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All Journal EKSAKTA: Journal of Sciences and Data Analysis BAREKENG: Jurnal Ilmu Matematika dan Terapan Sciencestatistics: Journal of Statistics, Probability, and Its Application
Rian Kurnia
Mathematics Department, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Energy Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Transportation

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ON PROPERTIES OF PRIME IDEAL GRAPHS OF COMMUTATIVE RINGS Kurnia, Rian; Abrar, Ahmad Muchlas; Syarifudin, Abdul Gazir; Wijaya, Verrel Rievaldo; Supu, Nur Ain; Suwastika, Erma
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 3 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss3pp1463-1472

Abstract

The prime ideal graph of in a finite commutative ring with unity, denoted by , is a graph with elements of as its vertices and two elements in are adjacent if their product is in . In this paper, we explore some interesting properties of . We determined some properties of such as radius, diameter, degree of vertex, girth, clique number, chromatic number, independence number, and domination number. In addition to these properties, we study dimensions of prime ideal graphs, including metric dimension, local metric dimension, and partition dimension; furthermore, we examined topological indices such as atom bond connectivity index, Balaban index, Szeged index, and edge-Szeged index.
Optimizing Medan Tourist Routes Using BiogeographyBased Optimization Zai, Fidelis Nofertinus; Nainggolan, Donni Andreas; Kurnia, Rian; -, Erwin
EKSAKTA: Journal of Sciences and Data Analysis VOLUME 7, ISSUE 1, April 2026
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20885/EKSAKTA.vol7.iss1.art8

Abstract

This study optimizes tourist routes across 14 destinations in the city of Medan using the Biogeography-Based Optimization (BBO) algorithm. The problem is formulated as a closed-path Traveling Salesman Problem (TSP) with an extension allowing for flexibility in freely selecting the starting point. The route is determined based on the distance between two locations, where the distance is assumed to be asymmetric to account for real-world urban road conditions such as one-way systems, while ignoring traffic conditions and other costs. Simulation results show that even though the starting point is freely determined, the BBO algorithm is still able to consistently produce routes that are close to optimal with stable convergence. The main contribution of this study is the provision of an adaptive and realistic route planning model to support tourism information systems in urban areas.
Time Series Analysis in Forecasting Nickel Prices Using the ARIMA and Double Exponential Smoothing Methods Vina Nurmadani; Rian Kurnia; Indah Suciati
Sciencestatistics: Journal of Statistics, Probability, and Its Application Vol. 4 No. 1 (2026): JANUARY
Publisher : Universitas Muhammadiyah Metro

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Abstract

Nickel is one of the strategic commodities that plays an important role in global industries, particularly as the primary raw material in the production of stainless steel and electric vehicle batteries. The increasing demand for nickel, driven by technological advancements and the need for more environmentally friendly energy sources, causes nickel prices to fluctuate, making it necessary to employ methods capable of forecasting future price movements. This study aims to forecast nickel prices using the Autoregressive Integrated Moving Average (ARIMA) method and the Double Exponential Smoothing method, as well as to compare the performance of both methods. The data used in this research consist of secondary daily nickel price data with 62 observation periods. The research stages include data preprocessing, stationarity testing, modeling, and model evaluation using Mean Squared Error (MSE) and Root Mean Squared Error (RMSE). The results show that the best ARIMA model is ARIMA(2,1,1), which produces an MSE of 0.2797 and an RMSE of 0.5288. Meanwhile, the Double Exponential Smoothing method results in an MSE of 0.1299 and an RMSE of 0.3604. Based on these evaluation results, the Double Exponential Smoothing method demonstrates better performance than ARIMA in forecasting nickel prices in this study. This method is able to produce more accurate and stable predictions that follow the trend patterns of the data. Therefore, the Double Exponential Smoothing method is recommended as a more optimal approach for nickel price forecasting
Application of Fuzzy C-Means with Variations in Weighting Exponent for Clustering the Human Development Index Suciati, Indah; Rian Kurnia; Vina Nurmadani; Fitri Nurjanah
Sciencestatistics: Journal of Statistics, Probability, and Its Application Vol. 4 No. 1 (2026): JANUARY
Publisher : Universitas Muhammadiyah Metro

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Abstract

Human development is commonly measured using the Human Development Index (HDI), which reflects the quality of life across regions. In Indonesia, disparities in HDI values indicate uneven development, requiring appropriate analytical approaches. This study aims to cluster Indonesian provinces based on HDI indicators using the Fuzzy C-Means (FCM) method with variations in the weighting exponent. The data consist of 38 provinces in 2025, including life expectancy, expected years of schooling, average years of schooling, and adjusted real expenditure per capita. The clustering results were evaluated using the Partition Coefficient Index (PCI). The optimal configuration was obtained at and , with a PCI value of 0.716399. The results show that provinces are grouped into clusters with relatively lower HDI, which are predominantly located in eastern Indonesia, and clusters with higher HDI, which are mostly found in western Indonesia. These findings demonstrate that FCM is effective in identifying regional development patterns.
Co-Authors Abrar, Ahmad Muchlas Erwin - Fitri Nurjanah Indah Suciati Nainggolan, Donni Andreas Suciati, Indah Supu, Nur Ain Suwastika, Erma Vina Nurmadani Wijaya, Verrel Rievaldo ZAI, FIDELIS NOFERTINUS