Fuzzy Subalgebras with Thresholds in Q-algebras

The concept of a fuzzy subalgebra with thresholds of Q-algebra is introduced, and some related properties are obtained. The relations between a fuzzy subalgebra with thresholds of Q-algebra and an(∈,∈∨q)-fuzzy subalgebra of Q-algebra are provided. The notion of t-implication-based fuzzy subalgebra of Q-algebra is also introduced, and the relations between fuzzy subalgebra with thresholds of Q-algebras and 0.5-implication–based fuzzy subalgebra of Q-algebra based respectively on Gaines-Rescher implication operator, Godel implication operator and the contraposition of Godel implication operator are discussed.