Fuzzy tri-ideals and fuzzy soft tri-ideals over semirings

다국어 초록 (Multilingual Abstract)

In this paper, we introduce the notion of fuzzy tri-ideal, fuzzy soft tri-ideal over semirings and study some of their properties. Every fuzzy soft left (right) ideal over semiring is a fuzzy soft right (left) tri- ideal over semiring. We characterize the regular semiring in terms of fuzzy left ( right) tri ideals and fuzzy soft left ( right) tri-ideals over semiring.

참고문헌 (Reference)

1 M. Murali Krishna Rao, "Tri-ideals of semirings" 10 (10): 145-155, 2020

2 H. Aktas, "Soft sets and soft groups" 177 (177): 2726-2735, 2007

3 D. Molodtsov, "Soft set theory-First results" 37 : 19-31, 1999

4 F. Feng, "Soft semirings" 56 : 2621-2628, 2008

5 M. K. Sen, "On k-ideals of semirings" 15 (15): 347-350, 1992

6 N. Kuroki, "On fuzzy semigroups" 53 : 203-236, 1991

7 M. Murali Krishna Rao, "Left bi-quasi ideals of semirings" 8 : 45-53, 2018

8 M. Murali Krishna Rao, "Fuzzy soft Γ-semirings homomorphism" 12 (12): 479-489, 2016

9 M. Murali Krishna Rao, "Fuzzy soft Γ-semiring and fuzzy soft k ideal over Γ-semiring" 9 (9): 12-25, 2015

10 J. Ghosh, "Fuzzy soft rings and fuzzy soft ideals" 2 (2): 66-74, 2011

11 M. Murali Krishna Rao, "Fuzzy soft bi-interior ideals over Γ-semirings" 10 (10): 47-62, 2021

12 L. A. Zadeh, "Fuzzy sets" 8 : 338-353, 1965

13 A. Rosenfeld, "Fuzzy groups" 35 : 512-517, 1971

14 A. Borumand Saeid, "Fuzzy (soft)quasi-interior ideals of semirings" 1 (1): 129-141, 2022

15 M. Murali Krishna Rao, "Bi-interior Ideals in semigroups" 38 (38): 239-254, 2018

16 M.Murali Krishna Rao, "A study of quasi-interior ideal of semiring" 2 : 287-300, 2019

17 M. Murali Krishna Rao, "A study of a bi-quasi-interior ideal as a new generalization of ideal of generalization of semiring" 8 : 519-535, 2018

18 P. J. Allen, "A fundamental theorem of homomorphism for semirings" 21 : 412-416, 1969