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Fuzzy Flip-Flops and Fuzzy Memory Elements

Fuzzy Flip-Flops and Fuzzy Memory Elements. Dr Shinichi Yoshida, Research Associate T.I.T. NOC & Hirota Lab 　（助手）. Why fuzzy memory?. Fuzzy combinatorial circuit （ Logic operator or inference ）. ＋. Fuzzy memory. I(t). Q(t+1)=f(I(t)). Q(t+1). Yamakawa 80, Olivieri 96

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Fuzzy Flip-Flops and Fuzzy Memory Elements

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  1. Fuzzy Flip-Flopsand Fuzzy Memory Elements Dr Shinichi Yoshida, Research Associate T.I.T. NOC & Hirota Lab　（助手）

  2. Why fuzzy memory? Fuzzy combinatorial circuit （Logic operator or inference） ＋ Fuzzy memory I(t) Q(t+1)=f(I(t)) Q(t+1) Yamakawa 80, Olivieri 96 Togai 86, Watanabe 93 Fuzzy sequential circuit Q(t+1) =f(I(t),Q(t)) I(t) Q(t+1)

  3. JK fuzzy flip-flop • Theoretical Research • Hirota 1989, Mori 1993, Gniewek・Kluska 1998 • Implementation and Applications • Ozawa 1989, Diamond 1994, Pedrycz 1995, Zhang 1997 Many functions Widely used as memory Problems in fuzzy logic e.g. membership registers

  4. D, T, SR-FFF JK-FFF：circuit area and delay time ⇒Large Problem More reasonable but fewer functions D, T, SR-FFF (Yoshida, 2000) (“T fuzzy memory cell”, Virant, Zimic, 1999)

  5. Flip-flops（ＦＦ） Binary memory elements • ・D-FF • ・T-FF Q(t+1)=D(t) T(t+1)=T(t)Q(t)+T(t)Q(t) • ・SR-FF • ・JK-FF Q(t+1)=J(t)Q(t)+K(t)Q(t) Q(t+1)=S(t)+R(t)Q(t)

  6. Characteristics of FFFs • T-FFF maxterm and minterm

  7. Characteristics of SR-FFF Set Reset

  8. Circuit implementation 1 T-FFF algebraic T-FFF Max-Min

  9. Circuit implementation 2 T-FFF drastic T-FFF bounded

  10. FFFs delay time

  11. FFFs circuit resources

  12. Set type SR-FFF 136 Eqs. ((t), ∧ is omitted)

  13. 3 7 2 2 Relations of set-type SR FFF 136 types of set-type SR-FFF Distributed lattice (136 elements) Boolean lattice Boolean lattice Least ambiguity

  14. Hasse Diagram of Set-type FFF Order of ambiguity

  15. Reset type SR-FFF 136 Eqs. ( (t), ∧ is omitted)

  16. Hasse diagram of reset-type FFF Order of ambiguity

  17. Logical Property D, T (and JK) FFFs Boolean lattice SR FFF (Also D, T, JK) Distributive lattice Max,Min composition of 2 different FFFs FFF

  18. 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: ?

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

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