Fuzzy Positive Implicative Filters of Hoops Based on Fuzzy Points

Rajab Ali Borzooei, Mona Aaly Kologani, Mahdi Sabet Kish and Young Bae Jun
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Rajab Ali Borzooei: Department of Mathematics, Shahid Beheshti University, Tehran 7561, Iran
Mona Aaly Kologani: Hatef Higher Education Institute, Zahedan 8301, Iran
Mahdi Sabet Kish: Department of Mathematics, Shahid Beheshti University, Tehran 7561, Iran
Young Bae Jun: Department of Mathematics, Shahid Beheshti University, Tehran 7561, Iran

Mathematics, 2019, vol. 7, issue 6, 1-14

Abstract: In this paper, we introduce the notions of ( ∈ , ∈ ) -fuzzy positive implicative filters and ( ∈ , ∈ ∨ q ) -fuzzy positive implicative filters in hoops and investigate their properties. We also define some equivalent definitions of them, and then we use the congruence relation on hoop defined in blue[Aaly Kologani, M.; Mohseni Takallo, M.; Kim, H.S. Fuzzy filters of hoops based on fuzzy points. Mathematics. 2019 , 7 , 430; doi:10.3390/math7050430] by using an ( ∈ , ∈ ) -fuzzy filter in hoop. We show that the quotient structure of this relation is a Brouwerian semilattice.

Keywords: hoop; sub-hoop; fuzzy points; fuzzy positive implicative filter; Brouwerian semilattice (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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