# A Simple Example for Fuzzy Logic

Erol (erol@pipeline.com)
Mon, 22 Dec 1997 18:35:05 +0100 (MET)

Hi,

On my web site I'll have simple examples for Computer Graphics, Artificial
Intelligence, Computer Games, etc. too.

Erol

begin 666 introduction_to_fuzzy_logic.htm
M/&AT;6P^#0H-"CQH96%D/@T*/'1I=&QE/E5S:6YG(\$9U>GIY(\$QO9VEC('1O
M(\$UA:6YT86EN(&\$@0V]M9F]R=&%B;&4@4F]O;2!496UP97)A='5R93PO=&ET
M;&4^#0H\;65T82!N86UE/2)'14Y%4D%43U(B(&-O;G1E;G0](DUI8W)O<V]F
M="!&<F]N=%!A9V4@,RXP(CX-"@T*/&UE=&\$@:'1T<"UE<75I=CTB4&%G92U%
M>&ET(B!C;VYT96YT/2)R979E86Q4<F%N<RA\$=7)A=&EO;CTQ+%1R86YS:71I
M;VX],3(I(CX-"@T*/&UE=&\$@;F%M93TB36EC<F]S;V9T(%1H96UE(B!C;VYT
M96YT/2)N;VYE(CX\+VAE860^#0H-"CQB;V1Y(&)G8V]L;W(](B,P,# P,# B
M('1E>'0](B-&1D9&1D8B/@T*/&9O;G0@<VEZ93TB-"(^#0H-"CQP(&%L:6=N
M/2)#14Y415(B/CPO9F]N=#X\9F]N="!S:7IE/2(U(CX\(2TM=V5B8F]T(&)O
M=#TB3F%V:6=A=&EO;B(@<RUT>7!E/2)B86YN97(B(',M<F5N9&5R:6YG/2)G
M<F%P:&EC<R(@<RUO<FEE;G1A=&EO;B!B+6EN8VQU9&4M:&]M92!B+6EN8VQU
M9&4M=7 @<W1A<G1S<&%N("TM/D\$@4VEM<&QE(\$5X86UP;&4\(2TM=V5B8F]T
M(&)O=#TB3F%V:6=A=&EO;B(@96YD<W!A;B!I+6-H96-K<W5M/2(U,S V,R(@
M+2T^/"]F;VYT/CQF;VYT(&9A8V4](DUA<FEG;VQD(CX\8CX\+W ^#0H-"CQP
M(&%L:6=N/2)#14Y415(B/CPO9F]N=#X\9F]N="!F86-E/2)-87)I9V]L9"(@
M<VEZ93TB-2(^)FYB<W [/"]P/@T*#0H\<#X\+V9O;G0^/&9O;G0@<VEZ93TB
M,B(^)FYB<W [/"]P/@T*#0H\<"!A;&EG;CTB;&5F="(^4')O8FQE;2!\$969I
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M:&5A="!S;&EG:'1L>2!O<B!M86ME(&ET(&\$@;&]T#0IW87)M97(L(&5T8RXI
M+B \+W ^#0H-"CQP/CQB/B9N8G-P.SPO<#X-"@T*/' @86QI9VX](FQE9G0B
M/DUE=&AO9#H\+V(^/"]P/@T*#0H\8FQO8VMQ=6]T93X-"B @/&)L;V-K<75O
M=&4^#0H@(" @/&9O;G0@<VEZ93TB,B(^/&9O;G0@<VEZ93TB,B(^/&9O;G0@
M<VEZ93TB,B(^/&9O;G0@<VEZ93TB,B(^/&9O;G0@<VEZ93TB,B(^/&9O;G0@
M<VEZ93TB,B(^/' @86QI9VX](FQE9G0B/FDN(\$-O;G-T<G5C="!T:&4@;65M
M8F5R<VAI<"!F=6YC=&EO;G,@9F]R(&EN<'5T('9A<FEA8FQE<SH@/&(^=&5M
M<#PO8CXL(#QB/FAU;6ED/"]B/@T*(" @(#PO<#X-"B @(" \9F]N="!S:7IE
M/2(R(CX\9F]N="!S:7IE/2(R(CX\9F]N="!S:7IE/2(R(CX\9F]N="!S:7IE
M/2(R(CX\9F]N="!S:7IE/2(R(CX\<"!A;&EG;CTB;&5F="(^:6DN#0H@(" @
M0V]N<W1R=6-T('1H92!M96UB97)S:&EP(&9U;F-T:6]N<R!F;W(@;W5T<'5T
M('9A<FEA8FQE.B \8CYD/"]P/@T*(" @(#PO8CX\<"!A;&EG;CTB;&5F="(^
M:6EI+B!#;VYS=')U8W0@=&AE(&-O;G1R;VP@<G5L97,@*#QB/D9!33PO8CX@
M+3QU/D8\+W4^=7IZ>2 \=3Y!/"]U/G-S;V-I871I=F4-"B @(" \=3Y-/"]U
M/F5M;W)Y+2 \8CYT86)L93PO8CXI/"]P/@T*(" @(#QP(&%L:6=N/2)L969T
M(CYI=BX@0V]N9'5C="!T:&4@<VEM=6QA=&EO;CPO<#X-"B @(" \<"!A;&EG
M;CTB;&5F="(^)FYB<W [)FYB<W [)FYB<W [)FYB<W [)FYB<W [)FYB<W [
M)FYB<W [(&DN(%)E8V5I=F4@=&AE(&-R:7-P(&1A=&\$@9G)O;0T*(" @('1H
M92!S96YS;W)S/"]P/@T*(" @(#QP(&%L:6=N/2)L969T(CXF;F)S<#LF;F)S
M<#LF;F)S<#LF;F)S<#LF;F)S<#LF;F)S<#LF;F)S<#L@:6DN(\$9U>GII9GD@
M=&AE(&-R:7-P(&1A=&\$@<V\-"B @("!T:&%T(&ET(&-A;B!B92!E=F%L=6%T
M960\+W ^#0H@(" @/' @86QI9VX](FQE9G0B/B9N8G-P.R9N8G-P.R9N8G-P
M.R9N8G-P.R9N8G-P.R9N8G-P.R9N8G-P.R!I:6DN(\$%P<&QY('1H92!A<'!R
M;W!R:6%T90T*(" @(')U;&5S(&%N9"!D971E<FUI;F4@=&AE(&]U='!U=#PO
M<#X-"B @(" \<"!A;&EG;CTB;&5F="(^)FYB<W [)FYB<W [)FYB<W [)FYB
M<W [)FYB<W [)FYB<W [)FYB<W [(&EV+B!\$969U>GII9GD@=&AE(&]U='!U
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M/F%N9#QB/B!H=6UI9#PO8CXN(\$EN<'5T('9A<FEA8FQE(#QB/G1E;7 @/"]B
M/F1E;F]T97,@=&AE(')O;VT-"B @("!T96UP97)A='5R92!A;F0@/&(^:'5M
M:60\+V(^)FYB<W [(&1E;F]T97,@=&AE(&-U<G)E;G0@:'5M:61I='D@;&5V
M96PN(\$D@=VEL;"!U<V4@;7D@;W=N#0H@(" @)W1A<W1E)R!T;R!P;&]T('1H
M92!G<F%P:"X@5F5R=&EC86P@87AI<R!I<R \9F]N="!F86-E/2)3>6UB;VPB
M/FT\+V9O;G0^(&%N9"!T:&4-"B @("!H;W)I>F]N=&%L(&%X:7,@:7,@/&(^
M=&5M<#PO8CXN(\$EN('1H92!S96-O;F0@9W)A<&@@=F5R=&EC86P@87AI<R!I
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M(C(B/CQP(&%L:6=N/2)L969T(CY(97)E(\$D@:&%V92!U<V5D('1H92!F;VQL
M;W=I;F<@;&%B96QS.B \=3YV/"]U/F5R>2 \=3YD<GD\+W4^+ T*(" \=3YD
M<GD\+W4^+" \=3YS/"]U/F]M97=H870@/'4^:'5M:60\+W4^+" \=3YH=6UI
M9#PO=3XL(#QU/G8\+W4^97)Y(#QU/FAU;6ED/"]U/BP@/'4^93PO=3YX=')E
M;65L>0T*(" \=3YH=6UI9#PO=3XN(\$EN('1H92!F:7)S="!G<F%P:" \=3YV
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M969T(CY(97)E(\$D@:&%V92!U<V5D('1H92!F;VQL;W=I;F<@;&%B96QS.B!.
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M=3Y60CPO=3XL(#QU/E \+W4^;W-I=&EV90T*(" \=3Y%0CPO=3XN(\$9O<B!S
M;VUE(')E87-O;B!T:&4@<V]F='=A<F4@9&ED(&YO="!P<FEN="!T:&4@;&%B
M96P@4\$5".B!T:&ES(&ES('1H92!L87-T(&QI;F4-"B @9G)O;2!T:&4@;&5F
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M<F1E<CTB,2(@8V5L;'-P86-I;F<](C\$B(&-E;&QP861D:6YG/2(W(B!W:61T
M:#TB-3DP(CX-"B @(" \='(^#0H@(" @(" \=&0@=VED=&@](C\$T)2(@=F%L
M:6=N/2)43U B/CQF;VYT('-I>F4](C(B/CQB/CQP(&%L:6=N/2)224=(5"(^
M2'5M:60\+W ^#0H@(" @(" \<#Y496UP/"]B/CPO9F]N=#X\+W1D/@T*(" @
M(" @/'1D('=I9'1H/2(Q-"4B('9A;&EG;CTB5\$]0(CX\9F]N="!S:7IE/2(R
M(CX\:3YV9')Y/"]I/CPO9F]N=#X\+W1D/@T*(" @(" @/'1D('=I9'1H/2(Q
M-"4B('9A;&EG;CTB5\$]0(CX\9F]N="!S:7IE/2(R(CX\:3YD<GD\+VD^/"]F
M;VYT/CPO=&0^#0H@(" @(" \=&0@=VED=&@](C\$T)2(@=F%L:6=N/2)43U B
M/CQF;VYT('-I>F4](C(B/CQI/G-H=6UI9#PO:3X\+V9O;G0^/"]T9#X-"B @
M(" @(#QT9"!W:61T:#TB,30E(B!V86QI9VX](E1/4"(^/&9O;G0@<VEZ93TB
M,B(^/&D^:'5M:60\+VD^/"]F;VYT/CPO=&0^#0H@(" @(" \=&0@=VED=&@]
M(C\$T)2(@=F%L:6=N/2)43U B/CQF;VYT('-I>F4](C(B/CQI/G9H=6UI9#PO
M:3X\+V9O;G0^/"]T9#X-"B @(" @(#QT9"!W:61T:#TB,30E(B!V86QI9VX]
M(E1/4"(^/&9O;G0@<VEZ93TB,B(^/&D^96AU;6ED/"]I/CPO9F]N=#X\+W1D
M/@T*(" @(#PO='(^#0H@(" @/'1R/@T*(" @(" @/'1D('=I9'1H/2(Q-"4B
M('9A;&EG;CTB5\$]0(CX\9F]N="!S:7IE/2(R(CX\:3Y#;VQD/"]I/CPO9F]N
M=#X\+W1D/@T*(" @(" @/'1D('=I9'1H/2(Q-"4B('9A;&EG;CTB5\$]0(CX\
M9F]N="!S:7IE/2(R(CX\<"!A;&EG;CTB0T5.5\$52(CY04SPO9F]N=#X\+W1D
M/@T*(" @(" @/'1D('=I9'1H/2(Q-"4B('9A;&EG;CTB5\$]0(CX\9F]N="!S
M:7IE/2(R(CX\<"!A;&EG;CTB0T5.5\$52(CY0/"]F;VYT/CPO=&0^#0H@(" @
M(" \=&0@=VED=&@](C\$T)2(@=F%L:6=N/2)43U B/CQF;VYT('-I>F4](C(B
M/CQP(&%L:6=N/2)#14Y415(B/E \+V9O;G0^/"]T9#X-"B @(" @(#QT9"!W
M:61T:#TB,30E(B!V86QI9VX](E1/4"(^/&9O;G0@<VEZ93TB,B(^/' @86QI
M9VX](D-%3E1%4B(^4\$(\+V9O;G0^/"]T9#X-"B @(" @(#QT9"!W:61T:#TB
M,30E(B!V86QI9VX](E1/4"(^/&9O;G0@<VEZ93TB,B(^/' @86QI9VX](D-%
M3E1%4B(^4%9"/"]F;VYT/CPO=&0^#0H@(" @(" \=&0@=VED=&@](C\$T)2(@
M=F%L:6=N/2)43U B/CQF;VYT('-I>F4](C(B/CQP(&%L:6=N/2)#14Y415(B
M/E!60CPO9F]N=#X\+W1D/@T*(" @(#PO='(^#0H@(" @/'1R/@T*(" @(" @
M/'1D('=I9'1H/2(Q-"4B('9A;&EG;CTB5\$]0(CX\9F]N="!S:7IE/2(R(CX\
M:3Y#;V]L/"]I/CPO9F]N=#X\+W1D/@T*(" @(" @/'1D('=I9'1H/2(Q-"4B
M('9A;&EG;CTB5\$]0(CX\9F]N="!S:7IE/2(R(CX\<"!A;&EG;CTB0T5.5\$52
M(CY05E,\+V9O;G0^/"]T9#X-"B @(" @(#QT9"!W:61T:#TB,30E(B!V86QI
M9VX](E1/4"(^/&9O;G0@<VEZ93TB,B(^/' @86QI9VX](D-%3E1%4B(^4%93
M/"]F;VYT/CPO=&0^#0H@(" @(" \=&0@=VED=&@](C\$T)2(@=F%L:6=N/2)4
M3U B/CQF;VYT('-I>F4](C(B/CQP(&%L:6=N/2)#14Y415(B/E!3/"]F;VYT
M/CPO=&0^#0H@(" @(" \=&0@=VED=&@](C\$T)2(@=F%L:6=N/2)43U B/CQF
M;VYT('-I>F4](C(B/CQP(&%L:6=N/2)#14Y415(B/E!3/"]F;VYT/CPO=&0^
M#0H@(" @(" \=&0@=VED=&@](C\$T)2(@=F%L:6=N/2)43U B/CQF;VYT('-I
M>F4](C(B/CQP(&%L:6=N/2)#14Y415(B/E \+V9O;G0^/"]T9#X-"B @(" @
M(#QT9"!W:61T:#TB,30E(B!V86QI9VX](E1/4"(^/&9O;G0@<VEZ93TB,B(^
M/' @86QI9VX](D-%3E1%4B(^4#PO9F]N=#X\+W1D/@T*(" @(#PO='(^#0H@
M(" @/'1R/@T*(" @(" @/'1D('=I9'1H/2(Q-"4B('9A;&EG;CTB5\$]0(CX\
M9F]N="!S:7IE/2(R(CX\:3Y787)M/"]I/CPO9F]N=#X\+W1D/@T*(" @(" @
M/'1D('=I9'1H/2(Q-"4B('9A;&EG;CTB5\$]0(CX\9F]N="!S:7IE/2(R(CX\
M<"!A;&EG;CTB0T5.5\$52(CY.4SPO9F]N=#X\+W1D/@T*(" @(" @/'1D('=I
M9'1H/2(Q-"4B('9A;&EG;CTB5\$]0(CX\9F]N="!S:7IE/2(R(CX\<"!A;&EG
M;CTB0T5.5\$52(CY.4SPO9F]N=#X\+W1D/@T*(" @(" @/'1D('=I9'1H/2(Q
M-"4B('9A;&EG;CTB5\$]0(CX\9F]N="!S:7IE/2(R(CX\<"!A;&EG;CTB0T5.
M5\$52(CY./"]F;VYT/CPO=&0^#0H@(" @(" \=&0@=VED=&@](C\$T)2(@=F%L
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M+W1D/@T*(" @(" @/'1D('=I9'1H/2(Q-"4B('9A;&EG;CTB5\$]0(CX\9F]N
M="!S:7IE/2(R(CX\<"!A;&EG;CTB0T5.5\$52(CY.4SPO9F]N=#X\+W1D/@T*
M(" @(" @/'1D('=I9'1H/2(Q-"4B('9A;&EG;CTB5\$]0(CX\9F]N="!S:7IE
M/2(R(CX\<"!A;&EG;CTB0T5.5\$52(CY.4SPO9F]N=#X\+W1D/@T*(" @(" @
M/'1D('=I9'1H/2(Q-"4B('9A;&EG;CTB5\$]0(CX\9F]N="!S:7IE/2(R(CX\
M<"!A;&EG;CTB0T5.5\$52(CY./"]F;VYT/CPO=&0^#0H@(" @(" \=&0@=VED
M=&@](C\$T)2(@=F%L:6=N/2)43U B/CQF;VYT('-I>F4](C(B/CQP(&%L:6=N
M/2)#14Y415(B/DY"/"]F;VYT/CPO=&0^#0H@(" @(" \=&0@=VED=&@](C\$T
M)2(@=F%L:6=N/2)43U B/CQF;VYT('-I>F4](C(B/CQP(&%L:6=N/2)#14Y4
M15(B/DY60CPO9F]N=#X\+W1D/@T*(" @(" @/'1D('=I9'1H/2(Q-"4B('9A
M;&EG;CTB5\$]0(CX\9F]N="!S:7IE/2(R(CX\<"!A;&EG;CTB0T5.5\$52(CY.
M5D(\+V9O;G0^/"]T9#X-"B @(" \+W1R/@T*(" \+W1A8FQE/@T*(" \9F]N
M="!S:7IE/2(R(CX\<#XF;F)S<#L\+W ^#0H@(#QP/B9N8G-P.SPO<#X-"B @
M/&QI/CQP(&%L:6=N/2)L969T(CY,970G<R!C;VYD=6-T(&\$@<VEM=6QA=&EO
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M*#QB/FAU;6ED/"]B/B ](&AU;6ED*2!42\$5.("@\8CYD/"]B/B ](\$Y"*0T*
M(" @(&UI;B@P+C<U+# N-2D@/2 P+C4H3D(I(#PO<#X-"B @(" \<"!A;&EG
M;CTB;&5F="(^248@*#QB/G1E;7 \+V(^(#T@:&]T*2!!3D0@*#QB/FAU;6ED
M(#PO8CX]('9H=6UI9"D@5\$A%3B H/&(^9" \+V(^/2!.5D(I#0H@(" @;6EN
M*# N-S4L,"XU*2 ](# N-2A.5D(I(#PO<#X-"B @(" \<"!A;&EG;CTB;&5F
M="(^248H/&(^=&5M<#PO8CX@/2!W87)M*2!!3D0@*#QB/FAU;6ED/"]B/B ]
M(&AU;6ED*2!42\$5.("@\8CYD/"]B/B ](\$XI#0H@(" @;6EN*# N,C4L,"XU
M*2 ](# N,C4H3BD\+W ^#0H@(" @/' @86QI9VX](FQE9G0B/DE&("@\8CYT
M96UP/"]B/B ]('=A<FTI(\$%.1" H/&(^:'5M:60\+V(^(#T@=FAU;6ED*2!4
M2\$5.("@\8CYD/"]B/B ](\$Y"*0T*(" @(&UI;B@P+C(U+# N-2D@/2 P+C(U
M*\$Y"*3PO<#X-"B @(" \<"!A;&EG;CTB;&5F="(^)FYB<W [/"]P/@T*(" @
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M;65M8F5R<VAI<"!I;B!.*29N8G-P.R9N8G-P.R O)FYB<W [(%1O=&%L(\$UE
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M,"(^3&]O:VEN9R!F;W(@80T*:&5A9&5R(&9I;&4L('!A;#\@/&\$@:')E9CTB
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':'1M;#X-"@``
`
end