A generalization of \((\in, \in \vee q)\)-fuzzy subgroups

Abstract

More general form of quasi-coincident with' relation \((q)\) is introduced, and related properties are investigated. The notions of \((\in, \in\vee, q^{\delta}_0)\)-fuzzy subgroups, \(q^{\delta}_0\)-level sets and \(\in\vee, q^{\delta}_0\)-level sets are introduced, and related results are investigated. Relations between an \((\in, \in)\)-fuzzy subgroup and an \((\in, \in\vee, q^{\delta}_0)\)-fuzzy subgroup are discussed, and characterizations of \((\in, \in\vee, q^{\delta}_0)\)-fuzzy subgroups are displayed by using level sets and \(\in\vee, q^{\delta}_0\)-level sets. The concepts of \(\in\vee, q^{\delta}_0\)-admissible fuzzy sets, admissible \((\in, \in\vee, q^{\delta}_0)\)-fuzzy subgroups and \(\delta\)-characteristic fuzzy sets are introduced. Using these notions, characterizations of admissible \((\in,\in\vee, q^{\delta}_0)\)-fuzzy subgroups and admissible subgroups are considered.