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On imaginable T -fuzzy subalgebras and imaginable T -fuzzy closed ideals in BCH-algebras

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  • Young Bae Jun
  • Sung Min Hong

Abstract

We inquire further into the properties on fuzzy closed ideals. We give a characterization of a fuzzy closed ideal using its level set, and establish some conditions for a fuzzy set to be a fuzzy closed ideal. We describe the fuzzy closed ideal generated by a fuzzy set, and give a characterization of a finite-valued fuzzy closed ideal. Using a t -norm T , we introduce the notion of (imaginable) T -fuzzy subalgebras and (imaginable) T -fuzzy closed ideals, and obtain some related results. We give relations between an imaginable T -fuzzy subalgebra and an imaginable T -fuzzy closed ideal. We discuss the direct product and T -product of T -fuzzy subalgebras. We show that the family of T -fuzzy closed ideals is a completely distributive lattice.

Suggested Citation

  • Young Bae Jun & Sung Min Hong, 2001. "On imaginable T -fuzzy subalgebras and imaginable T -fuzzy closed ideals in BCH-algebras," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 27, pages 1-19, January.
    • Handle: RePEc:hin:jijmms:937805
    DOI: 10.1155/S0161171201006408
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