Fuzzy Flip-Flops and Fuzzy Memory Elements

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Fuzzy Flip-Flopsand Fuzzy Memory Elements
Dr Shinichi Yoshida, Research Associate T.I.T.
NOC Hirota Lab (??)
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Why fuzzy memory?
Fuzzy combinatorial circuit (Logic operator or
inference)

Fuzzy memory
Q(t1)f(I(t))
I(t)
Q(t1)
Yamakawa 80, Olivieri 96 Togai 86, Watanabe 93
Fuzzy sequential circuit
Q(t1) f(I(t),Q(t))
I(t)
Q(t1)
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JK fuzzy flip-flop
Many functions
Widely used as memory

• Theoretical Research
• Hirota 1989, Mori 1993, GniewekKluska 1998
• Implementation and Applications
• Ozawa 1989, Diamond 1994, Pedrycz 1995, Zhang
  1997

Problems in fuzzy logic
e.g. membership registers
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D, T, SR-FFF
JK-FFFcircuit area and delay time ?Large
Problem
More reasonable but fewer functions D, T, SR-FFF
(Yoshida, 2000)
(T fuzzy memory cell, Virant, Zimic, 1999)
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Flip-flops(FF)
Binary memory elements
D-FF
T-FF
Q(t1)D(t)
T(t1)T(t)Q(t)T(t)Q(t)
JK-FF
SR-FF
Q(t1)J(t)Q(t)K(t)Q(t)
Q(t1)S(t)R(t)Q(t)
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Characteristics of FFFs

• T-FFF maxterm and minterm

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Characteristics of SR-FFF
Set
Reset
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Circuit implementation 1
T-FFF algebraic
T-FFF Max-Min
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Circuit implementation 2
T-FFF drastic
T-FFF bounded
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FFFs delay time
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FFFs circuit resources
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Set type SR-FFF 136 Eqs.
((t), ? is omitted)
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Relations of set-type SR FFF
136 types of set-type SR-FFF
Distributed lattice (136 elements)
Boolean lattice
Boolean lattice
Least ambiguity
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Hasse Diagram of Set-type FFF
Order of ambiguity
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Reset type SR-FFF 136 Eqs.
( (t), ? is omitted)
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Hasse diagram of reset-type FFF
Order of ambiguity
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Logical Property
Boolean lattice
D, T (and JK) FFFs
SR FFF (Also D, T, JK)
Distributive lattice
Max,Min composition of 2 different FFFs
FFF
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Representation of FFFs
All fuzzy flip-flops are represented as ...
Boolean lattice
Join of Atoms
D-FFF 2 atoms T-FFF 1 atom JK-FFF 6 atoms
Distributive lattice
Join of join-irreducible elements
SR-FFF ?
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Recent Research

• ½ Problem and its logical condition
• Implementation of various fuzzy operations on
  FPGA and their performance comparison