Implicative filters of equality algebras treated as fuzzy points

Abstract

The notion of fuzzy points is used to study implicative filters in equality algebras. The concept of implicative (∈, ∈)-fuzzy filters is introduced, and its properties are investigated. The relationship between (∈, ∈)-fuzzy filters, implicative (∈, ∈)-fuzzy filters and positive implicative (∈, ∈)-fuzzy filters are established. Characterizations of implicative (∈, ∈)-fuzzy filters are discussed, and the conditions for the (positive implicative) (∈, ∈)-fuzzy filter to be an implicative (∈, ∈)-fuzzy filter are explored. The extension property for the implicative (∈, ∈)fuzzy filter is established. The properties associated with ∈t set and qt-set of a fuzzy set Ψ in E and also look for conditions under which they can become implicative filters are examined.