced generalization of Zhang's bipolar fuzzy sets, is a more generalized theory that can deal with real world problems more precisely than bipolar fuzzy set theory. We divide this research to two main parts. The first part presents the notions of doubt bipolar fuzzy subalgebras, ideals and H-ideals in BCK=BCI-algebras. Relations between these notions are discussed and some pertinent properties are explored. Characterizations of doubt bipolar fuzzy subalgebras, ideals and H-ideals by means of doubt positive t-level cut set and doubt negative s-level cut set are discussed. Also, the concepts of homomorphic preimages and doubt images of doubt bipolar fuzzy ideals and H-ideals in BCK=BCI-algebras are provided. In particular, the equivalence relations and Cartesian product of doubt bipolar fuzzy H-ideals in BCK=BCI-algebras are investigated. The second part discusses m-polar fuzzy set theory with applications in BCK=BCI-algebras. The notions of m-polar fuzzy subalgebras, normal m-polar fuzzy subalgebras, maximal m-polar fuzzy subalgebras, completely normal m-polar fuzzy subalgebras and m-polar fuzzy ideals in BCK=BCI-algebras are introduced, and several related properties are investigated. Moreover, the concept of quasi-coincidence of an mpolar fuzzy point with an m-polar fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea and as a generalization of m-polar fuzzy subalgebras and ideals in BCK=BCI-algebras, we introduce the notions of m-polar (a;b)-fuzzy subalgebras and ideals in BCK=BCI-algebras, where a;b are any of f2;q;2 _q;2 ^qg with a 6=2 ^q: Some interesting results of the algebraic BCK=BCI-algebras in terms of m-polar (a;b)-fuzzy subalgebras and ideals are given. In particular, the notions of m-polar (2;2 _q)-fuzzy subalgebras and ideals in BCK=BCI-algebras are studied. The characterization theorems of these notions are described by level cut subsets. Also, as a more general form of m-polar fuzzy subalgebras and ideals in BCK=BCI-algebras, the notions of m-polar (2bg ;2bg _qbd )-fuzzy subalgebras and m-polar (2;2_q)-fuzzy ideals in BCK=BCI-algebras are introduced and several characterization properties of these new concepts are provided. Finally, the notions of m-polar fuzzy positive implicative and commutative ideals in BCK-algebras are introduced. Related properties are investigated. Also, the notions of m-polar (2;2 _q)-fuzzy positive implicative and commutative ideals in BCK-algebras which is a generalization of m-polar fuzzy positive implicative and commutative ideals in BCK-algebras are defined. These generalized concepts are then linked with ordinary positive implicative and commutative ideals by means of level subsets. Furthermore, characterisations of BCK-algebras are explored using these concepts.,Ph.D | - |
| dc.language.iso | may | - |
| dc.publisher | UKM, Bangi | - |
| dc.relation | Faculty of Science and Technology / Fakulti Sains dan Teknologi | - |
| dc.rights | UKM | - |
| dc.subject | Algebras | - |
| dc.subject | Mathematics | - |
| dc.subject | Universiti Kebangsaan Malaysia -- Dissertations | - |
| dc.subject | Dissertations, Academic -- Malaysia | - |
| dc.title | Subalgebras and ideals in BCK/BCI-algebras based on bipolar and m-polar fuzziness structures | - |
| dc.type | Theses | - |
| dc.format.pages | 164 | - |
| dc.identifier.callno | QA155.A437 2020 tesis | - |
| dc.identifier.barcode | 006528(2022) | - |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
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|---|---|---|---|---|
| ukmvital_128136+SOURCE1+SOURCE1.0.PDF Restricted Access | 828.13 kB | Adobe PDF |  View/Open |
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