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  "body": "\n## Statement\n\n**Axiom h1. *Boundary condition**\n\n*h*(0, 0, ..., 0) = 0 and *h*(1, 1, ..., 1) = one\n\n**Axiom h2. *Monotonicity**\n\nFor any pair \\\u003c*a*\u003csub\u003e1\u003c/sub\u003e, *a*\u003csub\u003e2\u003c/sub\u003e, ..., *a*\u003csub\u003e*n*\u003c/sub\u003e\u003e and \\\u003c*b*\u003csub\u003e1\u003c/sub\u003e, *b*\u003csub\u003e2\u003c/sub\u003e, ..., *b*\u003csub\u003e*n*\u003c/sub\u003e\u003e of *n*-tuples such that *a*\u003csub\u003e*i*\u003c/sub\u003e, *b*\u003csub\u003e*i*\u003c/sub\u003e ∈ \\[0,1\\] for all *i* ∈ *N*\u003csub\u003e*n*\u003c/sub\u003e, if *a*\u003csub\u003e*i*\u003c/sub\u003e ≤ *b*\u003csub\u003e*i*\u003c/sub\u003e for all *i* ∈ *N*\u003csub\u003e*n*\u003c/sub\u003e, then *h*(*a*\u003csub\u003e1\u003c/sub\u003e, *a*\u003csub\u003e2\u003c/sub\u003e, ...,*a*\u003csub\u003e*n*\u003c/sub\u003e) ≤ *h*(*b*\u003csub\u003e1\u003c/sub\u003e, *b*\u003csub\u003e2\u003c/sub\u003e, ..., *b*\u003csub\u003e*n*\u003c/sub\u003e); that is, *h* is monotonic increasing in all its arguments.\n\n**Axiom h3. *Continuity**\n\n*h* is a continuous function.\n",
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        "locator": "Fuzzy set operations, section Aggregation operations \u003e Axioms for aggregation operations fuzzy sets",
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