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All Journal Journal of the Indonesian Mathematical Society Science and Technology Indonesia
Al-Sharqi, Faisal
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Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Environmental Science Materials Science & Nanotechnology Mathematics Physics

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Revolutionizing Multi-Criteria Decision Making with the Triangular Fuzzy Geometry Bonferroni Mean Operator (TFGBM) Hasnan, Qaiyyum Hafizi Bin; Rodzi, Zahari Bin Md.; Kamis, Nor Hanimah Binti; Amin, Farah Azaliney Binti Mohd; Al-Sharqi, Faisal; Sahak, Jamali Mat; Ahmad, Ghafur Bin
Science and Technology Indonesia Vol. 9 No. 1 (2024): January
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2024.9.1.1-6

Abstract

This study investigates the Multi-Criteria Decision Making (MCDM) topic to address the complexities of decision processes involving ambiguous information. We introduce the Triangular Fuzzy Geometric Bonferroni Mean (TFGBM) operator, a novel aggregation technique inspired by the Geometric Bonferroni Mean (GBM) concept. This operator is intended to aggregate triangular fuzzy numbers within MCDM problems effectively. We thoroughly investigate the properties of TFGBM and its distinct forms to ensure its practical utility. We introduce the Triangular Fuzzy Geometric Weighted Bonferroni Mean (TFGWBM) operator to accommodate situations where input factors have variable degrees of significance. Based on this foundation, we present a comprehensive framework for decision-making involving multiple attributes in ambiguous triangular fuzzy environments. A relevant case study regarding selecting an optimal location for a Halal center demonstrates the efficacy and applicability of our methodology. We emphasize the tangibility and efficiency of the suggested methodology in improving decision-making processes by emphasizing this real-world application.
On Spectrum and Energy of Non-Commuting Graph for Group U_{6n} Romdhini, Mamika Ujianita; Nawawi, Athirah; Al-Sharqi, Faisal; Al-Quran, Ashraf
Journal of the Indonesian Mathematical Society Vol. 31 No. 4 (2025): DECEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i4.1928

Abstract

Let $G$ be a group and $Z(G)$ be the center of $G$. In this paper, we discuss a specific type of graph known as the non-commuting graph, denoted by $\Gamma_G$, whose vertex set contains all group elements excluding central elements, $G\backslash Z(G)$. This graph has to satisfy a condition in which $v_p,v_q \in G\backslash Z(G)$ where $v_p \neq v_q$, are adjacent whenever $v_p v_q\neq v_q v_p$. This paper presents the spectrum and energy of the non-commuting graph for $U_{6n}$, $\Gamma_{U_{6n}}$ associated with the adjacency, degree sum, and degree sum adjacency matrices and their energy relationship.
Delta Degree-Based Indices of Prime Coprime Graph for Integers Modulo Group Abdurahim; Romdhini, Mamika Ujianita; Qudsi, Jihadil; Al-Sharqi, Faisal; Rodzi, Zahari Md.
Science and Technology Indonesia Vol. 11 No. 1 (2026): January
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2026.11.1.10-18

Abstract

Research on prime coprime graphs of finite groups has largely focused on structural properties, spectra, and classical topological indices, with limited attention given to delta degree-based indices. To address this gap, this study investigates delta degree-based topological indices of the prime coprime graph constructed on the group of integers modulo n, Zn. In this graph, the vertices correspond to the elements of Zn, and two distinct vertices are adjacent if and only if the greatest common divisor of their orders is either 1 or a prime number. In the present work, the focus lies on computing and analyzing several delta degree-based topological indices that are obtained by incorporating the concept of delta degree into classical topological indices, including the delta first Zagreb index, the delta second Zagreb index, the delta hyper Zagreb index, and the delta forgotten index. The methodology involves deriving formulas for these delta-based indices for various values of n, supported by systematic computations and data tabulation. Beyond purely algebraic computation, statistical tools are employed to investigate the relationships between different indices. In particular, a comparative distribution analysis is conducted to determine whether pairs of indices exhibit similar patterns of variability using the Levene test.
Co-Authors Abdurahim, Abdurahim Ahmad, Ghafur Bin Al-Quran, Ashraf Amin, Farah Azaliney Binti Mohd Hasnan, Qaiyyum Hafizi Bin Kamis, Nor Hanimah Binti Mamika Ujianita Romdhini, Mamika Ujianita Nawawi, Athirah Qudsi, Jihadil Rodzi, Zahari Bin Md. Rodzi, Zahari Md. Sahak, Jamali Mat