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241	MATHEMATICS AND STATISTICS	ABS-76
PCR-TOPSIS MULTIRESPONSE OPTIMIZATION BASED-ON TAGUCHI AND NEURAL NETWORK APPROACHES FOR WASTEWATER TREATMENT Devi Putri Isnarwaty (a*), Muhammad Mashurib(b), Hidayatul Khusna (b) a) Department of Statistic, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia *devisnarwaty[at]its.ac.id b) Department of Statistic, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia Abstract Waste is the result of waste from a production process, both industrial and domestic (household). Water treatment is carried out by adding several treatments such as adding coagulants or adjusting the stirring setting. This is done in order to normalize pH levels and reduce Total Solid Suspended (TSS) levels in wastewater, so it is necessary to optimize the level of treatment. This optimal level of administration is carried out in order to minimize the cost of wastewater treatment and achieve targets according to predetermined quality standards. In achieving an effective waste treatment process and maintaining good water quality, the researchers intend to optimize the multiresponse Process Capabilty Ratio-Technique for Order Preference by Similarity to Ideal Solution (PCR-TOPSIS) with the Taguchi design using a neural network approach. The Taguchi method is able to evaluate several factors with a minimum number of tests, while the Neural Network can be used to predict PCR-TOPSIS if the combination of factor levels that optimizes the response is not in the Orthogonal Array (OA) design. The utilized method can define that the optimal factor level combination of the waste treatment process. The best model combination criteria are selected based on the value of R2 and Mean Square Error (MSE). In this study, the OA design used is mixed level L8 which means that there is 1 factor that has 4 levels and 2 factors that have 2 levels. The results of the ANOVA calculations show that the optimum conditions can be achieved at the combination of the A4B1C2 level, namely Aluminum Sulfate (Al2(SO4)3) of 50 mg/L, stirring speed of 200 rpm and stirring time of 1 minute. The prediction results of the PCR-TOPSIS Neural Network were not significantly different from the prediction results of the multiresponse Taguchi PCR-TOPSIS method Keywords: Neural Network, Orthogonal Array, PCR-TOPSIS, Taguchi, Wastewater Treatment Share Link | Plain Format | Corresponding Author (Devi Putri Isnarwaty)

242	MATHEMATICS AND STATISTICS	ABS-78
Pricing of Call Options with The Down-and-Out Barrier using the Fuzzy Approach Agustina, F (1), Sidarto, K. A (2*) and Sumarti, N (2*) 1. Doctoral Program of Mathematics, Faculty of Mathematics and Natural, Institut Teknologi Bandung, Jl. Ganesha, 10, Bandung, 40132, Jawa Barat, Indonesia 2. Industrial and Financial Mathematics Group, Faculty of Mathematics and Natural, Institut Teknologi Bandung, Jl. Ganesha, 10, Bandung, 40132, Jawa Barat, Indonesia *kuntjoroadjisidarto[at]gmail.com *novriana[at]itb.ac.id Abstract An Option is an investor^s tool that is used for speculation or hedging purposes. The concept of fuzziness can be used to describe the options pricing parameters. In this paper, we apply fuzzy set theory to price down-and-out call options by setting the volatility and asset price parameters as the fuzzy number. We calculate the risk-neutral probabilities, which are represented as fuzzy numbers. Under fuzzy probabilities, the risk-neutral probabilities of down-and-out call options are determined for the Ritchken trinomial model and the bino-trinomial model. Using these models, the obtained tree will pass the barrier exactly at one or more nodes. Numerical simulations show that, when the membership degree of the fuzzy set numbers increases, the fuzzy price range gradually decreases in length. With this membership degree, financial investors can narrow option price intervals and make investment decisions. Keywords: fuzzy numbers, Ritchken trinomial model, bino-trinomial model, call down-and-out, barrier option pricing. Share Link | Plain Format | Corresponding Author (Fitriani Agustina)

243	MATHEMATICS AND STATISTICS	ABS-81
Supremum Image of Lower Semi-Continuous Function From Above Lalu Riski Wirendra Putra(a*), Umar Abdullah(a), Dastin Rangga Berani(a), Qurratul Aini(a) a)Department of Mathematics, Faculty of Mathematics and Natural Science,Mataram University, Jalan Majapahit 62, Mataram 83115, Indonesia. *laluriski04[at]gmail.com Abstract In Mathematics, one of the basic properties of the function that need to be known is the existence of the supremum value of the function image. In applied mathematics, supremum value of image function is used to determine a maximum value of the function. In the case of continuous function, the existence of supremum is assured by several assumptions, one of which is the function domain which is closed set and the function is bounded function. In some cases, the continuous function is not used, but rather the weaker function, i.e. lower semi-continuous function from above. In this paper, we want to know the properties that ensure the existence of supremum of the image of lower semo-continuous function from above. Keywords: Supremum, Image, Lower Semi-Continuous Function Share Link | Plain Format | Corresponding Author (Lalu Riski Wirendra Putra)

244	MATHEMATICS AND STATISTICS	ABS-338
The Locating Chromatic Number of Comb Product of Star Graph and Complete Graph Asmiati and Wenty Okzarima Department of Mathematics, Universitas Lampung, Lampung-Indonesia, 35145 Abstract Let -H=(V,E)- be a connected graph, Let -c- be a proper -k--coloring of -H- with color -\{1, 2, . . ., k\}- and - \Pi=\{A_1, A_2, ..., A_k\}- be a partition of -V(H)- which is induced by the coloring -c-. The color code -c_\Pi(w)- of -w- is the ordered -k--tuple -(d(w,A_1), d(w,A_2), ..., d(w,A_k)))- where -d(w,A_i)=- min -\{d(w,x)|x \in A_i\}- for any -i \in \{1,2,3,...,k\} -. If all distinct vertices of -H- have distinct color codes, then -c- is called a -k--locating coloring of -H-. The minimum number of colors used for locating coloring is called the locating chromatic number, denoted by -\chi_L(H)-. Let -S_n- and -K_n- be star graph and complete graph, respectively. Let -o- be a vertex of -K_n-. The comb product between -S_n- and -K_n-, denoted by -S_n \rhd K_n-, is a graph obtained by taking one copy of -S_n- and -|V(S_n)|- copies of -K_n- and grafting the -i--th copy of -K_n- at the vertex -o- to the -i--th vertex of -S_n-. In this paper, we obtain that -\chi_L(S_n \rhd K_n)=n+1- for -n\geq 3-. Keywords: locating chromatic number, star graph, complete graph, comb product. Share Link | Plain Format | Corresponding Author (Asmiati Asmiati)

245	MATHEMATICS AND STATISTICS	ABS-339
Facultative Reinsurance Limit Using Tail Value at Risk (TVaR) of Bank Loans with Mixture Distribution Utriweni Mukhaiyar (a*), David Eurico (b), Bagas Caesar Suherlan (b), Afifatul Ayu Astiani (b), I Kadek Darma Arnawa (b) a) Statistics Research Division, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jl. Ganesha No. 10 Bandung 40132, Indonesia *utriweni.mukhaiyar[at]itb.ac.id b) Master Program in Actuarial Science, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jl. Ganesha No. 10 Bandung 40132, Indonesia Abstract In general, Bank does lend loans to the public. Recent regulation suggests that a certain Bank should sign a facultative reinsurance contract as a protection for default risk of 15% of loans with the highest principal. This research is aimed to find the limit of the largest 15% of loans using Tail Value at Risk (TVaR) method since it seeks the expectation of the loan principal that will be protected under a facultative reinsurance contract. The 5,000 samples^ principal of the certain Bank loans be investigated. The behavior of these loans can be described by Mixture Gamma distribution with three components whose proportions and parameters are different. Those are 19% of Gamma with \(\alpha \) = 2.45, \(\beta\) = 0.04, 34.5% of Gamma with \(\alpha \) = 8.29, \(\beta\) = 0.07, and 46.5% of Gamma with \(\alpha \) = 30, \(\beta\) = 0.13. Furthermore, the limit of the facultative reinsurance contract obtained through TVaR is 274.9 million rupiah. The new loans with principal above the number before will automatically be protected under facultative reinsurance contract. Keywords: Bank- Facultative Reinsurance- Mixture Distribution- Risk- Tail Value at Risk Share Link | Plain Format | Corresponding Author (David Eurico)

246	MATHEMATICS AND STATISTICS	ABS-344
The Ideal of Semiring of The Non-negative Integer Aisyah Nur Adillah (a*), Fitriana Hasnani (b), Meryta Febrilian Fatimah (c), Nikken Prima Puspita (a) a) Mathematics Department, Faculty of Sciences and Mathematics, Diponegoro University Jl. Prof Jacub Rais, Semarang 50275, Indonesia *aisyahnuradillah[at]students.undip.ac.id b) Graduated Student of The Magister of Mathematics, Faculty of Mathematics and Natural Sciences, Gadjah Mada University Yogyakarta 55281, Indonesia c) Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Sulawesi Barat University Jl. Prof Dr. Baharuddin Lopa, S. H, Majene 91412, Indonesia Abstract A semiring is a generalization of a ring. Let (S,+,.) be a semiring. An ideal on a semiring defined analogue with the ideal on a ring. An ideal I of S is irreducible if I is an intersection ideal from any ideal A and B on S then I = A or I = B. We also known the strongly notion on irreducible concept. The ideal I of S is a strongly irreducible ideal when I is a subset of the intersection of A and B (ideal of S), then I is a subset of A or I is a subset of B. Here, we discussed the characteristics of the semiring of the non-negative integer set. We showed that kZ^{+} is an ideal of a semiring of the non-negative integer Z^{+} over addition and multiplication. In fact, kZ^{+} is a prime ideal and also a strongly irreducible ideal of the semiring Z^{+} if k is a prime number. Keywords: Semiring- Non-negative integer set- prime ideal- strongly irreducible ideal Share Link | Plain Format | Corresponding Author (Aisyah Nur Adillah)

247	MATHEMATICS AND STATISTICS	ABS-89
Process Monitoring of Dakwah and Politics Magazine with Multivariate P Control Chart and Univariate P Control Chart Surya Puspita Sari (*), Mega Silfiani Institut Teknologi Kalimantan *surya.puspita[at]lecturer.itk.ac.id Abstract Language is a tool to express an opinion or statement to be conveyed to others. There are two types of language in the media, namely spoken language, and written language. One work that uses written language as a medium of communication is a magazine. To write a magazine, it must comply with the rules of language. But often the writing in a magazine still error. The types of errors that often occur are grammar errors, language errors, punctuation errors, and typing errors. This study aims to determine whether the types of errors that have been mentioned in the magazine manufacturing process have been statistically controlled and to analyze the factors that affect the level of defects in the magazine manufacturing process. Quality control using a univariate P control chart, showing each type of error that occurs produces a graph containing out-of-control data. However, when quality control uses a multivariate P control chart, the resulting graph does not contain out-of-control data. Further identification was carried out with a Pareto control chart to determine the frequency of the type of defect that is more dominant. Meanwhile, to find out the factors that influence the instability of the magazine-making process, namely machine, method, human and environmental factors, a causal diagram is used. Keywords: Types of defects, univariate P control chart, multivariate P control chart, Pareto chart, Cause and effect chart Share Link | Plain Format | Corresponding Author (Surya Puspita Sari)

248	MATHEMATICS AND STATISTICS	ABS-346
Ruin Probabilities Simulation of Insurance Company Based on Premium and Claim Size Data Utriweni Mukhaiyar (a*), Febrina Puspa S. (b), Yovia Galuh S. (b), Elonasari (b), Rusniwati S. Imran (b) (a) Statistics Research Division, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jl. Ganesha No. 10, Bandung 40132, Indonesia *utriweni.mukhaiyar[at]itb.ac.id (b) Master Program in Actuarial Science, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jl. Ganesha No. 10, Bandung 40132, Indonesia Abstract Insurance company releases insurance products at the most competitive prices based on the demographics of the potential participants. The greater the number of participants or premiums earned at any given time, the greater the company^s source of income that can be used to cover the amount of claims that may occur. On the other hand, for participants who have paid a number of premiums, guarantees for risks that may arise will be borne by the company after the claim is submitted. In order for the insurance company^s financial reserves to continue to pay all incoming claims, the company must be able to predict the worst possible event so that it can be avoided, that is the bankruptcy. Ruin probability is estimated by a simulation using the general model of the company^s financial reserves. The simulation is based on gamma distributed insurance claim sizes data. Premiums are divided into 10 levels, with the difference of 5 USD in each level, start from 40 USD at first level till 85 USD at the 10th level. The simulation shows that the insurance company^s reserves at USD7 million, USD1 million, USD200 thousand, and USD5 thousand, all at premiums USD40 (first level), will have the biggest number of ruin probability but the longest day of first day of bankruptcy. They are, sequentially, 0.01 on the 356th day, ruin probability at 0.67 on the 122nd day, probability 0.93 on the 34th day, and 0.97 on the 14th day. The bigger amount of premiums, the smaller its probability of ruin. At insurance company^s reserve USD 5 thousand, the number of ruin probabilities are greater than 0, almost at all premiums level. Keywords: Ruin Probability, Gamma Distribution, Poisson, Claim Size Share Link | Plain Format | Corresponding Author (Febrina Puspa Sari)

249	MATHEMATICS AND STATISTICS	ABS-347
Generalized Poisson-Lindley Distribution for Overdispersion in Insurance Claims Data Utriweni Mukhaiyar(a*), Hamidah Qurrotun Nadwah(b), Arli Maghfirah Utami(b), Elisa Murti Dewi(b), Rizka Puspitasari(b) a) Statistics Research Division, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jl. Ganesha No. 10, Bandung 40132, Indonesia *utriweni.mukhaiyar[at]itb.ac.id b) Master Program in Actuarial Science, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jl. Ganesha No. 10, Bandung 40132, Indonesia Abstract A count data describes events within a certain period of time. The values of count data are only positive integers. Therefore, count data capable to describe the occurrence of insurance claims in a company. This study uses data on health insurance claims from the Health Insurance Administration for West Java region in 2016 as data to be tested for the type of distribution. Commonly, Poisson distribution can be used to describe this kind of data. Meanwhile, these data is known that the value of zero has an excessive frequency compared to other values. It is also known that variance value of data exceeds the average value, which is called overdispersion. Therefore, Poisson distribution can not be used in this data, as it violates Poisson distribution requisite that the mean and variance are same. Here, we compare Negative Binomial distribution and Generalized Poisson-Lindley distribution to describe the data. Generalized Poisson-Lindley distribution is an extended version of compound Poisson distribution which is obtained by mixing Poisson distribution with Generalized Poisson-Lindley distribution. Parameter values of Generalized Poisson-Lindley distribution can be estimated using maximum likelihood estimation method through Newton Raphson iteration numerical method. According to research results, it was determined that Generalized Poisson-Lindley distribution was appropriate to describe the distribution of overdispersion data which is compared with other distribution, specifically Negative Binomial distribution and Poisson distribution. This is evidenced by a comparison of the Akaike Information Criterion values to other distributions for overdispersion cases. In addition, results show that tolerance limit for overdispersion data when using Generalized Poisson-Lindley distribution is 0.222 to 0.513. Keywords: overdispersion, generalized Poisson-Lindley, AIC criteria, overdispersion tolerance limit Share Link | Plain Format | Corresponding Author (Hamidah Qurrotun Nadwah)

250	MATHEMATICS AND STATISTICS	ABS-92
Extreme Rainfall Analysis with Spatial Extreme Value through the Extremal-t Process Husna Miratin Nuroini- Dr. Sutikno, M. Si.- Dr. Purhadi, M. Sc. Sepuluh Nopember Institute of Technology Abstract The topographical conditions in Indonesia consist of coasts, lowlands, highlands, and mountains. This causes the area to have a high diversity of weather and climate, enabling several hydrological phenomena such as extreme rainfall, hurricanes, high temperatures, and storms. Nowadays, global warming has become a widely discussed environmental issue. One of its impacts is climate change, which affects the occurrence of extreme hydrological phenomena and potentially causes floods, disruption of transportation and communication, damage to infrastructure, harm to the agricultural sector, and threat to life. Therefore, this study aims to obtain the best model and return level of extreme rainfall in Ngawi Regency from 1990 to 2022 through Spatial Extreme Value (SEV) using Max-Stable Processes (MSP) method with the extremal-t process. The estimation parameters used are Maximum Likelihood Estimation (MLE) and Maximum Pairwise Likelihood Estimation (MPLE), then solved by Broyden-Fletcher-Goldfarb-Shanno (BFGS) Quasi-Newton numerical iteration methods. Based on the analysis result, the best trend surface model obtained with the average rainfall and variance influenced by latitude. Meanwhile, the shape of rainfall distribution is not affected by longitude or latitude because it is assumed to be isotropic. In addition, the value of return level prediction has better accuracy when used over 3-years period. Keywords: Extremal-t Process, Extreme Rainfall, Maximum Pairwise Likelihood Estimation, Max-Stable Process, Return Level. Share Link | Plain Format | Corresponding Author (Husna Miratin Nuroini)

251	MATHEMATICS AND STATISTICS	ABS-349
Modeling of Financial Losses Due to Traffic Accidents with Copula Gaussian Model Utriweni Mukhaiyar(a*), M. Akhirul R. (b), Novita Lestari P. (b), Lailatul Maziyah W.M. (b), dan I Gede Maha Hendra P. (b) a)Statistics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesa No.10 Bandung 40132, Indonesia. b)Master Program in Actuarial Science, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesa No.10 Bandung 40132, Indonesia. Abstract Abstract. Traffic accidents cause financial losses. The losses model will be used to estimate the future total losses. In this research, the modeling of the total loss due to traffic accidents in Indonesia in 2022 uses the distribution model without dependence and the Copula Gaussian model. The data used are total loss (Million Rupiah), severity amount of loss (Million Rupiah), and the number of accidents from 1992 to 2019 with monetary value adjustments using the concept of future value. The Goodness-of-Fit test shows that the Gamma, Weibull, and Geometric distribution can describe the total loss, severity loss, and the number of accidents, respectively. Furthermore, the correlation between the severity and frequency loss is highly negatively correlated. From the results of the Total Loss modeling, the calculation of VaR_(95%) and TVaR_(95%) for total loss without-dependence and Copula Gaussian model are respectively 369,015 and 341,817 billion Rupiah. The results of TVaR_(95%) are 425,462 and 386,498 billion Rupiah. The total loss in the without dependence distribution model shows greater estimation results in the calculation of VaR_(95%) and TVaR_(95%) under stochastic dominance theory, thus Copula Gaussian model is the least dangerous model at level 95%. Keywords: Copula gaussian- future value- goodness-of-fit- traffic accidents. Share Link | Plain Format | Corresponding Author (I Gede Maha Hendra Pratama)

252	MATHEMATICS AND STATISTICS	ABS-350
The Total Vertex Irregularity Strength of Foster^s Census Graph Rikayanti, Suhadi Wido Saputro, Edy Tri Baskoro Institut Teknologi Bandung Abstract Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order -n- with -n \le 512-. This census was then continued by Conder et al. (2006) and the last update can be seen in the list he has made up to the -10000- vertices. %, he continued his list up to 2048 points in 2006. The last update can be seen in the list he has made up to the -10000- vertices. In this paper, we determine the total vertex irregularity strength of such graphs obtained by Foster. As a result, all the values of the total vertex irregularity strengths of the symmetric cubic graphs of order -n- from Foster census strengthen the conjecture stated by Nurdin, Baskoro, Gaos \& Salman (2010), namely -\lceil (n+3)/4 \rceil-. Keywords: total vertex irregularity strength, cubic symmetric graph, algorithm, Foster^s Census Share Link | Plain Format | Corresponding Author (Rika yanti)

253	MATHEMATICS AND STATISTICS	ABS-96
Customer Churn Prediction using Machine Learning with Survival Effect Approach: An Empirical Study on Telecommunication Customer Behavior Soni Adiyatma (a*), Heri Kuswanto (a), Dedy Dwi Prastyo (a), Endah Setyowati (b) (a*) Department of Statistics, Institut Teknologi Sepuluh Nopember Surabaya Jalan Raya ITS, Sukolilo, Surabaya 60111, Indonesia *adiyatma.soni[at]gmail.com (b) Faculty of Islamic Economics and Business, Institut Agama Islam Negeri Ponorogo Jalan Puspita Jaya, Ponorogo 63492, Indonesia Abstract This research aims to obtain a predictive model of customer churn communication using a machine learning approach with a survival effect. Customer churn prediction is a process in business decisions by identifying customer behavior into the classes of churners and loyal customers. The methods used are machine learning (SVM and Random Forest), survival analysis (Cox Proportional Hazard), and machine learning with survival effect (Survival SVM and Random Survival Forest). The data used is the telecommunication customer behavior data at telco company X in 2019. The predictor variables used were gender, monthly charges, phone services, TV streaming services, senior citizens, dependents, and marital status. The result of data exploration showed that gender and phone services have no significant effect. The comparison of customer churn prediction methods showed that the performance of survival analysis models and machine learning with survival effects has a higher concordance index than machine learning methods. It showed that the higher concordance index in machine learning with survival analysis indicated that the model has an almost perfect discriminatory power. In addition, the combination of machine learning and survival analysis offers predictions of customer churn by considering the time the customer will churn. Keywords: Churn Prediction, Machine Learning, Survival Analysis Share Link | Plain Format | Corresponding Author (Endah Setyowati)

254	MATHEMATICS AND STATISTICS	ABS-97
Estimation of Missing Values in Economic Issues Using Cluster-based Multiple Imputation Mety Agustini (1,2), Dedy Dwi Prastyo (1) 1) Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia 2) Badan Pusat Statistik Provinsi Kepulauan Bangka Belitung, Pangkalpinang, Indonesia Abstract Missing values commonly occur in the data collection process, including in economic surveys and censuses. The existence of missing values not only detracts from the data set availability that can be analyzed but also compromises the statistical power of the research. Deleting missing values significantly impacts the estimation process, resulting in overestimated or underestimated values. Moreover, it affects a significant bias in the results and degrades the efficiency of the data. This research proposes an efficient imputation method for dealing with incomplete data. K-means clustering is a common algorithm applied to discover similarity or dissimilarity among units. Using multivariate imputation by chained equations (MICE), incomplete data will be imputed with plausible values generated from the data that do not contain missing values. Extended experiments reveal the efficacy of the proposed method in the imputation task. Model accuracy is evaluated quantitatively and graphically using plots of plausible value, regression, and density of imputed datasets. Keywords: Missing values, Missing data, MICE, Mulitple imputation, Clustering Share Link | Plain Format | Corresponding Author (Mety Agustini)

255	MATHEMATICS AND STATISTICS	ABS-98
Seasonal Autoregressive Integrated Moving Average Ensemble via Artificial Neural Networks for Electrical Load Forecasting Mega Silfiani(a,b,*), Surya Puspita Sari (a) a) Department of Statistics, Institut Teknologi Kalimantan, Jalan Soekarno Hatta KM.15, Balikpapan, Indonesia b)2Department of Economics, Gdansk University Armii Krajowej Street, 114-116, Sopot, Poland *) megasilfiani[at]lecturer.itk.ac.id Abstract The purpose of this research is to explore the performance of forecasting electrical load utilizing artificial neural network for combining the seasonal autoregressive integrated moving average (SARIMA) ensemble. A SARIMA ensemble member is created by modelling different autoregressive orders or moving averages. Meanwhile, the SARIMA ensemble is combined using artificial neural network. The datasets contain monthly electrical load for four categories, i.e., households, businesses, industries, and the public, from January 2016 to December 2020. The results show that in both categories and forecast horizons, SARIMA ensemble-based artificial neural networks outperformed all models. Further research should look into different techniques for creating and combining ensemble members. Keywords: ANN- Load Forecast- SARIMA- RMSE- MdAPE Share Link | Plain Format | Corresponding Author (Mega Silfiani)

256	MATHEMATICS AND STATISTICS	ABS-99
Modeling and Classification Multicollinear Data using Multinomial Ridge Logistic Regression with Wu-Asar Approach to Submit This Sample Abstract Giatma Dwijuna Ahadi(a*), Ismaini Zain (a), Santi Puteri Rahayu (a) (a) Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember Surabaya, Indonesia *giatmaahadi.206003[at]mhs.its.ac.id Abstract Classification method is an analysis used to classify an object into a certain category based on explanatory variable. Logistics Regression is a classic method that is used to solve classification problems. Multinomial Logistic Regression is a method to find relationships between nominal response variables with one or more predictor variables. Assumptions on logistics are models not contain multicollinearity. Schaefer, Loi & Wolfe introduced the Ridge Logistic Estimator to solve multicollinearity cases in Logistic Regression. Wu & Asar proposed a new method to reduce bias in parameter estimation. The selection of ridge constant values will be resolved using Ridge-Trace, SRW-constants, and Wu-Asar estimator. The performance test of the Wu-Asar ridge value will be applied to the Iris Dataset in R-software. Iris Data consists of three iris species (0:Setosa, 1:Versicolor, 2:Virginica) and four features as predictor. The best ridge-constant value is obtained by examination the smallest standard-error of parameter estimate. The calculation results show that the Wu-Asar approach is the best ridge constant and individual Wald-test shows significant results. Evaluation of classification based on confusion matrix. The performance of the Wu-Asar estimator on Multinomial Ridge Logistic Regression for the Iris dataset shows very good classification results with 98% global accuracy. Keywords: Classification, Multinomial, Ridge Logistic Regression, Wu-Asar, Confusion Matrix Share Link | Plain Format | Corresponding Author (Giatma Dwijuna Ahadi)

257	MATHEMATICS AND STATISTICS	ABS-357
Compositional Modelling of COVID-19 using category theory Rizal Afgani KK Analisis dan Geometri, Institut Teknologi Bandung Abstract In this paper we are using a novel approach of modelling epidemic based on open Petri nets and category theory developed by Evan Peterson et al. to model COVID-19 outbreak in Indonesia. Keywords: COVID-19, Petri Nets Share Link | Plain Format | Corresponding Author (Rizal Afgani)

258	MATHEMATICS AND STATISTICS	ABS-102
IMAGE CLUSTERING BASED ON DISTRIBUTION FUNCTION Husty Serviana Husain, Sapto Wahyu Indratno Institut Teknologi Bandung Abstract Image clustering has been widely studied for a long time and has resulted in many methods. The k-means algorithm is known to cluster extensive data efficiently but is limited to numerical data types. In this study, a new approach was carried out, the procedure for quantifying image data, so it is possible to process it using the k-means algorithm. It is known that the image is a collection of Red, Green Blue pixels with an intensity value of 0-255. The method to perform image clustering does not use numeric data but distribution functions to calculate the similarity of images to one another. The proposed approach represents the image as a probability density function of the pixel intensity value. Keywords: k-means, image, probability density function Share Link | Plain Format | Corresponding Author (Husty Serviana Husain Husain)

259	MATHEMATICS AND STATISTICS	ABS-103
Multivariate Fuzzy T2 Hotelling Control Chart with Alpha-Cut Using Trapezoidal Fuzzy Number (TrFN) and Its Application Nur Rezky Safitriani (a*), Muhammad Mashuri (a), Wibawati (a) a) Department of Statistics : Faculty of Science dan Data Analysis, Institut Teknologi Sepuluh Nopember, Jl. Arief Rahman Hakim, Surabaya, 60111, Indonesia *rezky.toaba[at]gmail.com m_mashuri[at]statistika.its.ac.id wibawati[at]statistika.its.ac.id Abstract The quality of a product is the most important factor in the manufacturing industry which can be maintained through statistical monitoring of the production process using the Statistical Process Control (SPC) method. One of them is a control chart which aims to know whether the process is running under controlled conditions or not. Quality control of a product consisting of two or more correlated quality characteristics is more efficient using a multivariate control chart than several univariate control charts. However, there are product qualities that cannot be measured and expressed numerically, so an assessment of linguistic criteria is required. This assessment can cause ambiguity which can be overcome using fuzzy set theory so that multivariate fuzzy control charts are developed. One of the multivariate fuzzy control chart that has ease of application and interpretation is fuzzy T2 Hotelling. This method is sensitive to mean shifts in the production process which is indicated by a decrease in ARL but is not sensitive to small mean shifts. To overcome these shortcomings, alpha-cut is added to improve the tightness of the inspection of each quality control process. Thus, fuzzy T2 Hotelling control chart with alpha-cut can detect small shifts in the mean for linguistic quality characteristics. Statistics fuzzy T2 Hotelling is based on representative values through membership functions where the Triangular Fuzzy Number (TFN) has often been used but rarely uses its development, namely the Trapezoidal Fuzzy Number (TrFN) which provides a better solution. This research developed multivariate fuzzy T2 Hotelling control chart with alpha-cut using TrFN and its application in the manufacturing industry, building materials industry at UD Tiga Beton as a producer of pressed bricks which had never before conducted statistical monitoring of the production process. The results of of the application show that multivariate fuzzy T2 Hotelling control chart with alpha-cut using TrFN can be used to simultaneously monitor the quality characteristics of each process related to multivariate linguistic data and can handle processes sensitive to small mean shifts. Keywords: Multivariate fuzzy control charts, Fuzzy T2 Hotelling, Alpha-cut, Linguistic, Building materials industry Share Link | Plain Format | Corresponding Author (Nur Rezky Safitriani)

260	MATHEMATICS AND STATISTICS	ABS-359
Waiting time of the Large earthquake in Cimandiri Fault using Appropriate Parameter Bayesian Online Changepoint detection algorithm Seli Siti Sholihat (a) a) Universitas Gunadarma, Depok, Indonesia Abstract Indonesia is located in pacific ring of fire and fault line. Several large earthquakes have struck in Indonesia. The latest deadly earthquake in Indonesia is in Cianjur, west java. The Meteorology, Climatology and Geophysics Agency (BMKG) said that the cause of the Cianjur earthquake was the activity of the Cimandiri fault. Appropriate parameters of bayesian online changepoint algorithm has been proposed for detecting the early warning of mount Merapi eruption using the earthquakes data. The study is to apply the algorithm to the earthquake data around the Cimandiri fault to detect large earthquake with shallow depth. The result shows the waiting time of the large earthquake in Cimandiri Fault. Keywords: waiting time earthquake, Cimandiri Fault, Changepoint detection Share Link | Plain Format | Corresponding Author (Seli Siti Sholihat)

261	MATHEMATICS AND STATISTICS	ABS-360
Direct Sum on Semi-cohereditary Module Properties Rizza Lestari Institut Teknologi Bandung Abstract This thesis discusses results of finite direct sum of semi-cohereditary module. This study first discusses some properties of cohereditary and injective modules to see that this properties can be fulfilled by semi-hereditary and weakly injective module as well. Furthermore, this paper discussed the finite direct sum results of semi-cohereditary module, whether the results is also a semi-hereditary module or not. Then a properties comparison table is given for hereditary and cohereditary modules, as well as properties comparison table of semi-hereditary and semi-cohereditary modules. Keywords: cohereditary module, injective module, semi-cohereditary module, weakly injective module, direct sum Share Link | Plain Format | Corresponding Author (Rizza Lestari)

262	MATHEMATICS AND STATISTICS	ABS-105
An Integrated Model for Time Series Regression with Islamic Calendar Variation and COVID 19 to Forecast Number of Train Passangers Mega Silfiani(a,b,*), Farida Nur Hayati (a) a)Department of Statistics, Institut Teknologi Kalimantan Jalan Soekarno Hatta KM. 15, Karang Joang, Balikpapan, Indonesia b)Department of Economics, Gdansk University Armii Krajowej Street, 114-116, Sopot, Poland *) megasilfiani[at]lecturer.itk.ac.id Abstract The purpose of this paper is to examine a forecasting model for the number of train passengers using an integrated time series regression with Islamic Calendar Variation and Covid 19 Effects. This study uses the number of train passengers in Jabodetabek, Jawa (Non Jabodetabek), and Sumatra from January 2006 to October 2022 as its data source. Integrated time series regression with Islamic Calendar Variation and Covid 19 Effects for Jabodetabek, Jawa (Non Jabodetabek), and Sumatra has RMSE values for each variable of 5433.681, 2788.881, and 185.207. In Jabodetabek and Jawa (non-Jabodetabek), variations in the Islamic calendar have no substantial impact on the number of train passengers. Meanwhile, Ied Fitr has a huge impact on the amount of train passengers in Sumatra. In general, the Covid 19 impact influences the number of railway passengers for each variable significantly. Keywords: Forecasting- Regression- Time Series- Train Passangers Share Link | Plain Format | Corresponding Author (Mega Silfiani)

263	MATHEMATICS AND STATISTICS	ABS-108
Analysis of Tektite Clusters in Australian Strewnfield Based on Geochemical Data Using the Hierarchical Average Linkage Method Romi Lentika Sinaga (a), Triyana Muliawati (a*) a) Department of Mathematics, Institut Teknologi Sumatera Jalan Terusan Ryacudu, Lampung 35365, Indonesia *triyana.muliawati[at]ma.itera.ac.id Abstract Tektite is a natural glass material formed by the impact of meteors on the earth^s crust. There are currently 4 strewnfield tektites associated with separate impact and ejection fields: North American, Central-European, Ivory-Coast and Australian. Of the four strewnfields, the Australian strewnfield has the widest distribution. One of them was found on Belitung Island, Indonesia. This study aims to classify tektite in the Australian Strewnfield based on geochemical data and analyze the characteristics of the tektite from the grouping results obtained. The method used is the Hierarchical Average Linkage method with 60 textite data and 8 geochemical composition variables. Principal Component Analysis is carried out to take the k main components that represent the diversity of the data. Before using the average linkage method, the Silhoutte method was used to obtain the k cluster values used for confirmation in the analysis of the results. The results showed that the tektite at Australian Strewnfield formed 3 clusters where the first cluster consisted of 36 samples with the lowest silica but the highest aluminum oxide. The third cluster of 10 samples has the highest silica and the second cluster of 14 samples has silica whose value is between the second and third clusters. Keywords: Tektite- Australian Strewnfield- Cluster- Average Linkage Share Link | Plain Format | Corresponding Author (Romi Lentika Sinaga)

264	MATHEMATICS AND STATISTICS	ABS-110
Ground Water Potability Model in Nueva Vizcaya, Philippines Richard J. Taclay, Karen D. Taclay, Ethel Rhianie H. Sinacay, Geneva S. Aragon, and Joribel T. Oldico Nueva Vizcaya State University, University of the Philippines Baguio Abstract This paper describes the characteristics of groundwater sources in one of the Northern Philippines^ municipalities. The paper included clustering of water sources based on Bacteriological test results as well as factors affecting water potability. Water samples were collected from 60 untreated pump wells in the identified municipality^s eight low-lying barangays. The water samples were subjected to bacteriological testing in the Provincial Health Office (PHO). Surveys were also conducted in the vicinity of the water pumps. The factors influencing groundwater potability were determined using Spearman^s rho and Chi-square. The discriminant analysis was used to create a model that could distinguish between water pumps that used potable and non-potable water. The study discovered that the distance between the septic tank and the flooring around the pump well were the factors influencing water potability. Based on bacteriological testing, the spatial pattern was determined to be random. The established model uses the septic tank distance, dirty drainage distance, well depth, and the presence or absence of concrete flooring around the pump well as indicators to determine the pump well^s water potability status. The model^s classification rate index was 88.89 percent. Keywords: Water potability, Groundwater, Moran^s I, Discriminant Analysis, Mathematical Model Share Link | Plain Format | Corresponding Author (Richard Jallorina Taclay)

265	MATHEMATICS AND STATISTICS	ABS-366
Study of Community Behavior in West Java and East Java Provinces in Complying with Health Protocols during a Pandemic using Cluster Analysis Sonny H. B. Harmadi, Udjianna S. Pasaribu*, Nur F. Sa^idah, A. Sonhaji Development Studies Department, Faculty of Creative Design and Digital Business, Institut Teknologi Sepuluh Nopember, Indonesia Statistics Research Group, Department of Mathematics, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Indonesia Doctoral Program in Department of Industrial Engineering and Management, Faculty of Industrial Engineering, Institut Teknologi Bandung, Indonesia Doctoral Program in Department of Mathematics, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Indonesia *corresponding author: udjianna[at]math.itb.ic.id Abstract Since the Covid-19 pandemic, the 3M health protocol (wearing a mask, washing hands with soap, and keeping distance) has been the basis for people^s behavior. The aim of this protocol is to break the chain of transmission and reduce the spread rate. Thus, a survey was conducted to monitor public awareness and compliance with 3M in November 2020. As the biggest contributors to the Covid-19 case, the provinces of West Java and East Java were chosen to be the objects in this study. Six questions (random variables) related to the level of compliance were analyzed using the Agglomerative Hierarchical Cluster Analysis. The analysis classifies city/district through the single linkage method. The result shows that 23 out of 27 cities/regencies in West Java were grouped into seven (7) clusters. There are four clusters with one member each. Areas bordering other provinces such as Depok, Bogor, Karawang and Kuningan districts, as well as cities in the central part of the province tend to have the same compliance characteristics. On the other hand, 37 out of 38 cities/regencies in East Java formed 11 clusters. Eight of the clusters only consist of one (1) member. More than 65% of cities in the province are in the same cluster, namely the northern and southern parts of East Java. The average compliance level for each city/district in this cluster is more than 0.86. In other words, almost all health protocols are complied with. The similarity in the grouping results in West Java and East Java is that clusters consisting of one member are cities/regencies with less than four respondents. In these areas, it is necessary to study further through other data so that the grouping is more representative. The results can be used as a reference for policy makers to understand community behavior in setting policies, regardless of pandemic conditions. Keywords: Hierarchical Cluster Analysis, Covid-19, behavior change, health protocol Share Link | Plain Format | Corresponding Author (Abdullah Sonhaji)

266	MATHEMATICS AND STATISTICS	ABS-111
Hotspots Model of Dengue Cases in Nueva Vizcaya Richard J. Taclay and Reymond C. Parinas Nueva Vizcaya State University, University of the Philippines Baguio Abstract Dengue Hemorrhagic Fever has become a worldwide threat. In 2018, the Philippines, along with Bangladesh, Cambodia, India, Myanmar, Malaysia, Pakistan, Thailand, and Yemen, had reported dengue cases. It should be noted that the Philippines, along with Thailand, had the first recorded DHF since the 1950s. The hotspot of dengue cases in the province of Nueva Vizcaya was identified in this study, and the prevention practices of the hotspot and cold spot areas were investigated. The study^s data was derived from confirmed dengue cases in the fifteen municipalities of Nueva Vizcaya. Moreover, Moran^s I was used to identify clustering patterns and dengue hotspots. According to the findings, the province^s center had the highest number of reported dengue cases. Three-quarters of Nueva Vizcaya^s 275 barangays had reported dengue cases. In addition, spatial clustered patterns existed and were not attributed to random chance. Within the 99% confidence interval, there were 22 and 14 barangays in the hotspot and coldspot areas, respectively. When the prevention practices of the two groups were compared, it was discovered that barangays in coldspot areas implement dengue prevention programs more stringently. Furthermore, the modified dengue prevention program proposed was based on the most widely used dengue prevention programs in coldspot areas. Keywords: Dengue Cases, Hotspots, Prevention Programs, Spatial Clustered Patterns Share Link | Plain Format | Corresponding Author (Richard Jallorina Taclay)

267	MATHEMATICS AND STATISTICS	ABS-370
An Epidemic Mathematical Model to Compare the Impact of SARS-CoV-2 Variants: The case of COVID-19 in South Kalimantan, Indonesia Muhammad Ahsar Karim (a*), Mochammad Idris (a), Yuni Yulida (a) a) Study Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lambung Mangkurat, Banjarbaru 70714, South Kalimantan, Indonesia. *m_ahsar[at]ulm.ac.id Abstract In this study, an epidemic mathematical model was formed to analyze the comparison of the impact of SARS-Cov-2 variants, namely Alpha, Delta, and Omicron. The model solution was determined by using the Extended Runge-Kutta method. The study is based on the COVID-19 case in South Kalimantan, Indonesia. For comparison purposes, three parameters were determined: transmission rate, recovery rate, and death rate. Parameters are estimated by using the Least Square Nonlinear method. Then, a comparative analysis of the impact of the Alpha, Delta, and Omicron variants on COVID-19 cases in South Kalimantan is provided. The results showed that the Omicron variant has the highest transmission rate, the Delta variant has the highest death rate, and the Alpha variant has the highest recovery rate, respectively, compared to the other variants. Keywords: Epidemic Mathematical Model- COVID-19- Extended Runge-Kutta- Least Square Nonlinear- South Kalimantan Share Link | Plain Format | Corresponding Author (Muhammad Ahsar Karim)

268	MATHEMATICS AND STATISTICS	ABS-372
ANALYSIS OF CHARACTERISTICS AND DISTRIBUTION TYPES OF EARTHQUAKE DISTANCE SPREADING IN 2018 TOWARDS TANJUNG CITY (CAPITAL OF WEST LOMBOK REGENCY) WITH EUCLIDEAN DISTANCE METHOD APPROACH AND KOLMOGOROV-SMIRNOV TEST Henry Wattimanela Universitas Pattimura Abstract Lombok Island, located in the Nusa Tenggara Province, is one of the earthquake-prone areas in Indonesia because it is located at the confluence of three major plates (Indo-Australia, Eurasia, and the Pacific). The 2018 Earthquake on Lombok Island was an earthquake that caused considerable damage and casualties, especially in North Lombok Regency. This study aims to determine the type of earthquake distance distribution to Tanjung City (the capital of North Lombok Regency). The distance calculation uses the Euclidean Distance Method, while the determination of the type of distribution uses the Kolmogorov-Smirnov test. The distance calculation results are divided into 4 groups (R1, R2, R3, and R4) and a map of the earthquake distribution is shown based on distance groups. Determination of the type of distribution is also carried out on the depth of each group of predetermined distances (Z1, Z2, Z3, and Z4). The data used is 2018 earthquake data with the criteria of magnitude -\geq 4.0- Mw and depth < 60km. The results of this study are expected to be used by the North Lombok Regency Government in disaster mitigation programs including the City/Regency Governments on Lombok island, West Nusa Tenggara. Keywords: Please Just Try to Submit This Sample Abstract Share Link | Plain Format | Corresponding Author (Henry Wattimanela)

269	MATHEMATICS AND STATISTICS	ABS-375
Modeling Indonesian Interest Rates Using Trigonometric Functions: A Comparison of Heuristic and Hybrid Analytical-Heuristic Methods Andrew Nilsen (a), Udjianna Sekteria Pasaribu (b*), Adilan Widyawan Mahdiyasa (b) a) Master Program in Actuarial Science, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jl. Ganesha No. 10, Bandung 40132, Indonesia b) Statistics Research Division, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jl. Ganesha No. 10, Bandung 40132, Indonesia *Corresponding Author: udjianna[at]math.itb.ac.id Abstract Modeling interest rates is important for understanding the economic environment and making informed decisions about monetary and fiscal policy. A trigonometric function can provide better predictions of future movements due to its ability to capture periodic patterns and trends. In this study, we applied both heuristic and hybrid analytical heuristic methods to estimate the parameters of such a function using Indonesian interest rate data from March 2009 to July 2016. The hybrid analytical heuristic method was least squares with basin hopping approximation, a method for finding parameters that minimizes the sum of the squared error. It is often used because it can be done analytically and is robust to the presence of outliers in the data. The heuristic method was Particle Swarm Optimization, an optimization method that is fast, efficient, easy to implement, and is used to find the optimal solution to complex problems with many variables. After estimating the parameters of the trigonometric function using both the heuristic and analytic methods, we interpolated the data to find the mean squared error MSE, mean absolute error MAE, and coefficient of determination R^2 for each method. From the results, it can be concluded that the least squares method with basin hopping approximation performed better than Particle Swarm Optimization, with an error of MSE: 4.76xE-6, MAE: 0.0017, and R^2: 0.9125, compared to the error of MSE which is 4.93xE-6, MAE: 0.0017, and R^2: 0.91 for Particle Swarm Optimization. Keywords: Interest rate modelling, trigonometric function, least squares, basin hopping, particle swarm optimization Share Link | Plain Format | Corresponding Author (Andrew Nilsen)

270	MATHEMATICS AND STATISTICS	ABS-126
On the adjoint of bounded operators in a semi-inner product space R. Respitawulan, Q.Y. Pangestu, E. Kusniyanti, F. Yuliawan, P. Astuti Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung Abstract The notion of semi-inner product (SIP) spaces is a generalization of inner product (IP) spaces notion by reducing the positive definite property of the product to positive semi-definite. Hence, it is natural to question which properties, results and characterizations of IP spaces that can be generalized to SIP spaces. In this article we are interested in investigating the adjoint of linear operators on SIP spaces. As in IP spaces, the existence of an adjoint of a linear operator on a SIP space is guaranteed when the operator is bounded. However, in contrast, a bounded linear operator on SIP space can have more than one adjoint linear operators. In this article we give an alternative proof of those results using the generalized Riesz Representation Theorem in SIP space. Further, the description of all adjoint operators of a bounded operator in SIP space will be identified. Keywords: adjoint operator, semi-inner product, Riesz representation theorem Share Link | Plain Format | Corresponding Author (R. Respitawulan)

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