Fuzzy rule

Fuzzy rules are used within fuzzy logic systems to infer an output based on input variables. Modus ponens and modus tollens are the most important rules of inference.[1] A modus ponens rule is in the form

Premise: x is A
Implication: IF x is A THEN y is B
Consequent: y is B

In crisp logic, the premise x is A can only be true or false. However, in a fuzzy rule, the premise x is A and the consequent y is B can be true to a degree, instead of entirely true or entirely false.[2] This is achieved by representing the linguistic variables A and B using fuzzy sets.[2] In a fuzzy rule, modus ponens is extended to generalised modus ponens:.[2]

Premise: x is A*
Implication: IF x is A THEN y is B
Consequent: y is B*

The key difference is that the premise x is A can be only partially true. As a result, the consequent y is B is also partially true. Truth is represented as a real number between 0 and 1, where 0 is false and 1 is true.

  1. ^ B., Enderton, Herbert (2001). A mathematical introduction to logic (2nd ed.). San Diego, Calif.: Academic Press. ISBN 978-0122384523. OCLC 45830890.{{cite book}}: CS1 maint: multiple names: authors list (link)
  2. ^ a b c Mendel, Jerry M. (2001). Uncertain rule-based fuzzy logic systems : introduction and new directions. Upper Saddle River, NJ: Prentice Hall PTR. ISBN 978-0130409690. OCLC 45314121.