Research Article Open Access

Fuzzy Subalgebras and Fuzzy T-ieals in TM-Algebras

Kandasamy Megalai and Angamuthu Tamilarasi

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 of Mathematics and Statistics
Volume 7 No. 2, 2011, 107-111

DOI: https://doi.org/10.3844/jmssp.2011.107.111

Submitted On: 4 May 2011 Published On: 18 May 2011

How to Cite: Megalai, K. & Tamilarasi, A. (2011). Fuzzy Subalgebras and Fuzzy T-ieals in TM-Algebras. Journal of Mathematics and Statistics, 7(2), 107-111. https://doi.org/10.3844/jmssp.2011.107.111

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Keywords

  • TM-algebra
  • fuzzy subalgebra
  • fuzzy ideals
  • homomorphism
  • cartesian product
  • level subset
  • conditions stated