A study of generalized roughness in $(\in ,\in \vee qk)$-fuzzy filters of ordered semigroups

Abstract

Concept of generalized rough approximations for fuzzy filters in ordered semigroups is introduced. Then this idea is extended to rough approximations of fuzzy bi-filters and fuzzy quasi-filters in ordered semigroups. $\left ( \in ,\in \vee q\right )$-fuzzy filters are a generalization of fuzzy filters and these can be further generalized by $\left ( \in ,\in \vee qk\right )$-fuzzy filters. Generalized roughness has been studied for both $\left ( \in ,\in \vee q\right )$ and $\left ( \in ,\in \vee qk\right )$-fuzzy filters of ordered semigroups.

Keywords

• Fuzzy sets
• Rough sets
• Approximation of fuzzy filters and their generalization
• Approximation of (∈, ∈ ∨q) and (∈, ∈ ∨qk)-fuzzy filters and their generalization