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

  • Received: 10 April 2021 Accepted: 11 August 2021 Published: 17 August 2021
  • MSC : 03G10, 06B99, 06B75

  • 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.

    Citation: Mona Aaly Kologani, Rajab Ali Borzooei, Hee Sik Kim, Young Bae Jun, Sun Shin Ahn. Construction of some algebras of logics by using intuitionistic fuzzy filters on hoops[J]. AIMS Mathematics, 2021, 6(11): 11950-11973. doi: 10.3934/math.2021693

    Related Papers:

  • 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.



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