Authors:Corina Karim, Ekadion Maulana Pages: 152 - 157 Abstract: Generalized strongly -convex functions of higher order is a new concept of convex functions which introduced by Saleem et al. in 2020. The Schur type inequality for generalized strongly -convex functions of higher order also studied by them. This paper aims to revise Schur type inequality for generalized strongly -convex functions of higher order in their paper. In order to revise it, we show that the contradiction was true. This paper showed that Schur type inequality for generalized strongly -convex functions of higher order previously is not valid and we give the correct Schur type inequality for generalized strongly -convex functions of higher order PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.12938 Issue No:Vol. 7, No. 2 (2022)
Authors:Utriweni Mukhaiyar, Syahri Ramadhani Pages: 158 - 172 Abstract: In general, the Generalized Space Time Autoregressive (GSTAR) model of space-time assumes constant error variance. In this study, a GSTAR model was built with an error variance that was not constant or had a heteroscedasticity effect, namely the combination of GSTAR–Autoregressive Conditional Heteroskedasticity (ARCH). The parameters of the GSTAR–ARCH model were estimated using the Generalized Least Square (GLS) method to obtain an efficient parameter estimation. As a case study, the GSTAR–ARCH model was applied to the daily mean wind speed data of New Orleans, Florida and Mississippi to predict the occurrence of Hurricane Katrina that occurred in 2005. The results obtained show that the GSTAR model (3;0,0,1)–ARCH(1) predicts Hurricane Katrina very well. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.13097 Issue No:Vol. 7, No. 2 (2022)
Authors:Yudi Ari Adi, Nursyiva Irsalinda, Meksianis Z Ndii Pages: 173 - 185 Abstract: This paper introduces an optimal control problem in a two-strain SIR epidemic model with viral mutation and vaccine administration. The purpose of this study was to investigate the efficacy and cost-effectiveness of two disease prevention strategies, namely restriction of community mobility to prevent disease transmission and vaccine intervention. We consider the time-dependent control case, and we use Pontryagin’s Maximum Principle to derive necessary conditions for the optimal control of the disease. We also calculate the Average Cost-Effectiveness Ratio (ACER) and the Incremental Cost-Effectiveness Ratio (ICER) to investigate the cost-effectiveness of all possible strategies of the control measures. The results of this study indicate that the most cost-effective disease control strategy is a combination of mobility restriction and vaccination. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.13184 Issue No:Vol. 7, No. 2 (2022)
Authors:Naomi Nessyana Debataraja, Dadan Kusnandar, Rossie Wiedya Nusantara Pages: 186 - 194 Abstract: Geographically weighted regression (GWR) is an exploratory analytical tool that creates a set of location-specific parameter estimates. The estimates can be analysed and represented on a map to provide information on spatial relationships between the dependent and the independent variables. A problem that is faced by the GWR users is how best to map these parameter estimates. This paper introduces a simple mapping technique that plots local t-values of the parameters on one map. This study employed GWR to evaluate chemical parameters of water in Pontianak City. The chemical oxygen demand (COD) was used as the dependent variable as an indicator of water polution. Factors used for assessing water pollution were pH (X1), iron (X2), fluoride (X3), water hardness (X4), nitrate (X5), nitrite (X6), detergents (X7) and dissolved oxygen, DO, (X8). Samples were taken from 42 locations. Chemical properties were measured in the laboratory. The parameters of the GWR model from each site were estimated and transformed using Geographic Information Systems (GIS). The results of the analysis show that X1, X2, X3, X5, and X7 influence the amount of COD in water. The resulting map can assist the exploration and interpretation of data. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.13266 Issue No:Vol. 7, No. 2 (2022)
Authors:Nanang Ondi, Francis Yunito Rumlawang, Yopi Andry Lesnussa Pages: 195 - 206 Abstract: COVID-19 (Coronavirus Disease 2019) was first reported in Wuhan city, China at the end of December 2019 and spread to Indonesia specifically in Maluku Province at the end of March 2020. This study aims to predict the spread of COVID-19 cases in Maluku province as well as explore the phases of its spread using the Richards Curve which is an extension of the Logistic Curve. After estimating the parameters of the Richards Function with cumulative case data of COVID-19 in Maluku province from March 23 to November 4, 2020, the results of the spread of COVID-19 cases in Maluku province reached a turning point on October 22, 2020, and ended on May 25, 2023, with a total cumulative case of 9,451 cases PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.13323 Issue No:Vol. 7, No. 2 (2022)
Authors:Ongky Denny Wijaya, Abdul Rouf Alghofari, Noor Hidayat, Mohamad Muslikh Pages: 207 - 219 Abstract: Zadeh have introduced fuzzy set in 1965 and Atanassov have introduced intuitionistic fuzzy set in 1986 in theirs paper. Now, many of researcher connecting intuitionistic fuzzy set with algebraic structure. We interested to combine some concepts over intuitionistic fuzzy set, module of a ring, t-norm, t-conorm, and intuitionistic anti fuzzy. In this paper, we discusses about intuitionistic anti fuzzy module t-norm and t-conorm (IAFMTC) and their properties with respect to module homomorphism, maps, pre-image, and anti-image from intuitionistic fuzzy sets. We have investigate all properties of IAFMTC. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.13351 Issue No:Vol. 7, No. 2 (2022)
Authors:Kwardiniya Andawaningtyas, Evi Ardiyani, Corina Karim Pages: 220 - 230 Abstract: Human life is full of uncertainty that has enormous risks. Insurance is a one of methods that can help humans reduce those risks. Human needs for insurance causes competition among insurance companies in Indonesia to become very competitive. One factor that makes insurance companies to compete is to have its customers who make insurance renewals. Thesis discusses analysis of factors that influence insurance renewal using Analytical Hierarchy Process (AHP) method and the ranking of customer’s favorite insurance for renewal using the Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) method. Five criteria have been determined with each criterion having subcriteria in this study. AHP method is used to calculate the weight of criteria and to determine the factors that influence customers the most to do renewal. The FTOPSIS method is used to determine the best alternative. The results of the analysis using these methods conclude was the main factor that influences the customers in conducting renewals is feature with the subcriteria of health protection needs. Meanwhile, the ranking of customer’s favorite insurance in conducting renewal is Takafulink Salam Cendikia with proximity coefficient value of 0,645, Takaful Al-Khairat with value 0,563, Takaful Dana Pendidikan with value 0,552, and Takafulink Salam with value 0,341 PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.13356 Issue No:Vol. 7, No. 2 (2022)
Authors:Susilo Hariyanto, Zaenurrohman Zaenurrohman, Titi Udjiani SRRM Pages: 231 - 239 Abstract: COVID-19 is still a pandemic in Indonesia, and Central Java is no exception. New positive cases of COVID-19 in Central Java are being discovered every day. Therefore, researchers try to predict new positive cases in Central Java. Many forecasting methods are currently developing, one of which is fuzzy time series (FTS). FTS has been also developed until now, one of which is a development of the FTS by combining the Markov chain as a defuzzification process. In FTS there is no definite formula to determine the length of the interval, so the researcher uses an average based to determine the length of the interval in the FTS Markov chain. Next, the researcher repartitioned based on the modified frequency density. The results of this study are that forecasting new positive cases of COVID-19 in Central Java using the average based-FTS Markov chain based on a modified frequency density partitioning method has a good level of accuracy, this can be seen from the MAPE value of the method. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.13371 Issue No:Vol. 7, No. 2 (2022)
Authors:Hasrat Ifolala Zebua, I Gede Nyoman Mindra Jaya Pages: 240 - 248 Abstract: Tuberculosis is an infectious disease caused by infection with the bacterium Mycobacterium tuberculosis. Central Java is one of the three provinces with the highest tuberculosis cases in Indonesia. Some of the risk factors used in this research are the spatial lag of the number of tuberculosis cases representing the agent component, the morbidity rate representing the host component, population density, proper sanitation, and proper drinking water which represent environmental components. This study uses the Spatial Autoregressive (SAR) model. The SAR model is a regression model where the response variable has a spatial correlation. The estimation method usually used in SAR model is maximum likelihood. The value of Moran's I on the number of tuberculosis cases in Central Java is 0.499 and is significant, which means that there is a positive spatial autocorrelation. The model was chosen based on the LM test and AIC. The best model is the SAR model. The results of the analysis obtained show that the greater the number of tuberculosis cases is influenced by the number of tuberculosis cases in the surrounding area. Proper sanitation has a negative effect, on the contrary, the dense population has a positive effect on the number of tuberculosis cases in the province of Central Java. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.13451 Issue No:Vol. 7, No. 2 (2022)
Authors:Sri Lestari Mahmud, Resmawan Resmawan, Sumarno Ismail, Nurwan Nurwan, Febriani Taki Pages: 249 - 266 Abstract: The economic model which deals with the economic cycle is Goodwin's Model. It presents the relationship between the employment rate and wage shares. In this study, the modification model was made, taking into three types of workers, namely high, medium, and low-skilled workers. Studies of the model are conducted by determining the equilibrium point and its stability analysis. Furthermore, a numerical simulation is given to see which model satisfies the ideal of Goodwin‘s model cycle prediction by using Indonesian data from 2000 to 2020. In the end, an investigation into the effects of reducing the wage gap between the three types of workers was conducted. The results showed two equilibrium points, namely The Equilibrium Point without Employment Rate and The Wages Share (T1) and the Existence Equilibrium Point of Employment Rate and Wages Share (T2). T1 achieves a stable node condition when ScQ<d+pi+et while T2 reaches a stable center condition when ScQ>d+pi+et. The simulation showed Goodwin's model of high- and low-skilled workers produced the ideal of Goodwin model cycle predictions, whereas Goodwin's model of medium-skilled workers and the entire economy (capitalist) didn’t produce the ideal of Goodwin model cycle predictions. Eventually, the effects of reducing the wage gap make the economy unstable. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.13458 Issue No:Vol. 7, No. 2 (2022)
Authors:Edi Kurniadi, Nurul Gusriani, Betty Subartini Pages: 267 - 280 Abstract: Let be the Lie algebra of the semi-direct sum of the real vector space and the Lie algebra of the sets of all real matrices. In this paper, a Frobenius functional is constructed in order for the Lie algebra to be the real Frobenius Lie algebra of dimension 8. Moreover, a bilinear form corresponding to this Frobenius functional is symplectic. Then the obtained symplectic bilinear form induces the left-symmetric algebra structures on . In other words, the Lie algebra is the left-symmetric algebra. In particular, we give the formulas of its left-symmetric algebra structure explicitely. The left-symmetric algebra structures for case of higher dimension of this Lie algebra type are still an open problem to be investigated. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.13462 Issue No:Vol. 7, No. 2 (2022)
Authors:Nurviana Nurviana, Amelia Amelia, Riezky Purnama Sari Riezky Purnama Sari, Ulya Nabilla Ulya Nabilla, Taufan Talib Pages: 281 - 292 Abstract: Indonesia targets Aceh to be one of the paddy production centers and be able to carry out self-sufficient production in paddy and become a national granary. However, in reality, Aceh's paddy production in its province is not consistent from year to year. This province has not been able to meet the food needs of paddy independently, so that it supplies paddy from other regions due to the difficulty of detecting the presence of a surplus of paddy. The purpose of this research is to estimate the results of paddy production in Aceh for the future. The mathematical model that can be used is a time series model namely Autoregressive Integrated Moving Average (ARIMA) and Exponential Smoothing. The results of the estimation of paddy production in the next 5 years using the ARIMA (1,1,3) model are 2000616; 2017549; 1903585; 1944499; and 1929810. While the estimation results using the Winter Exponential Smoothing model are 1625925; 1645196; 1687667; 1605530; and 1555213. ARIMA model (1,1,3) produces an MSE/MAD value of , while the Winter Exponential Smoothing model produces an MSE/MAD value of . Therefore, it can be concluded that the Winter Exponential Smoothing model. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.13701 Issue No:Vol. 7, No. 2 (2022)
Authors:Royyan Amigo, Noor Hidayat, Vira Hari Krisnawati Pages: 293 - 301 Abstract: In this paper, we study with the definition of B-algebras, commutative B-algebras and fuzzy ideal in B-algebras. We consider the terminology of multipolar intuitionistic fuzzy ideal. We propose about multipolar intuitionistic fuzzy ideal in B-algebras and some related properties. Then, we discuss about theorems and propositions which contain some conditions for a multipolar intuitionistic fuzzy set become a multipolar intuitionistic fuzzy ideal in B-algebras. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.14003 Issue No:Vol. 7, No. 2 (2022)
Authors:Gumgum Darmawan, Dedi Rosadi, Budi N Ruchjana Pages: 302 - 315 Abstract: Hybrid models between Singular Spectrum Analysis (SSA) and Autoregressive Integrated Moving Average (ARIMA) have been developed by several researchers. In the SSA-ARIMA hybrid model, SSA is used in the decomposition and reconstruction process, while forecasting is done through the ARIMA model. In this paper, hybrid SSA-ARIMA uses two auto grouping models. The first model, namely the Alexandrov method and the second method, is alternative auto grouping with a long memory approach. The two-hybrid models were tested for two types of seasonal patterns, multiplicative and additive seasonal time series data. The analysis results using both methods give accurate results; as seen from the MAPE generated the 12 observations for the future, the value is below 5%. The hybrid SSA-ARIMA method with Alexandrov auto grouping is more accurate for an additive seasonal pattern, but the hybrid SSA-ARIMA with alternative auto grouping is more accurate for a multiplicative seasonal pattern. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.14136 Issue No:Vol. 7, No. 2 (2022)
Authors:Jovian Dian Pratama, Ratna Herdiana, Susilo Hariyanto Pages: 316 - 331 Abstract: This article discusses the Elliptical Orbits Mode (EOM) as a method of approximating the function of changing the volume of fuel in the Underground Yank (UT). This research was conducted at the 45.507.21 Candirejo Tuntang Pertamina Gas Station. The calculation of the approximation method will be applied to the measuring book data from the Semarang Metrology Regency specifically for the Pertalite (Fuel Product of Pertamina) buried tank, because the calculation of the gas station is not smooth, it is necessary for a smoother data fitting by considering Residual Square Error (RSS) and Mean Square Error (MSE). The result of this research is the application of EOM(θ) measuring book with elliptical height control produces smaller RSS and MSE compared to using COM, EOM, Least Square degree two and three. PubDate: 2022-03-11 DOI: 10.18860/ca.v7i2.14407 Issue No:Vol. 7, No. 2 (2022)
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