Abstract
The notion of interval-valued fuzzy sets was first introduced by Zadeh in 1975 as a generalization of fuzzy sets. Using the concept of interval-valued fuzzy sets, we introduce a new kind of generalized fuzzy subalgebra of a K-algebra called, an interval-valued ( α , β ) -fuzzy subalgebra. We present some interesting properties of an interval-valued ( α , β ) -fuzzy subalgebra of a K-algebra. Some characterization theorems of the interval-valued ( ∈ , ∈ ∨ q ) -fuzzy subalgebra are established. Next we investigate the properties of interval-valued fuzzy subalgebras with thresholds. Finally we present characterization theorems of implication based interval-valued fuzzy subalgebras.
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