Axioms for aggregation operations fuzzy sets

Statement

*Axiom h1. Boundary condition

h(0, 0, ..., 0) = 0 and h(1, 1, ..., 1) = one

*Axiom h2. Monotonicity

For any pair <a₁, a₂, ..., a_n> and <b₁, b₂, ..., b_n> of n-tuples such that a_i, b_i ∈ [0,1] for all i ∈ N_n, if a_i ≤ b_i for all i ∈ N_n, then h(a₁, a₂, ...,a_n) ≤ h(b₁, b₂, ..., b_n); that is, h is monotonic increasing in all its arguments.

*Axiom h3. Continuity

h is a continuous function.