MMN-2849

Fuzzy sub-hoops based on fuzzy points

  • R. A. Borzooei, Shahid Beheshti University, Department of Mathematics, 1983963113 Tehran, Iran, borzooei@sbu.ac.ir
  • M. Mohseni Takallo, Shahid Beheshti University, Department of Mathematics, 1983963113 Tehran, Iran, mohammad.mohseni1122@gmail.com
  • M. Aaly Kologani, Hatef Higher Education Institute, Zahedan, Iran, mona4011@gmail.com
  • Y.B. Jun, Gyeongsang National University, Department of Mathematics Education, 52828 Jinju, Korea, skywine@gmail.com

Abstract

Using the belongs to relation (\in) and quasi-coincident with relation (q) between fuzzy points and fuzzy sets, the notions of an (\in;\in)-fuzzy sub-hoop, an (\in;\in \vee q)-fuzzy sub-hoop and a (q;\in \vee q)-fuzzy sub-hoop are introduced, and several properties are investigated. Characterizations of an (\in;\in)-fuzzy sub-hoop and an (\in;\in \vee q)-fuzzy sub-hoop are displayed. Relations between an (\in;\in)-fuzzy sub-hoop, an (\in;\in \vee q)-fuzzy sub-hoop and a (q;\in \vee q)-fuzzy sub-hoop are discussed. Conditions for a fuzzy set to be a (q;\in \vee q)-fuzzy sub-hoop are considered, and condition for an (\in;\in \vee q)-fuzzy sub-hoop to be a (q;\in \vee q)-fuzzy sub-hoop are provided.


Vol. 22 (2021), No. 1, pp. 91-106
DOI: 10.18514/MMN.2021.2849


Download: MMN-2849