Fuzzy identities with application to fuzzy semigroups

  • Authors:
  • Branka Budimirović;Vjekoslav Budimirović;Branimir Šešelja;Andreja Tepavčević

  • Affiliations:
  • -;-;-;-

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2014

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Abstract

The notion of a fuzzy identity is introduced on a fuzzy subalgebra in the framework of fuzzy equalities instead of the crisp one. A fuzzy identity may be satisfied by a fuzzy subalgebra, while the underlying crisp algebra need not satisfy the analogous crisp identity. Among other properties, it is shown that for every fuzzy subalgebra @m of A there is a least fuzzy equality such that a fuzzy identity holds on @m. As an application, fuzzy semigroups are introduced with respect to a fuzzy equality. In particular, fuzzy semilattices, cancellative and regular fuzzy semigroups are investigated.