INTERIOR IDEAL FUZZY SEMIRING

Saman Abdurrahman

Abstract


Semiring is one of the ring extensions, which eliminates the inverse axiom in the first operation. One of the topics on the semiring is the ideal interior. This study introduces the concept of the ideal interior semiring and the ideal interior fuzzy semiring. Further, it examined the properties of the ideal fuzzy semiring interior and the nature of the existence of the ideal interior semiring if the ideal fuzzy interior is given.


Keywords


semiring, interior ideal, fuzzy interior ideal

Full Text:

PDF

References


Abdurrahman, S. (2018). Interior Subgrup Fuzzy. Jurnal Fourier, 7(1), 13–21. https://doi.org/10.14421/fourier.2018.71.13-21

Abdurrahman, S. (2020a). Karakteristik subsemiring fuzzy. Jurnal Fourier, 9(1), 19–23. https://doi.org/10.14421/fourier.2020.91.19-23

Abdurrahman, S. (2020b). 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

Ahsan, J., Mordeson, J. N., & Shabir, M. (2012a). Fundamental Concepts. In Fuzzy Semirings with Applications to Automata Theory (pp. 3–13). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-27641-5_1

Ahsan, J., Mordeson, J. N., & Shabir, M. (2012b). Fuzzy Ideals of Semirings. In Fuzzy Semirings with Applications to Automata Theory (pp. 15–29). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-27641-5_2

Ésik, Z. (2008). Iteration Semirings. In M. Ito & M. Toyama (Eds.), Developments in Language Theory (pp. 1–20). Springer Berlin Heidelberg.

Golan, J. S. (1999). Hemirings and Semirings: Definitions and Examples. In Semirings and their Applications (pp. 1–18). Springer Netherlands. https://doi.org/10.1007/978-94-015-9333-5_1

Jezewski, M., Czabanski, R., & Leski, J. (2017). Introduction to Fuzzy Sets. In P. Prokopowicz, J. Czerniak, D. Mikołajewski, Ł. Apiecionek, & D. Ślȩzak (Eds.), Theory and Applications of Ordered Fuzzy Numbers: A Tribute to Professor Witold Kosiński (pp. 3–22). Springer International Publishing. https://doi.org/10.1007/978-3-319-59614-3_1

Jian-ming, Z., & Xue-ling, M. A. (2008). On Fuzzy Interior Ideals in Semigroups. Journal of Mathematical Research & Exposition, 28(1), 103–110. https://doi.org/10.3770/j.issn

Kuroki, N. (1982). Fuzzy Semiprime Ideals in Semigroup. Fuzzy Sets and Systems, 8(1), 71–79. https://doi.org/https://doi.org/10.1016/0165-0114(82)90031-8

Mandal, D. (2014). Fuzzy Ideals and Fuzzy Interior Ideals in Ordered Semirings. Fuzzy Inf. Eng, 6, 101–114. http://jmre.dlut.edu.cn

N. Mordeson, J., R. Bhutani, K., & Rosenfeld, A. (2005). Fuzzy Subsets and Fuzzy Subgroups. 39, 1–39. https://doi.org/10.1007/10936443_1

Nasehpour, P. (2020). Some remarks on semirings and their ideals. Asian-European Journal of Mathematics, 13(1), 1–14. https://doi.org/10.1142/S1793557120500023

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

Sung, M. H., Young, B. J., & Meng, J. (1995). Fuzzy interior ideals in semigroups 1995.pdf. Indian J. Pure Appl. Math, 26(9), 859–863.

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




DOI: https://doi.org/10.20527/epsilon.v15i2.4894

Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN

Indexed by:

          

 

EDITORIAL OFFICE 

           

 

 

 

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