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:10.3934/MATH.2021693

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

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	11950-11973
Number of pages	24
Journal	AIMS Mathematics
Volume	6
Issue number	11
DOIs	https://doi.org/10.3934/MATH.2021693
State	Published - 2021

Keywords

Brouwerian semilattice
Heyting algebra
Hoop
Intuitionistic fuzzy (implicative, positive implicative, fantastic) filter
Wajesberg hoop

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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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AU - Jun, Young Bae

AU - Ahn, Sun Shin

PY - 2021

Y1 - 2021

N2 - 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.

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

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