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Fuzzy rule
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<p>Fuzzy rules are used within <a href="/facts/Fuzzy_logic/1PvN4Att">fuzzy logic systems</a> to infer an output based on input variables. <a href="/facts/Modus_ponens/Wq4NcmrG">Modus ponens</a> and <a href="/facts/Modus_tollens/sqf3PTlf">modus tollens</a> are the most important rules of inference. A modus ponens rule is in the form </p> Premise: <i>x is A</i> Implication: <i>IF x is A THEN y is B</i> Consequent: <i>y is B</i> <p>In crisp logic, the premise <i>x is A</i> can only be true or false. However, in a fuzzy rule, the premise <i>x is A</i> and the consequent <i>y is B</i> can be true to a degree, instead of entirely true or entirely false. This is achieved by representing the linguistic variables <i>A</i> and <i>B</i> using <a href="/facts/Fuzzy_set/BGWudHJq">fuzzy sets</a>. In a fuzzy rule, modus ponens is extended to <i>generalised modus ponens:.</i> </p> Premise: <i>x is A</i>* Implication: <i>IF x is A THEN y is B</i> Consequent: <i>y is B</i>* <p>The key difference is that the premise <i>x is A</i> can be only partially true. As a result, the consequent <i>y is B</i> is also partially true. Truth is represented as a <a href="/facts/Real_number/R02gw5Pb">real number</a> between 0 and 1, where 0 is false and 1 is true. </p>