@article {10.3844/jmssp.2011.107.111,
article_type = {journal},
title = {Fuzzy Subalgebras and Fuzzy T-ieals in TM-Algebras},
author = {Megalai, Kandasamy and Tamilarasi, Angamuthu},
volume = {7},
year = {2011},
month = {May},
pages = {107-111},
doi = {10.3844/jmssp.2011.107.111},
url = {https://thescipub.com/abstract/jmssp.2011.107.111},
abstract = {In this study, we introduce the concepts of fuzzy subalgebras and fuzzy ideals in TM-algebras
and investigate some of its properties. Problem statement: Let X be a TM-algebra, S be a subalgebra of X
and I be a T-ideal of X. Let µ and v be fuzzy sets in a TM-algebra X. Approach: Define the upper level
subset µt of µ and the cartesian product of µ and v from X×X to [0,1] by minimum of µ (x) and v (y) for all elements (x, y) in X×X. Result: We proved any subalgebra of a TM-algebra X can be realized as a level subalgebra of some fuzzy subalgebra of X and µt is a T-ideal of X. Also we proved, the cartesian product of µ and v is a fuzzy T-ideal of X×X. Conclusion: In this article, we have fuzzified the subalgebra and ideal of TM-algebras into fuzzy subalgrbra and fuzzy ideal of TM-algebras. It has been observed that the TM-algebra satisfy the various conditions stated in the BCC/ BCK algebras. These concepts can further be generalized.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}