On linear fuzzifications of groupoids with special emphasis on BCK-algebras

  • Authors:

  • Jeong Soon Han;Hee Sik Kim;J. Neggers

  • Affiliations:

  • Department of Applied Mathematics, Hanyang University, Ahnsan, Korea;Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul, Korea;Department of Mathematics, University of Alabama, Tuscaloosa, AL, USA

  • Venue:
  • Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
  • Year:
  • 2013

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Abstract

In this paper, for a given groupoid X, * and a relation R on X we consider a related structure LFRX = { ∈ X3 | xRy, yRz}, and we discuss three different types on LFRX, and we construct a linear fuzzy real BCK-algebra LF≤X, $\ominus$, ε0 and a new BCK-algebra LF≤X, $\oast$, ε0 from a BCK-algebra X, *, 0.