Fuzzy rule

<h2 id="comparison-between-boolean-and-fuzzy-logic-rules">Comparison between Boolean and fuzzy logic rules</h2>
As an example, consider a rule used to control a three-speed fan. A binary IF-THEN statement may be then

IF temperature 
 
 
 
 ≥
 
 
 {\displaystyle \geq }
 
 30
THEN fan speed is 3
The disadvantage of this rule is that it uses a strict temperature as a threshold, but the user may want the fan to still function at this speed when temperature = 29.9. A fuzzy IF-THEN statement may be

IF temperature is hot
THEN fan speed is fast
where hot and fast are described using <a href="/facts/Fuzzy_set/BGWudHJq">fuzzy sets</a>.

<h2 id="fuzzy-rule-connectors">Fuzzy rule connectors</h2>
Rules can connect multiple variables through <a href="/facts/Fuzzy_set_operations/I5HFju1C">fuzzy set operations</a> using <a href="/facts/T-norm/oYR3JgIy">t-norms</a> and <a href="/facts/T-norm/oYR3JgIy">t-conorms</a>.
T-norms are used as an AND connector.<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a><a class="footnote-ref" id="fnref:6" href="#fn:6">6</a><a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> For example,

IF temperature is hot AND humidity is high
THEN fan speed is fast
The degree of truth assigned to temperature is hot and to humidity is high. The result of a t-norm operation on these two degrees is used as the degree of truth that fan speed is fast.
T-conorms are used as an OR connector.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a> For example,

IF temperature is hot OR humidity is high
THEN fan speed is fast
The result of a t-conorm operation on these two degrees is used as the degree of truth that fan speed is fast.
The <a href="/facts/Complement_(set_theory)/yWUePIYY">complement</a> of a fuzzy set is used as a negator.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> For example,

IF temperature is NOT hot
THEN fan speed is slow
The fuzzy set not hot is the complement of hot. The degree of truth assigned to temperature is not hot is used as the degree of truth that fan speed is slow.
T-conorms are less commonly used as rules can be represented by AND and OR connectors exclusively.

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Fuzzy_logic/1PvN4Att">Fuzzy logic</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn: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) <a href="978-0122384523" target="_blank">978-0122384523</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">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. <a href="978-0130409690" target="_blank">978-0130409690</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">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. <a href="978-0130409690" target="_blank">978-0130409690</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">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. <a href="978-0130409690" target="_blank">978-0130409690</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Martin Larsen, P. (1980). "Industrial applications of fuzzy logic control". International Journal of Man-Machine Studies. 12 (1): 3–10. doi:10.1016/s0020-7373(80)80050-2. ISSN 0020-7373. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Mamdani, E.H. (1974). "Application of fuzzy algorithms for control of simple dynamic plant". Proceedings of the Institution of Electrical Engineers. 121 (12): 1585. doi:10.1049/piee.1974.0328. ISSN 0020-3270. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">H.-J., Zimmermann (1991). Fuzzy Set Theory - and Its Applications (Second, revised ed.). Dordrecht: Springer Netherlands. ISBN 9789401579490. OCLC 851369348. <a href="9789401579490" target="_blank">9789401579490</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">H.-J., Zimmermann (1991). Fuzzy Set Theory - and Its Applications (Second, revised ed.). Dordrecht: Springer Netherlands. ISBN 9789401579490. OCLC 851369348. <a href="9789401579490" target="_blank">9789401579490</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">H.-J., Zimmermann (1991). Fuzzy Set Theory - and Its Applications (Second, revised ed.). Dordrecht: Springer Netherlands. ISBN 9789401579490. OCLC 851369348. <a href="9789401579490" target="_blank">9789401579490</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
</ol>

Fuzzy rule open-in-new

Fuzzy rule