Fuzzy Subalgebras and Fuzzy p-ideals in TM-Algebras

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 sub algebra of X and I be a p-ideal of X. Let and v be fuzzy sets in a TM-algebra X. Approach Define the upper level subset t of and the cartesian product of and v from XX to [0, 1] by minimum of (x) and v (y) for all elements (x, y) in XX. Result We proved any subalgebra of a TM-algebra X can be realized as a level subalgebra of some fuzzy subalgebra of X and t is a p-ideal of X. Also we proved, the cartesian product of and v is a fuzzy p-ideal of XX. 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.