Anggraeni, Ria and Prof. Dr. Agus Widodo,, M.Kes. and Dr. Noor Hidayat,, M.Si. (2019) Ideal Bipolar Anti Fuzzy Pada K-Aljabar. Magister thesis, Universitas Brawijaya.
Abstract
Dalam tesis ini dibahas tentang penerapan bipolar anti fuzzy pada K-aljabar. Suatu pemetaan yang memiliki nilai interval bilangan real [0,1] pada kodomainnya disebut himpunan fuzzy. Teori fuzzy merupakan suatu teori yang banyak diterapkan dalam struktur aljabar. Teori bipolar fuzzy merupakan pengembangan dari teori fuzzy, yang kodomainnya terletak pada interval bilangan real [-1,1]. Himpunan bipolar fuzzy merupakan pasangan dari dua himpunan fuzzy yaitu nilai keanggotaan dan non-keanggotaan, yang secara berurutan direpresentasikan dengan nilai positif dan negatif. Seperti halnya teori fuzzy, teori bipolar fuzzy juga dapat diterapkan dalam beberapa struktur aljabar, salah satunya k-aljabar.Suatu struktur aljabar yang dibangun dari grup G dan memenuhi beberapa aksioma disebut dengan K-aljabar. Seperti halnya bipolar fuzzy, teori bipolar anti fuzzy juga dapat diterapkan pada K-aljabar. Pada tesis ini dibahas tentang sifat-sifat ideal bipolar anti fuzzy pada K-aljabar, karakterisasi ideal bipolar anti fuzzy pada K-aljabar, anti image dan anti preimage ideal bipolar anti fuzzy pada K-aljabar, dan translasi bipolar fuzzy, perluasan bipolar fuzzy, pergandaan bipolar fuzzy pada ideal bipolar anti fuzzy pada K-aljabar.
English Abstract
This thesis discuss about application of bipolar anti fuzzy theory in K-algebras. A mapping whose real interval [0,1] in the codomain is called bipolar fuzzy set. Fuzzy theory is applied in some algberaic structure. Bipolar fuzzy theory is developed from fuzzy theory, but the codomain is a closed interval between -1 and 1. Bipolar fuzzy set is a pair of two fuzzy set, called membership function and non-membership function, respectively represented by positive value and negative value. As well as fuzzy theory, bipolar fuzzy theory also applied in several algebraic structure, one of which is K-algebra. An algebraic structure which is built by group G and fulfilling several axioms is called K-algebra. As well as bipolar fuzzy theory, bipolar anti fuzzy theory also applied in K-algebra. This thesis introduced the notion of bipolar anti fuzzy ideal of K-algebra and it’s properties, characterization bipolar anti fuzzy ideal of K-algebra by means anti positive -cut and anti negative -cut, anti image and anti preimage bipolar anti fuzzy ideal of K-algebra, and bipolar fuzzy translation, bipolar fuzzy extention, bipolar fuzzy multiplication of bipolar anti fuzzy ideal in K-algebra
Other obstract
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| Item Type: | Thesis (Magister) |
|---|---|
| Identification Number: | 041902944 |
| Subjects: | 500 Natural sciences and mathematics > 512 Algebra > 512.2 Groups and group theory |
| Divisions: | S2/S3 > Magister Matematika, Fakultas MIPA |
| Depositing User: | Nur Cholis |
| Date Deposited: | 04 Oct 2022 07:17 |
| Last Modified: | 04 Oct 2022 07:17 |
| URI: | http://repository.ub.ac.id/id/eprint/195322 |
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