Fuzzy Time Series (FTS) has been growing rapidly in recent years. There are many models that were developed. In this paper, we propose a new method to forecast exchange rate data by combining some models. Firstly, we use the average-based interval to make optimal interval numbers. Secondly, we use frequency density-based partitioning for optimal partitioning. In this part, we divide the three highest frequency of intervals into four, three, and two sub-intervals, respectively, and discarding intervals if there is no data distributed. And thirdly, we use k-means clustering to construct the Fuzzy Logical Relationship Group (FLRG). We divide Fuzzy Logical Relationship (FLR) into 16 initial clusters. Then we evaluate model by calculating the error value using MSE (Mean Squared Error) and AFER (Average Forecasting Error Rates). The study case of this paper is daily exchange rate data (USD to IDR) started from January until May with its unstable fluctuation caused by Pandemic Covid-19. The study aims to obtain a forecasting model of exchange rate data as the preparation and evaluation for future conditions.

Forecasting method based on fuzzy time series has been widely developed in recent years. In this paper, we propose a new improvement at determining universe of discourse, variation historical data and partitioning stage. At early stage, we define the universe of discourse then calculate the basis value to find out how much interval should be used with variatin historical data. Secondly, we are partitioning the main intervals into several numbers of sub-intervals. The empirical analysis shows that sub-interval caused the fuzzy number getting closer to crisp value. It causes the better forecasting value. We use the data of yearly production petrolium Indonesia for simulation. We compare the forecasting results and error value of the method with previous existing methods The modifications give better forecasting results than previous methods indicated with smaller The Means Squared Error (MSE) and Average Forecasting Error (AFER).

FTS is popular in many recent years. Researchers are competing to outperform existing method by making new improvement including modifications at clustering step. Here we discuss about clustering process, i.e., partitioning based metric frequency density and firefly clustering algorithm. In the simulation, we compare the forecasting results and error value of the method with previous existing methods. The modifications give better forecasting results than previous methods indicated with smaller Root Means Errors (RMSEs) and Average Forecasting Error (AFER).

This paper is addressed to discuss the edge super trimagic total labeling on some graphs which are corona, double ladder, quadrilateral snake and alternate triangular snake. The main results are the edge super trimagic total label for these graphs. Furthermore, it was prove that corona is a graph with edge super trimagic total labeling, a double ladder with odd ladder is graph with edge super trimagic total labeling, quadrilateral snake is a graph with edge super trimagic total labeling and finally an alternate triangular snake with odd ladder is graph with edge super trimagic total labeling.

The pandemic caused by the novel corona virus (covid-19) has affected various aspects of life throughout the world. Indonesia is one of the country with a daily high number of Covid-19-19 spread cases. This study aims to obtain a forecasting model of Covid-19 cases that can be used to predict Covid-19 cases daily and it can increase the readiness of Covid-19 health protocols system. In this study, we get a very good model for Covid-19 forecasting in Indonesia obtained by the fuzzy time series method using frequency density-based partitioning. The universe of this method is the percentage of case changes from day to day. The percentage change as a universe in fuzzy time series forecasting method makes the results of comparison of actual data and predictions increasingly similar. We use data of the Covid 19 cases taken from the Nasional Kompas website during June 2020. Forecast results show very good with MSE value of 457,83 and small AFER value of 0,0425138%.