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  "body": "\n## Statement\n\n**Axiom c1. *Boundary condition**\n\n*c*(0) = 1 and *c*(1) = 0\n\n**Axiom c2. *Monotonicity**\n\nFor all *a*, *b* ∈ \\[0, 1\\], if *a* \\\u003c *b*, then *c*(*a*) \u003e *c*(*b*)\n\n**Axiom c3. *Continuity**\n\n*c* is continuous function.\n\n**Axiom c4. *Involutions**\n\n*c* is an involution, which means that *c*(*c*(*a*)) = *a* for each *a* ∈ \\[0,1\\]\n\n*c* is a *strong negator* (a.k.a. *fuzzy complement*).\n\nA function c satisfying axioms c1 and c3 has at least one fixpoint a\u003csup\u003e\\*\u003c/sup\u003e with c(a\u003csup\u003e\\*\u003c/sup\u003e) = a\u003csup\u003e\\*\u003c/sup\u003e, and if axiom c2 is fulfilled as well there is exactly one such fixpoint. For the standard negator c(x) = 1-x the unique fixpoint is a\u003csup\u003e\\*\u003c/sup\u003e = 0.5 .\n",
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        "locator": "Fuzzy set operations, section Fuzzy complements \u003e Axioms for fuzzy complements",
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