Interval valued (∈, ∈∨q)-fuzzy filters in MTL-algebras
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In the present paper, the interval valued (∈, ∈∨q)-fuzzy filter theory in MTL-algebras is further studied. Some new concepts of interval valued (∈, ∈∨q)-fuzzy prime, ultra, regular, strong and divisible filters are introduced and their properties and equivalent characterizations are investigated. Relationships among the above new concepts and interval valued (∈, ∈∨q)-fuzzy Boolean, MV- and G-filters are discussed. It is proved that an interval valued (∈, ∈∨q)-fuzzy filter is an interval valued (∈, ∈∨q)-fuzzy MV-filter if and only if it is both an interval valued (∈, ∈∨q)-fuzzy regular filter and an interval valued (∈, ∈∨q)-fuzzy divisible filter.
Abstract
In the present paper, the interval valued (∈, ∈∨q)-fuzzy filter theory in MTL-algebras is further studied. Some new concepts of interval valued (∈, ∈∨q)-fuzzy prime, ultra, regular, strong and divisible filters are introduced and their properties and equivalent characterizations are investigated. Relationships among the above new concepts and interval valued (∈, ∈∨q)-fuzzy Boolean, MV- and G-filters are discussed. It is proved that an interval valued (∈, ∈∨q)-fuzzy filter is an interval valued (∈, ∈∨q)-fuzzy MV-filter if and only if it is both an interval valued (∈, ∈∨q)-fuzzy regular filter and an interval valued (∈, ∈∨q)-fuzzy divisible filter.
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