Matriks Kabur dan Karakteristiknya

Muhammad Abdy(1*), Maya Sari Wahyuni(2), Muh. Hadi Purnomo(3),

(1) Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Makassar
(2) Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Makassar
(3) Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Makassar
(*) Corresponding Author




DOI: https://doi.org/10.35580/jmathcos.v2i1.12459

Abstract


Penelitian ini mengkaji definisi, operasi, dan teorema pada matriks kabur dan karakteristiknya. Literatur yang digunakan sebagai acuan adalah artikel yang ditulis oleh Pal (2016), Sidky & Emam (1992), dan Suroto & Wardayani (2015). Hasilnya dapat diberikan perbaikan pada operasi yang digunakan pada matriks kabur serta teorema himpunan matriks kabur persegi dapat diperluas menjadi teorema himpunan matriks kabur. Selain itu, disimpulkan bahwa himpunan matriks kabur persegi memenuhi sifat aljabar untuk semigrup dan semi ring. Namun tidak memenuhi sifat aljabar untuk grup dan ring.

Kata Kunci: Himpunan Kabur, Matriks, Matriks Kabur, Grup, Ring, Semiring.

 

This research examines the definitions, operations, and theorems of fuzzy matrices and their characteristics. The literature used as a reference is an article written by Pal (2016), Sidky & Emam (1992), and Suroto & Wardayani (2015). The results can be given improvements to the operations used in the fuzzy matrix and the set of square fuzzy matrix theorems can be extended to fuzzy matrix set theorems. In addition, it was concluded that the set of square fazzy matrix fulfilled the algebraic properties for semigroup and semiring. But it does not fulfill algebraic properties for groups and rings.

Keywords: Fuzzy Set, Matrix, Fuzzy Matrix, Group, Ring, Semiring.

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References


Judson, T. W. (2013). Abstract Algebra; Theory and Applications. Texas: Free Software Foundation

Pal, M. (2016). Fuzzy Matrix and its Application. Fuzzy Matrices. 1-11.

Sidky, F., & Emam, E. (1992). Some Remarks on Sections of a Fuzzy Matrix. J.K.A.U, 145-155.

Suroto, & Wardayani, A. (2015). Semi Modul Interval [0,1] atas Semi Ring Matriks Fuzzy Persegi. Jurnal Jurusan Matematika Universitas Jenderal Soedirman. 79-84

Thomason, M. G. (1977). Convergence of Powers of a Fuzzy Matrix. Journal of Mathematical Analysis and Applications, 57. 476-480.

Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8. 338-353.


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