AIMS Mathematics (Aug 2021)

Construction of some algebras of logics by using intuitionistic fuzzy filters on hoops

  • Mona Aaly Kologani,
  • Rajab Ali Borzooei ,
  • Hee Sik Kim,
  • Young Bae Jun,
  • Sun Shin Ahn

DOI
https://doi.org/10.3934/math.2021693
Journal volume & issue
Vol. 6, no. 11
pp. 11950 – 11973

Abstract

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In this paper, we define the notions of intuitionistic fuzzy filters and intuitionistic fuzzy implicative (positive implicative, fantastic) filters on hoops. Then we show that all intuitionistic fuzzy filters make a bounded distributive lattice. Also, by using intuitionistic fuzzy filters we introduce a relation on hoops and show that it is a congruence relation, then we prove that the algebraic structure made by it is a hoop. Finally, we investigate the conditions that quotient structure will be different algebras of logics such as Brouwerian semilattice, Heyting algebra and Wajesberg hoop.

Keywords