---
tag: EVTA3EP9AC
kind: statement
role: proposition
name: Axioms for aggregation operations fuzzy sets
sources:
- wikipedia: en:1651811@r1360435730
locator: Fuzzy set operations, section Aggregation operations > Axioms for aggregation operations fuzzy sets
note: adopted
mention: wikipedia://en/1651811#W676
sections: [Statement]
inventory: [Z8XVWK0TV6]
---
## Statement
**Axiom h1. *Boundary condition**
*h*(0, 0, ..., 0) = 0 and *h*(1, 1, ..., 1) = one
**Axiom h2. *Monotonicity**
For any pair \<*a*1, *a*2, ..., *a**n*> and \<*b*1, *b*2, ..., *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*(*a*1, *a*2, ...,*a**n*) ≤ *h*(*b*1, *b*2, ..., *b**n*); that is, *h* is monotonic increasing in all its arguments.
**Axiom h3. *Continuity**
*h* is a continuous function.