fismatpc.ps

a collection of M-files to study concepts in the following areas of Fuzzy-Set-Theory: Fuzzy or Multi

1939 y(\\liaison")i(op)q(erator)e(AND.)g(The)h(consequen)o(t)g(v)o(ector)f
Fl(Y)26 b Fn(comprises)16 b(of)g Fl(k)g Fn(linguistic)300 1996
y(v)m(ariables.)33 b(There)19 b(is)h(no)f(relationship)i(b)q(et)o(w)o(een)e
(this)h(linguistic)i(v)m(ariable)e Fl(y)1689 2003 y Fk(j)1727
1996 y Fn(and)300 2052 y(the)e(other)h(linguistic)h(v)m(ariables)g
Fl(y)915 2059 y Fk(l)928 2052 y Fn(,)f Fl(l)g Fi(6)p Fn(=)f
Fl(j)s Fn(.)29 b(Therefore)18 b(suc)o(h)h(an)f(inference)i(migh)o(t)300
2109 y(b)q(e)f(decomp)q(osed)g(in)o(to)g Fl(k)g Fn(inference)h(with)e(an)o
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2165 y(linguistic)k(v)m(ariable)f Fl(y)698 2172 y Fk(j)716
2165 y Fn(,)g Fl(j)i Fn(=)d(1)p Fl(;)8 b Fn(2)p Fl(;)g(:::;)f(k)19
b Fn(separately)l(.)36 b(Therefore)20 b(without)h(loss)f(of)300
2222 y(generalit)o(y)e(w)o(e)e(can)h(assume)g(that)f(the)h(consequen)o(t)h
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Fl(k)14 b Fn(=)f(1.)371 2334 y(F)l(or)j(making)i(an)g(inference)h(\\Y)e(is)h
Fi(B)1029 2318 y Ff(0)1041 2334 y Fn(")f(from)g(set)g(of)h(rules)g
Fl(P)24 b Fn(and)18 b(observ)m(ation)300 2391 y Fl(Q)p Fn(,)13
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(Max-Min,)f(Max-Pro)q(duct)h(,)f(ha)o(v)o(e)h(b)q(een)h(sho)o(wn.)p
eop
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445 y Fn(,)f(n)o(umer-)300 502 y(ous)h(metho)q(ds)f(for)g(defuzzi\014cation)j
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671 y(the)j(output)g(fuzzy)g(v)m(alues,)i(the)e(global)h(cen)o(troid)f(can)g
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Fn(In)22 b(this)f(part)g(of)f(rep)q(ort,)i(at)e(\014rst)h(the)g(terminology)g
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b(Alw)o(a)o(ys)19 b(matrices)g(expressed)h(b)o(y)f Fl(A)g Fn(or)f
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Fn(,)f Fl(A)1632 1110 y Fj(2)1652 1103 y Fn(,..\))30 b(are)300
1160 y(matrices)16 b(of)f(mem)o(b)q(ership)i(function)f(suc)o(h)g(that)f(eac)
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Fn(\(can)15 b(b)q(e)h Fl(U)792 1336 y Fj(1)812 1329 y Fn(,)e
Fl(U)870 1336 y Fj(2)890 1329 y Fn(,..\))19 b(for)14 b Fl(A)i
Fn(and)f Fl(V)25 b Fn(for)14 b Fl(B)r Fn(.)300 1386 y Fc(Example)e(1:)18
b Fn(Consider)13 b(a)f(pro)q(duction)h(rule)g(with)f(4)g(rules,)h(2)f(inputs)
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1499 y(follo)o(ws;)686 1555 y Fl(U)5 b Fn(1)12 b(=)h([0)f(:)g
Fl(:)p Fn(1)g(:)h(1])686 1612 y Fl(U)5 b Fn(2)12 b(=)h([10)f(:)g(4)g(:)h(30])
686 1668 y Fl(V)22 b Fn(=)13 b([)p Fi(\000)p Fn(3)f(:)h(1)f(:)g(3])300
1724 y(The)i(matrices)f(of)g(mem)o(b)q(ership)h(v)m(alue)h
Fl(A)1025 1731 y Fj(1)1045 1724 y Fn(,)e Fl(A)1105 1731 y Fj(2)1138
1724 y Fn(and)h Fl(B)i Fn(o)o(v)o(er)c(the)i(univ)o(erse)g(of)f
Fl(U)1703 1731 y Fj(1)1723 1724 y Fn(,)g Fl(U)1780 1731 y Fj(2)300
1781 y Fn(and)i Fl(V)25 b Fn(are)15 b(matrices)g(of)g(4)g Fi(\002)g
Fn(11)g(and)g(4)g Fi(\002)h Fn(6)f(and)g(4)g Fi(\002)g Fn(7.)566
1966 y Fl(A)p Fn(1)e(=)684 1844 y Fb(2)684 1917 y(6)684 1942
y(6)684 1967 y(6)684 1993 y(4)732 1881 y Fn(0)41 b(0)g(0)h
Fl(:)p Fn(1)f Fl(:)p Fn(3)f Fl(:)p Fn(6)h Fl(:)p Fn(9)47 b(1)54
b(1)g(1)48 b(1)732 1937 y(1)41 b(1)g(1)h Fl(:)p Fn(8)f Fl(:)p
Fn(6)f Fl(:)p Fn(4)h Fl(:)p Fn(2)47 b(0)54 b(0)g(0)48 b(0)732
1994 y(0)41 b(0)g(0)h Fl(:)p Fn(1)f Fl(:)p Fn(5)f Fl(:)p Fn(9)48
b(1)f Fl(:)p Fn(9)41 b Fl(:)p Fn(5)g Fl(:)p Fn(1)g(0)732 2050
y(0)g(0)g(0)h Fl(:)p Fn(1)f Fl(:)p Fn(5)f Fl(:)p Fn(9)48 b(1)f
Fl(:)p Fn(9)41 b Fl(:)p Fn(5)g Fl(:)p Fn(1)g(0)1506 1844 y
Fb(3)1506 1917 y(7)1506 1942 y(7)1506 1967 y(7)1506 1993 y(5)746
2227 y Fl(A)p Fn(2)12 b(=)863 2105 y Fb(2)863 2178 y(6)863
2203 y(6)863 2228 y(6)863 2255 y(4)911 2142 y Fn(0)48 b(0)g
Fl(:)p Fn(5)40 b Fl(:)p Fn(9)48 b(1)f(1)911 2199 y(0)42 b Fl(:)p
Fn(4)47 b(1)54 b(1)47 b Fl(:)p Fn(4)41 b(0)911 2255 y(0)h Fl(:)p
Fn(6)47 b(1)g Fl(:)p Fn(6)h(0)f(0)911 2311 y(1)h(1)g Fl(:)p
Fn(5)40 b Fl(:)p Fn(2)48 b(0)f(0)1327 2105 y Fb(3)1327 2178
y(7)1327 2203 y(7)1327 2228 y(7)1327 2255 y(5)p eop
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bop 717 574 a Fl(B)16 b Fn(=)815 452 y Fb(2)815 525 y(6)815
550 y(6)815 575 y(6)815 601 y(4)863 489 y Fn(0)41 b Fl(:)p
Fn(2)g Fl(:)p Fn(4)g Fl(:)p Fn(6)g Fl(:)p Fn(8)47 b(1)h(1)863
545 y(0)g(0)f Fl(:)p Fn(4)g(1)54 b(1)48 b Fl(:)p Fn(4)41 b(0)863
602 y(0)48 b(0)f Fl(:)p Fn(7)g(1)h Fl(:)p Fn(7)f(0)h(0)863
658 y(1)g(1)53 b(1)48 b Fl(:)p Fn(6)41 b Fl(:)p Fn(3)47 b(0)h(0)1355
452 y Fb(3)1355 525 y(7)1355 550 y(7)1355 575 y(7)1355 601
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900 y(terminology)j(used)g(is)f Fl(A)756 907 y Fk(p)799 900
y Fn(\(can)g(b)q(e)h Fl(A)p Fn(1)1033 907 y Fk(p)1053 900 y
Fn(,)g Fl(A)p Fn(2)1146 907 y Fj(2)1166 900 y Fn(,...\))40
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b(i)p 788 590 V 17 w(rule4.m)30 b([11])449 b(reasdemo.m)325
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b([25])357 b(turksen.m)30 b([13])13 b([14])325 1155 y(grademf.m)29
b([26])14 b([27])49 b(moreless.m)30 b([12])409 b(union.m)31
b([12])325 1211 y(imply)l(.m)g([6])210 b(not.m)29 b([12])511
b(v)o(ery)l(.m)45 b([12])325 1268 y(impldemo.m)204 b(quan)o(tize.m)512
b(zadeh.m)30 b([12])14 b([28])g([3])g([18])889 1480 y Fm(References)292
1597 y Fn([1])21 b(S.)13 b(Y)l(asunobu)g(&)g(S.)f(Miy)o(amoto,)f
Fa(Automatic)h(T)l(rain)h(Op)q(eration)g(System)f(b)o(y)h(Pre-)362
1653 y(dictiv)o(e)i(F)l(uzzy)f(Con)o(trol)r Fn(,)e(Elsevier)i(Science)h
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2280 y([6])21 b(M.)e(Mizumoto,)g(\\F)l(uzzy)h(con)o(trol)f(under)h(v)m
(arious)g(reasoning)g(metho)q(d,")f Fa(Infor-)362 2337 y(mation)c(Sciences)d
Fn(45)7 b(\(1988\),)13 b(129{151.)292 2406 y([7])21 b(P)l(.)d(J.)f(P)o(acini)
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o(king,")362 2462 y Fa(In)o(telligen)o(t)g(Systems