Abstract
The concepts of interval-valued ∈,∈∨κ∗˜,qκ˜-fuzzy subalgebras, interval-valued ∈,∈∨κ∗˜,qκ˜-fuzzy ideals, and interval-valued ∈∨κ∗˜,qκ˜,∈∨κ∗˜,qκ˜-fuzzy ideals are introduced, and related properties are studied. Many examples are given in support of these new notions. Furthermore, interval-valued ∈,∈∨κ∗˜,qκ˜-fuzzy commutative ideals are defined, and some important properties are discussed. For a BCK-algebra X, it is proved that every interval-valued ∈,∈∨κ∗˜,qκ˜-fuzzy commutative ideal of BCK-algebra X is an interval-valued ∈,∈∨κ∗˜,qκ˜-fuzzy ideal of X, but the converse need not be true, in general, and then a counterexample is constructed.