Fuzzy (m, n)-filters based on fuzzy points in ordered semigroups

Abstract

In this paper, by generalizing the notions of \((\in ,\in \vee q)\)-fuzzy bi-filters, \((\in ,\in \vee q)\)-fuzzy left filters and \((\in ,\in \vee q)\)-fuzzy right filters, the notions of \((\in ,\in \vee q)\)-fuzzy (m, n)-filters, \((\in ,\in \vee q)\)-fuzzy left m-filters and \((\in ,\in \vee q)\)-fuzzy right n-filters of the ordered semigroups are introduced. We prove that \((\in ,\in \vee q)\)-fuzzy bi-filters and \((\in ,\in \vee q)\)-fuzzy left (resp. right) filters are \((\in ,\in \vee q)\)-fuzzy (m, n)-filters and \((\in ,\in \vee q)\)-fuzzy left (resp. right n) m-filters but the converse statement does not hold and in this support an example is provided. Also, we provide certain conditions under which these notions coincide. Furthermore, we present the characterizations and equivalent condition of \((\in ,\in \vee q)\)-fuzzy (m, n)-filters. Moreover, the associated properties of \((\in ,\in \vee q)\)-fuzzy (m, n)-filters and fuzzy prime generalized \((\in ,\in \vee q)\)-fuzzy (m, n)-ideals are considered.

Keywords: characterizations. fuzzy. generalizing. converse.