KARAKTERISTIK MATRIKS SOFT
Keywords: gabungan, intersection and complement, irisan dan konplemen, matriks soft, soft matrix, union
Abstract
A soft set is a concept of the set that plays an essential role in overcoming vagueness. The soft set is an extension of the fuzzy set concept. One of the products of the soft set is a soft matrix. A soft matrix is a matrix formed into a soft set's membership value whose entries are elements at {0,1}. This paper aims to introduce operations on soft matrices, i.e., intersection, union, and complements. Further, algebraic properties of soft matrix operations were investigated, commutative, associative, distributive laws, De Morgan’s laws, and absorption.
Himpunan soft merupakan suatu konsep himpunan yang berperan penting dalam mengatasi ketidakpastian. Himpunan soft merupakan perluasan dari konsep himpunan fuzzy. Salah satu produk dari himpunan soft adalah matriks soft. Matriks soft adalah matriks yang dibentuk dari nilai keanggotaan himpunan soft yang entri-entrinya elemen di {0,1}. Paper ini, bertujuan memperkenalkan operasi-operasi pada matriks soft, yaitu irisan, gabungan, dan komplemen. Lebih lanjut, diselidiki sifat-sifat aljabar operasi matriks soft, yaitu komutatif, asosiatif, hukum distributive, hukum De Morgan’s, dan absorpsi.
Downloads
References
Abdurrahman, S. (2020). ω – fuzzy subsemiring.pdf. Jurnal Matematika, Sains, dan Teknologi, 21(1), 1–10. https://doi.org/https://doi.org/10.33830/jmst.v21i1.673.2020.
Çaǧman, N. & Enginoǧlu, S. (2010). Soft matrix theory and its decision making. Computers and Mathematics with Applications, 59(10), 3308–3314. https://doi.org/10.1016/j.camwa.2010. 03.015.
Lipschutz, S. (1998). Set and Basic Operations on Sets. In Schaum's Outline of Theory and Problems of Set Theory (2nd ed, pp. 1–33). The McGraw-Hili Companies, Inc.
Maji, P. K., Biswas, R., & Roy, A. R. (2003). Soft set theory. Journal Computers and Mathematics with Applications, 45(4–5), 555–562. https://doi.org/10.1016/S0898-1221(03)00016-6.
Michael, L. O. (2016). Set Theory. In A First Course In Mathematical Logic And Set Theory (pp. 117–155). John Wiley & Sons, Inc., Hoboken, New Jersey.
Molodtsov, D. (1999). Soft set theory first results. Journal Computers and Mathematics with Applications, 37, 19–31. https://www.sciencedirect.com/science/article/pii/ S0898122199000565.
Mondal, S., & Pal, M. (2011). Soft matrices. African Journal of Mathematics and Computer Science Research, 7(13), 379–388. https://doi.org/https://doi.org/10.5897/AJMCSR.9000057.
Rosenfeld, A. (1971). Fuzzy groups. Journal of Mathematical Analysis and Applications, 35(3), 512–517. https://doi.org/10.1016/0022-247X(71)90199-5.
Vijayabalaji, S., & Ramesh, A. (2013). A new decision making theory in soft matrices. International Journal of Pure and Applied Mathematics, 86(6), 927–939. https://doi.org/http://dx.doi.org/ 10.12732/ijpam.v86i6.6.
Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8(3), 338–353. https://doi.org/https://doi.org/10.1016/S0019-9958(65)90241-X.
Zhang, Z. (2014). A new method for decision making based on soft matrix theory. Journal of Scientific Research and Reports, 3(15), 2110–2117. https://doi.org/10.9734/jsrr/2014/10507.