PRODUK KARTESIAN IDEAL FUZZY PADA RING

Sapuah Sapuah, Saman Abdurrahman, Nurul Huda

Abstract


The concept of algebra fuzzy was initially introduced by Rosenfeld in 1971. In 1991, Malik and Moderson explained if cartesian product of two fuzzy subgroup from same group, then it was fuzzy subgroup too and if cartesian product of two fuzzy ideal from same ring, then it was fuzzy ideal too. We discuss the cartesian product of two or more fuzzy subgroups from different group, then it was fuzzy subgroup too and cartesian product of two or more fuzzy ideal from different ring, then it was fuzzy ideal too.

Keywords


group, ring, fuzzy subgroup, fuzzy ideal, cartesian product.

Full Text:

PDF

References


Abdurrahman, Saman. 2015. Produk Kartesius dari Ideal Fuzzy Near-ring. Prosiding Seminar Nasional Matematika dan Pendidikan Matematika. Universitas Negeri Yogyakarta. 43 : 479-482.

Clark, Pete L. 2011. Commutative Algebra. Department of Mathematics Georgia University.

Dummit, David S. & Richard M. Foote. 2004. Abstract Algebra, 3rd ed. John Wiley and Sons, Inc., United States Of America.

Ersoy, B.A. 2004. On The Generalization of Cartesian Product of Fuzzy Subgroups And Ideals. Journal of Engineering and Natural Sciences. Yildiz Technical University, Istanbul. 3 : 96-100.

Frailegh, J.B.. 2003. A first Course in Abstract Algebra, 7nd ed. Addison–Wasley, Publishing Company, New York.

Judson, Thomas W. 2009. Abstract Algebra Theory and Applications. Stephen F. Austin State University, Texas.

Malik, D. S. & Mordeson, John N. 1991. Fuzzy Relations on Rings and Groups. Fuzzy Sets and Systems. 43: 117-123.

Rosenfeld, Azriel. 1971. Fuzzy Groups. Journal of Mathematical Analysis and Applications. University of Maryland. 35 : 512-517.

Zadeh L. A. 1965. Fuzzy sets. Information and Control. 8 : 383-353.




DOI: https://doi.org/10.20527/epsilon.v11i1.114

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON

Indexed by:

          

 

EDITORIAL OFFICE 

           

 

 

 

Creative Commons License
JMMTE is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.