Near-Generalized Approximations di Grup Terhadap Pemetaan Bernilai Himpunan

Setyawati, Dian Winda (2024) Near-Generalized Approximations di Grup Terhadap Pemetaan Bernilai Himpunan. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

Text 7002202003-Dissertation.pdf - Accepted Version Restricted to Repository staff only until 1 October 2026. Download (793kB) | Request a copy

Abstract

Subgrup normal di grup dapat mempartisi grup menjadi beberapa kelas ekivalensi sehingga approximations di grup dapat dikonstruksi. Near approximations di grup merupakan perluasan approximations di grup. Konstruksi dari approximations di grup melibatkan sebuah subgrup normal di grup sedangkan near approximations di grup melibatkan beberapa subgrup normal di grup. Sifat – sifat approximations di grup dan near approximations di grup telah dibahas. Suatu pemetaan bernilai himpunan T dari himpunan tak kosong U ke himpunan semua himpunan bagian tak kosong di V dapat membentuk approximations di himpunan V terhadap pemetaan bernilai himpunan T. Sifat – sifat approximations di suatu himpunan terhadap pemetaan bernilai himpunan telah dibahas. Pada disertasi ini, diberikan pengertian baru generalized approximations di grup terhadap pemetaan bernilai himpunan yang merupakan perluasan approximations di suatu himpunan terhadap pemetaan bernilai himpunan. Kemudian, gagasan baru dapat dibentuk untuk near-generalized approximations di grup terhadap pemetaan bernilai himpunan. Konsep near-generalized approximations di grup terhadap pemetaan bernilai himpunan dikembangkan dari generalized approximations di grup terhadap pemetaan bernilai himpunan dan near approximations di grup. Selanjutnya, diselidiki sifat-sifat near-generalized approximations di grup terhadap pemetaan bernilai himpunan.
=================================================================================================================================
A normal subgroup of a group can partition a group into some equivalence classes, the approximations in a group can be constructed. The near approximations in a group are an extension of approximations in a group. The construction of approximations in a group involves a subgrup normal of a grup whereas near approximations in a group involve several normal subgroups of a group. The properties of approximations in a group and near approximations in a group have been obtained. A set-valued mapping T from a non-empty set U to the set of all non-empty subsets of a set V can establish the approximations in a set V based on a set-valued mapping T. The properties of approximations in a set based on a set-valued mapping have been obtained. In this dissertation, we introduce the notion of generalized approximations in a group based on a set-valued mapping, an extension concept of approximations in a set based on a set-valued mapping. Then, the new notions can be created for near-generalized approximations in a group based on a set-valued mapping. The concept of near-generalized approximations in a group based on a set-valued mapping is developed from generalized approximations in a group based on a set-valued mapping and near approximations in a group. Furthermore, we will investigate properties of near-generalized approximation.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	Group, Normal subgroup, Approximations, Near-generalized, Grup, Subgrup normal, Near approximations, Generalized approximations, Near-generalized approximations
Subjects:	Q Science > QA Mathematics > QA159 Algebra
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44002-(S3) PhD Thesis
Depositing User:	Dian Winda Setyawati
Date Deposited:	19 Aug 2024 06:27
Last Modified:	19 Aug 2024 06:27
URI:	http://repository.its.ac.id/id/eprint/115469

Actions (login required)

View Item