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All Journal Journal of Tropical Life Science : International Journal of Theoretical, Experimental, and Applied Life Sciences CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of Food and Life Sciences KEMBARA Syntax Literate: Jurnal Ilmiah Indonesia BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Matematika UNAND
Noor Hidayat, Noor
Fakultas Kesehatan Masyarakat, Universitas Ahmad Dahlan Yogyakarta
Agriculture, Biological Sciences & Forestry Humanities Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Environmental Science Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Mathematics Mechanical Engineering Physics Public Health Social Sciences Transportation Other

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Multipolar Intuitionistic Fuzzy Positive Implicative Ideal in B-Algebras Amigo, Royyan; Hidayat, Noor; Krisnawati, Vira Hari
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 1 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i1.23164

Abstract

In this paper, we start with the concept of B-algebras, commutative B-algebras and fuzzy ideal in B-algebras. We also study about multipolar intuitionistic fuzzy ideal. We explain the notion of multipolar intuitionistic fuzzy positive implicative ideal in B-algebras and some characterizes. In addition, we examine some theorems and proportions which contain the conditions for a multipolar intuitionistic fuzzy set become a multipolar intuitionistic fuzzy positive implicative ideal in B-algebras. One of the result is a multipolar intuitionistic fuzzy set (l,s) over commutative B-algebra X is a multipolar intuitionistic fuzzy positive implicative ideal (l,s) over commutative B-algebra X if and only if (x*y)*z=0 implies l(x)= Inf{l(y),l(z)} and s(x) = Sup{s(y),s(z)}, for all x,y,z.
Energy and Topological Indices of Complete Bipartite Subgraphs Meilina, Kiki Amanda Eka; Hidayat, Noor; Krisnawati, Vira Hari
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.32765

Abstract

This paper investigates the complete bipartite subgraphs induced within the zero-divisor graph of a commutative ring formed by the direct product of three distinct modular integer rings. The set of nonzero zero-divisors is partitioned into six disjoint subsets based on the position of the zero component in each element. Six complete bipartite subgraphs are constructed and analysed by pairing subsets with zeros in different positions. For each subgraph, we compute the energy, Laplacian energy, and three degree-based multiplicative topological indices, namely the Narumi–Katayama index, and the first and second multiplicative Zagreb indices. The results are expressed in closed-form formulas and reveal consistent structural patterns, highlighting the relationship between the algebraic properties of the ring and the graph theoretic characteristics of the induced subgraphs.
On Group-Vertex-Magic Labeling of Simple Graphs Khuluq, Muhammad Husnul; Krisnawati, Vira Hari; Hidayat, Noor
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v8i2.23621

Abstract

Let A be an Abelian group with identity 0. The A-vertex-magic labeling of a graph G is a mapping from the set of vertices in G to A-{0} such that the sum of the labels of every open neighborhood vertex of v is equal, for every vertex v in G. In this article, we discuss group-vertex-magic labeling of some simple graphs by using the Abelian group Zk, with natural numbers k1. We investigated some classes of simple graphs are path graphs, complete graphs, cyclic graphs, and star graphs. The method we used in this article is literature study and then developing the properties of vertex-magic labeling of some simple graphs, that are path graphs, complete graphs, cyclic graphs, and star graphs. We obtain that complete graphs, cyclic graphs, and star graphs have Zk-vertex-magic labeling, while path graphs have vertex-magic labeling only for n=2,3.
m-Polar Fuzzy B-ideal of B-algebra Amandani, Dian Kartika; Hidayat, Noor; Rouf, Abdul
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v8i2.20694

Abstract

B-algebra is an algebraic structure related to BCI/BCK-algebra. Many researchers have studied fuzzy B-ideal on B-algebra, m-polar fuzzy set on BCI-algebra and B-algebra, m-polar fuzzy subalgebra on BCI-algebra and B-algebra, m-polar fuzzy ideal on BCI-algebra, m-polar (∈,∈)-fuzzy p-ideal on BCI-algebra, m-polar (∈,∈)-fuzzy q-ideal on BCI-algebra, and m-polar (∈,∈)-fuzzy a-ideal on BCI-algebra. We build a new structure, namely m-polar (∈,∈)-fuzzy B-ideal on B-algebra. This research aims to extend the knowledge of m-polar fuzzy sets, which can be combined with other algebraic structures, besides BCI-algebra. In this study, we investigate and describe the properties of m-polar (∈,∈)-fuzzy B-ideal of B-algebra. We also investigate the connection among m-polar (∈,∈)-fuzzy B-ideal, m-polar fuzzy subalgebra, and m-polar fuzzy ideal. We serve a condition that causes an m-polar fuzzy ideal to become an m-polar (∈,∈)-fuzzy B-ideal. We also serve expansion properties of an m-polar (∈,∈)-fuzzy B-ideal. Futhermore, examples showing the modification of π_i formula are added. The properties of m-polar (∈,∈)-fuzzy B-ideal of B-algebra are obtained by combining and modifying the properties of m-polar (∈,∈)-fuzzy p-ideal, m-polar (∈,∈)-fuzzy q-ideal, and m-polar (∈,∈)-fuzzy a-ideal of BCI-algebra
Indeks Wiener dari Graf Identitas dan Graf Pangkat pada Grup Siklis Berhingga Darmajid, Darmajid; Hidayat, Noor; Wicaksono, Wildan Bagus; Musyarrofah, Ayunda Faizatul
Syntax Literate Jurnal Ilmiah Indonesia
Publisher : Syntax Corporation

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36418/syntax-literate.v9i7.16994

Abstract

Graf identitas atas suatu grup didefinisikan sebagai graf dengan himpunan titiknya berupa unsur- unsur grup dan dua titik dihubungkan oleh sebuah sisi jika hasil kalinya merupakan unsur identitas atau tepat salah satu dari kedua titik merupakan unsur identitas pada grup. Graf pangkat atas suatu grup didefinisikan sebagai graf dengan himpunan titiknya berupa unsur-unsur grup dan dua titik dihubungkan oleh sebuah sisi jika satu titik dapat dituliskan sebagai perpangkatan dari titik lainnya. Pada penelitian ini dikaji formulasi indeks Wiener dari graf identitas dan graf pangkat pada grup siklik berhingga. Hasil formulasi indeks Wiener dari graf identitas terbagi atas grup siklis orde 1, orde ganjil lebih dari 1 dan orde genap sedangkan dari graf pangkat difokuskan pada grup siklis berode perpangkatan bilangan prima dan perkalian dua prima berbeda.
On Relations between Some Types of (α,β)-Intuitionistic Fuzzy Ideals of Ternary Semigroups Hutama, Damarian Prawira; Hidayat, Noor; Al-ghofari, Abdul Rouf
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 5, No 2 (2021): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v5i2.5171

Abstract

In this article, the notion of (α,β)-intuitionistic fuzzy ideals (briefly, (α,β)-IF ideals) of ternary semigroups is described using ”belong to” relation (ϵ) and “quasi-coincidence with” relation (q) connecting two objects, i.e., an intuitionistic fuzzy point (IFP, for short) and an intuitionistic fuzzy set (briefly, IFS). Throughout this paper, α∈{ϵ,q,ϵ∨q} and β∈{ϵ,q,ϵ∨q,ϵ∧q}.  The main purposes of this research are to construct the definition of (α,β)-intuitionistic fuzzy ideals of ternary semigroups and to investigate the relations between some types of these ideals. To achieve these goals, we use literature review method to study previous researches regarding (α,β)-fuzzy ideals of ternary semigroups and (α,β)-IF ideals of semigroups. As a result, we find the conditions for an IFS and an ideal of a ternary semigroup to be classified as an (α,ϵ∨q)-IF ideal of ternary semigroup. Relations between some types of (α,β)-IF ideals of a ternary semigroup are also discussed here.
An η-Intuitionistic Fuzzy Rings Structure Hidayahningrum, Syafitri; Hidayat, Noor; Marjono, Marjono
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.11833

Abstract

In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuzzy ring is a structure which is built with combinating the definition of fuzzy ring, intuitionistic fuzzy set, and η-intuitionistic fuzzy set. The η-intuitionistic fuzzy set is characterized by any value η∈[0,1], where the degree of membership μ_(A^η ) (k) is obtained based on the averaging operator of the degree of membership μ_A (k) and the value of η∈[0,1]. While the degree of non membership ν_(A^η ) (k) is obtained based on the averaging operator of the degree of non membership ν_A (k) and the value of 1-η∈[0,1]. In its development, new concepts were obtained, namely the η-intuitionistic fuzzy ideal and its properties related to the sum and product operation of η-intuitionistic fuzzy ideals. Furthermore, the η-intuitionistic fuzzy ideals concept can be developed into an η-intuitionistic fuzzy quotient ring, η-intuitionistic fuzzy homomorphism, and its properties on the next research. 
Co-Authors A.A. Ketut Agung Cahyawan W Abdul Rouf Abdul Rouf Alghofari Al-ghofari, Abdul Rouf Amandani, Dian Kartika Amigo, Royyan Damarian Prawira Hutama, Damarian Prawira Darmajid, Darmajid Dwi Mifta Mahanani, Dwi Mifta Edi Priyo Utomo Estri Laras Arumingtyas Fatimah, Farah Maulidya Fira Fitriah Fitriah, Zuraidah Hidayahningrum, Syafitri Indah Yanti Joni Kusnadi Karim, Corina Khuluq, Muhammad Husnul Krisnawati, Vira Hari Kurfia, Mustika Ana M.Pd S.T. S.Pd. I Gde Wawan Sudatha . Marjono Marjono Meilina, Kiki Amanda Eka Mohamad Muslikh Musyarrofah, Ayunda Faizatul Putra, M. Rafael Andika shalsabilla, Az Zahra Syaiful Anam Wicaksono, Wildan Bagus Wijaya, Ongky Denny