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

doi:10.3934/math.2021693

AIMS Mathematics

2021, Volume 6, Issue 11: 11950-11973. doi: 10.3934/math.2021693

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

1.
Hatef Higher Education Institute, Zahedan, Iran
2.
Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
3.
Research Institute for Natural Sci., Department of Mathematics, Hanyang University, Seoul 04763, Korea
4.
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
5.
Department of Mathematics Education, Dongguk University, Seoul 04620, Korea

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.
- Hoop,
- intuitionistic fuzzy (implicative, positive implicative, fantastic) filter,
- Brouwerian semilattice,
- Heyting algebra,
- 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

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Abstract

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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