Matriks Invers Moore-penrose Dalam Penyelesaian Sistem Persamaan Linier

In this paper we define and study about The Moore Penrose Inverse of any matrices under the rank. We apply our result to study of Solution Linear Equation Siste

MICE Implementation to Handle Missing Values in Rain Potential Prediction Using Support Vector Machine Algorithm

Support Vector Machine (SVM) is a machine learning algorithm used for classification. SVM has several advantages such as the ability to handle high-dimensional data, effective in handling nonlinear data through kernel functions, and resistance to overfitting through soft margins. However, SVM has weaknesses, especially when handling missing values in data. The use of SVM must consider the missing values strategy chosen. Missing values in data mining is a serious problem for researchers because it causes many problems such as loss of efficiency, complications in data handling and analysis, and the occurrence of bias due to differences between missing data and complete data. To overcome the above problems, this research focuses on understanding the characteristics of missing values and handling them using the Multiple Imputation by Chained Equations (MICE) technique. In this study, we utilized secondary data experiments that contain missing values from the Meteorological, Climatological, and Geophysical Agency (called BMKG) related to predictions of potential rain, especially in DKI Jakarta. Identification of types or patterns of missing values, exploration of the relationship between missing values and other variables, incorporation of the MICE method to handle missing values, and the Support Vector Machine Algorithm for classification will be carried out to produce a more reliable and accurate prediction model for rain potential. It shows that the imputation method with the MICE gives better results than other techniques (such as Complete Case Analysis, Imputation Method Mean, Median, Mode, and K-Nearest neighbor), namely an accuracy of 89% testing data when applying the Support Vector Machine algorithm for classification

The cross-association relation based on intervals ratio in fuzzy time series

The fuzzy time series (FTS) is a forecasting model based on linguistic values. This forecasting method was developed in recent years after the existing ones were insufficiently accurate. Furthermore, this research modified the accuracy of existing methods for determining and the partitioning universe of discourse, fuzzy logic relationship (FLR), and variation historical data using intervals ratio, cross association relationship, and rubber production Indonesia data, respectively. The modifed steps start with the intervals ratio to partition the determined universe discourse. Then the triangular fuzzy sets were built, allowing fuzzification. After this, the FLR are built based on the cross association relationship, leading to defuzzification. The average forecasting error rate (AFER) was used to compare the modified results and the existing methods. Additionally, the simulations were conducted using rubber production Indonesia data from 2000-2020. With an AFER result of 4.77%<10%, the modification accuracy has a smaller error than previous methods, indicating  very good forecasting criteria. In addition, the coefficient values of D1 and D2 were automatically obtained from the intervals ratio algorithm. The future works modified the partitioning of the universe of discourse using frequency density to eliminate unused partition intervals

MATRIKS INVERS MOORE PENROSE ATAS DAERAH INTEGRAL

The Inverse Moore Penrose matrix has been applied in various areas, for example in statistic and optimization. In this paper we study Inverse Moore Penrose matrix which is applied to Integral Domain. We will first discuss the characterization of all matrices over Integral Domain which admits Moore Penrose Inverse. With this characterization we will derive necessary and sufficient conditions for a matrix to have a Moore Penrose Inverse. We also show the relations between Moore Penrose Inverse matrix and Compound matrix. The aim of this paper is to obtain an explicit formula for the Moore Penrose Inverse when it exist and gives a necessary and sufficient condition for a matrix to have a Moore Penrose Inverse under the assumption that a matrix has a rank factorization

INVERS MATRIKS MOORE PENROSE ATAS RING KOMUTATIF DENGAN ELEMEN SATUAN

Jika A adalah matriks dengan elemen Ring komutatif dengan elemen satuan yang berukuran mxn maka matriks invers dari A yang disebut dengan matriks invers Moore Penrose dari A ditulis G(A) dapat diperoleh dengan memenuhi syarat perlu dan cukup agar G(A) merupakan invers Moore Penrose dari

Grup dan Semigrup Topologis

A group G with topology τ on G can be turned topological group (G,τ) if multiplication mapping G x G ⟶ G continuous such that inverse mapping is continuous. A semigrup S with topology τ on S can be turned topological semigroup (S,τ) if the multiplication S,as a mapping of S x S ⟶ S is continuous. A group(semigroup) G can be turned into a topological group(semigroup) by providing it with the discrete topology

METODE REDUCED-GRADIENT PADA OPTIMASI NONLINIER BERKENDALA PERTIDAKSAMAAN NONLINIER

Metode Reduced-Gradient merupakan salah satu metode yang dikembangkan berdasarkan metode Titik Fisibel, yaitu suatu metode yang digunakan untuk menyelesaikan permasalahan optimasi nonlinier berkendala. Metode Reduced-Gradient khusus digunakan untuk menyelesaikan permasalahan optimasi nonolinier berkendala nonlinier. Dalam tugas akhir ini hanya dibahas mengenai metode Reduced-Gradient pada optimasi nonlinier berkendala pertidaksamaan nonlinier. Inti dari metode Reduced-Gradient adalah menentukan arah pencarian. Arah pencarian yang diperoleh pada setiap iterasi ini nantinya akan menuju ke suatu titik fisibel baru yang memberikan nilai objektif yang lebih baik. Penentuan arah pencarian terus dilakukan sampai ditemukan solusi optimal. Pada metode Reduced-Gradient arah pencarian ditinjau dari kondisi ruang Null sehingga terdapat jaminan bahwa arah pencarian tersebut selalu berada pada daerah fisibel. Dari sini, setiap titik yang dihasilkan pada setiap iterasi akan selalu berada pada daerah fisibel. Oleh karena itu, metode ini mampu menjamin bahwa solusi optimal yang dihasilkan juga berada pada daerah fisibel

MATRIKS INVERS MOORE PENROSE ATAS DAERAH INTEGRAL

Abstract. The Inverse Moore Penrose matrix has been applied in various areas, for example in statistic and optimization. In this paper we study Inverse Moore Penrose matrix which is applied to Integral Domain. We will first discuss the characterization of all matrices over Integral Domain which admits Moore Penrose Inverse. With this characterization we will derive necessary and sufficient conditions for a matrix to have a Moore Penrose Inverse. We also show the relations between Moore Penrose Inverse matrix and Compound matrix. The aim of this paper is to obtain an explicit formula for the Moore Penrose Inverse when it exist and gives a necessary and sufficient condition for a matrix to have a Moore Penrose Inverse under the assumption that a matrix has a rank factorization. Key words: Integral Domain, rank, minor