TY - JOUR
AU - Megalai, Kandasamy
AU - Tamilarasi, Angamuthu
PY - 2011
TI - Fuzzy Subalgebras and Fuzzy T-ieals in TM-Algebras
JF - Journal of Mathematics and Statistics
VL - 7
IS - 2
DO - 10.3844/jmssp.2011.107.111
UR - https://thescipub.com/abstract/jmssp.2011.107.111
AB - 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.