Falling Shadow Theory with Applications in Hoops

Rajab Ali Borzooei; Gholam Reza Rezaei; Mona Aaly Kologhani; Young Bae Jun

doi:10.18778/0138-0680.2021.03

Authors

Rajab Ali Borzooei Shahid Beheshti University, Faculty of Mathematical Sciences, Department of Mathematics Author https://orcid.org/0000-0001-7538-7885
Gholam Reza Rezaei University of Sistan and Baluchestan, Department of Mathematics Author https://orcid.org/0000-0001-5693-402X
Mona Aaly Kologhani Hatef Higher Education Institute Author https://orcid.org/0000-0002-5234-2876
Young Bae Jun Gyeongsang National University, Department of Mathematics Education Author https://orcid.org/0000-0002-0181-8969

DOI:

https://doi.org/10.18778/0138-0680.2021.03

Keywords:

Hoop, fuzzy subhoop, fuzzy filter, falling fuzzy subhoop, falling fuzzy filter

Abstract

The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between falling fuzzy subhoops and falling fuzzy filters are discussed, and conditions for a falling fuzzy subhoop to be a falling fuzzy filter are provided. Also conditions for a falling shadow of a random set to be a falling fuzzy filter are displayed.

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