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  "body": "\n## Statement\n\n**Axiom i1. *Boundary condition**\n\n*i*(*a*, 1) = *a*\n\n**Axiom i2. *Monotonicity**\n\n*b* ≤ *d* implies *i*(*a*, *b*) ≤ *i*(*a*, *d*)\n\n**Axiom i3. *Commutativity**\n\n*i*(*a*, *b*) = *i*(*b*, *a*)\n\n**Axiom i4. *Associativity**\n\n*i*(*a*, *i*(*b*, *d*)) = *i*(*i*(*a*, *b*), *d*)\n\n**Axiom i5. *Continuity**\n\n*i* is a continuous function\n\n**Axiom i6. *Subidempotency**\n\n*i*(*a*, *a*) \\\u003c *a* for all 0 \\\u003c *a* \\\u003c 1\n\n**Axiom i7. *Strict monotonicity**\n\n*i* (*a*\u003csub\u003e1\u003c/sub\u003e, *b*\u003csub\u003e1\u003c/sub\u003e) \\\u003c *i* (*a*\u003csub\u003e2\u003c/sub\u003e, *b*\u003csub\u003e2\u003c/sub\u003e) if *a*\u003csub\u003e1\u003c/sub\u003e \\\u003c *a*\u003csub\u003e2\u003c/sub\u003e and *b*\u003csub\u003e1\u003c/sub\u003e \\\u003c *b*\u003csub\u003e2\u003c/sub\u003e\n\nAxioms i1 up to i4 define a **t-norm** (a.k.a. **fuzzy intersection**). The standard t-norm min is the only idempotent t-norm (that is, *i* (*a*\u003csub\u003e1\u003c/sub\u003e, *a*\u003csub\u003e1\u003c/sub\u003e) = *a* for all *a* ∈ \\[0,1\\]).\n",
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        "locator": "Fuzzy set operations, section Fuzzy intersections \u003e Axioms for fuzzy intersection",
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