Fuzzy Subalgebras and Fuzzy T-ieals in TM-Algebras
Kandasamy Megalai and Angamuthu Tamilarasi
DOI : 10.3844/jmssp.2011.107.111
Journal of Mathematics and Statistics
Volume 7, Issue 2
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.
© 2011 Kandasamy Megalai and Angamuthu Tamilarasi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.