Recently, resolving a problem based on multi-criteria decision-making systems has become an attractive method. One of recent techniques is trapezoidal fuzzy VIKOR method which was used for selecting the best option among criteria. This research is aimed to utilize the VIKOR method in prioritization of watershed reforestation in Semarang City, Indonesia. Several criteria have been set for the prioritization of reforestation areas to select watersheds as reforestation targets. In this case, the six criteria and six alternatives were used in order to determine the best priority of reforestation. The result showed that VIKOR method was successfully applied to determine the best option and Kali Garang watershed was the top priority as it has the highest rank and it meets reforestation criteria compared with other watersheds criteria.

Fuzzy time series (FTS) is one of the forecasting methods that has been developed until now. The fuzzy time series is a forecasting method that uses the concept of fuzzy logic, which Song and Chissom first introduced. The fuzzy time series (FTS) Markov chain uses the Markov chain in defuzzification. The determination of the length of the interval in the fuzzy time series plays an important role in forming a fuzzy logic relationship (FLR), and this FLR will be used to determine the forecasting value. One method that can be used to determine the interval length is average-based. However, several studies use partitioning based on frequency density to obtain the optimal interval length to get better forecasting accuracy. This study combines the fuzzy time series Markov chain, Average-based fuzzy time series, and Fuzzy time series based on frequency density partitioning to become average-based fuzzy time series Markov chain based on the Frequency Density Partition which conducts redivided intervals based on frequency density in the average-based fuzzy time series Markov chain method. This method is implemented in forecasting the Indonesian Islamic stock index (ISSI) for the selected period. The calculation of the accuracy level using the mean square error (MSE) and the mean average percentage error (MAPE) shows that the fuzzy Markov chain-based fuzzy time series based on the frequency density partition has a high level of accuracy in forecasting.

Bilangan kromatik total graf G adalah bilangan bulat terkecil k dimana titik-titik dan sisi-sisi graf G dapat diwarnai dengan k warna sedemikian hingga dua titik yang adjecent dan sisi yang insiden dengan titik-titik tersebut diberikan warna yang berbeda. Dalam paper ini dibahas mengenai pewarnaan total pada Graf Bintang Sierpinski, 𝑆𝑆𝑆𝑆 𝑛𝑛 . Bilangan kromatik untuk pewarnaan total pada Graf 𝑆𝑆𝑆𝑆 𝑛𝑛 adalah 1 untuk 𝑛𝑛 = 1 dan 1 + 3. 2 𝑛𝑛−2 untuk 𝑛𝑛 ≥ 2. Kata Kunci: Graf Bintang Sierpinski, Pewarnaan total, Bilangan Kromatik.

Tuberculosis has been an endemic disease leading to high level of mortality. A model of TB epidemic incorporating the asymptomatic and symptomatic infection stages of individuals are studied and introducing treatments for these stages. The local behavior of the model is analyzed using linearization for non endemic equilibrium and using bifurcation at R0 = 1 for endemic equilibrium. Non endemic state and endemic state are proven locally asymptotically stable. Numerical simulations show the effectiveness of treatment in asymptomatic and symptomatic infection stages can reduce the rate of spread of TB.

Masalah transportasi merupakan masalah pendistribusian suatu barang dari beberapa sumber ke beberapa tujuan untuk mendapatkan total biaya transportasi yang minimum. Masalah transportasi umumnya diselesaikan dengan dua tahap yaitu menggunakan metode solusi fisibel awal dan metode solusi optimal. Penelitian terkait metode untuk menentukan solusi fisibel awal sangat beragam dan sampai sekarang masih terus dikembangkan. Dibutuhkan suatu metode untuk menentukan solusi fisibel awal yang efisien dan akurat sehingga memudahkan dalam proses penyelesaiaan masalah transportasi. Pada tulisan ini, dibahas metode baru untuk menemukan solusi fisibel awal masalah transportasi, yaitu metode Minimum Demand Method. Metode ini membantu untuk menyelesaikan masalah transportasi dengan iterasi yang lebih sedikit dan mendapatkan hasil solusi fisibel awal yang mendekati solusi optimal. Dalam Minimum Demand Method untuk menentukan solusi fisibel awal berfokus pada baris permintaan yang nilainya paling kecil atau paling sedikit. Formulasi matematika untuk meminimumkan biaya transportasi menggunakan metode MDM juga disajikan. Prosedur dalam mendapatkan solusi fisibel awal dijelaskan dalam simulasi numerik. Minimum Demand Method diaplikasikan untuk menyelesaikan permasalahan transportasi pada studi kasus UD Indah Mandiri. Pada studi kasus didapatkan solusi fisibel awal yang sama dengan solusi optimal. Dengan pembuktian menggunakan Teorema didapatkan solusi fisibel awal yang sudah optimal sehingga tidak perlu dicari solusi optimalnya menggunakan metode MODI. Penggunaan Minimum Demand Method untuk mencari solusi fisibel awal pada UD Indah Mandiri diperoleh total biaya transportasi minimum dan mengalami penurunan sebesar 45,3%.