Abstract

Fuzzy-logic inference engines are in use in various disciplines such as control systems, medicine, and the like. The use of optical tools to implement such engines may improve the performance and the flexibility of inference procedures. The optical processor works in a two-dimensional environment, whereas the inference engine might have to handle more than two independent input channels. Here several approaches to generating the first, to our knowledge, N-dimensional optical fuzzy processor are addressed. The first approach uses space multiplexing, the second approach uses polarization multiplexing, and the third approach uses wavelength multiplexing to increase the dimension of the processor.

© 2000 Optical Society of America

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References

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  1. P. J. King, E. H. Mamdani, “The application of fuzzy control systems to industrial processes,” Automatica 13, 235–242 (1977).
    [CrossRef]
  2. K. Saito, H. Hashimoto, M. Echigo, A. Uchiyama, “A fatty liver diagnosis support system using fuzzy theory,” Trans. Inst. Electron. Eng. Jpn. Sect. C 115, 127–132 (1995).
  3. P. Ramaswamy, R. M. Edwards, K. Y. Lee, “An automatic tuning method of a fuzzy logic controller for nuclear reactors,” IEEE Trans. Nucl. Sci. 40, 1253–1262 (1994).
  4. L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1965).
    [CrossRef]
  5. M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 9, pp. 133–135; Chap. 10, pp. 159–176.
  6. E. Gur, D. Mendlovic, Z. Zalevsky, “Optical implementation of fuzzy-logic controllers: part I,” Appl. Opt. 37, 6937–6945 (1998).
    [CrossRef]
  7. W. Pritzik, Fuzzy Control and Fuzzy Systems, 2nd extended ed. (Research Studies Press, Wiley, New York, 1993), Chap. 6, pp. 157–176.
  8. J. W. Goodman, Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, New York, 1996), Chap. 7, p. 207.

1998 (1)

1995 (1)

K. Saito, H. Hashimoto, M. Echigo, A. Uchiyama, “A fatty liver diagnosis support system using fuzzy theory,” Trans. Inst. Electron. Eng. Jpn. Sect. C 115, 127–132 (1995).

1994 (1)

P. Ramaswamy, R. M. Edwards, K. Y. Lee, “An automatic tuning method of a fuzzy logic controller for nuclear reactors,” IEEE Trans. Nucl. Sci. 40, 1253–1262 (1994).

1977 (1)

P. J. King, E. H. Mamdani, “The application of fuzzy control systems to industrial processes,” Automatica 13, 235–242 (1977).
[CrossRef]

1965 (1)

L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1965).
[CrossRef]

Chew, G.

M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 9, pp. 133–135; Chap. 10, pp. 159–176.

Echigo, M.

K. Saito, H. Hashimoto, M. Echigo, A. Uchiyama, “A fatty liver diagnosis support system using fuzzy theory,” Trans. Inst. Electron. Eng. Jpn. Sect. C 115, 127–132 (1995).

Edwards, R. M.

P. Ramaswamy, R. M. Edwards, K. Y. Lee, “An automatic tuning method of a fuzzy logic controller for nuclear reactors,” IEEE Trans. Nucl. Sci. 40, 1253–1262 (1994).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, New York, 1996), Chap. 7, p. 207.

Gur, E.

Hashimoto, H.

K. Saito, H. Hashimoto, M. Echigo, A. Uchiyama, “A fatty liver diagnosis support system using fuzzy theory,” Trans. Inst. Electron. Eng. Jpn. Sect. C 115, 127–132 (1995).

Kandel, A.

M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 9, pp. 133–135; Chap. 10, pp. 159–176.

King, P. J.

P. J. King, E. H. Mamdani, “The application of fuzzy control systems to industrial processes,” Automatica 13, 235–242 (1977).
[CrossRef]

Langholz, G.

M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 9, pp. 133–135; Chap. 10, pp. 159–176.

Lee, K. Y.

P. Ramaswamy, R. M. Edwards, K. Y. Lee, “An automatic tuning method of a fuzzy logic controller for nuclear reactors,” IEEE Trans. Nucl. Sci. 40, 1253–1262 (1994).

Mamdani, E. H.

P. J. King, E. H. Mamdani, “The application of fuzzy control systems to industrial processes,” Automatica 13, 235–242 (1977).
[CrossRef]

Mendlovic, D.

Pritzik, W.

W. Pritzik, Fuzzy Control and Fuzzy Systems, 2nd extended ed. (Research Studies Press, Wiley, New York, 1993), Chap. 6, pp. 157–176.

Ramaswamy, P.

P. Ramaswamy, R. M. Edwards, K. Y. Lee, “An automatic tuning method of a fuzzy logic controller for nuclear reactors,” IEEE Trans. Nucl. Sci. 40, 1253–1262 (1994).

Saito, K.

K. Saito, H. Hashimoto, M. Echigo, A. Uchiyama, “A fatty liver diagnosis support system using fuzzy theory,” Trans. Inst. Electron. Eng. Jpn. Sect. C 115, 127–132 (1995).

Schneider, M.

M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 9, pp. 133–135; Chap. 10, pp. 159–176.

Uchiyama, A.

K. Saito, H. Hashimoto, M. Echigo, A. Uchiyama, “A fatty liver diagnosis support system using fuzzy theory,” Trans. Inst. Electron. Eng. Jpn. Sect. C 115, 127–132 (1995).

Zadeh, L. A.

L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1965).
[CrossRef]

Zalevsky, Z.

Appl. Opt. (1)

Automatica (1)

P. J. King, E. H. Mamdani, “The application of fuzzy control systems to industrial processes,” Automatica 13, 235–242 (1977).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

P. Ramaswamy, R. M. Edwards, K. Y. Lee, “An automatic tuning method of a fuzzy logic controller for nuclear reactors,” IEEE Trans. Nucl. Sci. 40, 1253–1262 (1994).

Inf. Control (1)

L. A. Zadeh, “Fuzzy sets,” Inf. Control 8, 338–353 (1965).
[CrossRef]

Trans. Inst. Electron. Eng. Jpn. Sect. C (1)

K. Saito, H. Hashimoto, M. Echigo, A. Uchiyama, “A fatty liver diagnosis support system using fuzzy theory,” Trans. Inst. Electron. Eng. Jpn. Sect. C 115, 127–132 (1995).

Other (3)

M. Schneider, A. Kandel, G. Langholz, G. Chew, Fuzzy Expert System Tools (Wiley, New York, 1996), Chap. 9, pp. 133–135; Chap. 10, pp. 159–176.

W. Pritzik, Fuzzy Control and Fuzzy Systems, 2nd extended ed. (Research Studies Press, Wiley, New York, 1993), Chap. 6, pp. 157–176.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, New York, 1996), Chap. 7, p. 207.

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Figures (7)

Fig. 1
Fig. 1

Fuzzy inference engine. The inputs pass through four stages (left to right: fuzzification, inference engine, defuzzification, and application of a combination rule) before output is established.

Fig. 2
Fig. 2

2-D optical fuzzy inference engine. I 1, I 2, inputs; O 1, output.

Fig. 3
Fig. 3

5 × 5 criteria rule matrix for a four-input inference engine. The 2-D matrix on the left-hand side contains 2-D 5 × 5 submatrices. Each block indicated by R (rule table) contains a 5 × 5 rule table as given on the right-hand side. NL, negative large; NS, negative small; Z, zero; PS, positive small; PL, positive large.

Fig. 4
Fig. 4

2-D optical fuzzy inference engine for four input channels. I 1, I 2, I 3, I 4, inputs; O 1 output. Note that the first two AOD’s are imaged onto the plane of the final two.

Fig. 5
Fig. 5

Rotating plate with grating for choosing active wavelength from a polychromatic light source. The entire setup is given in (a) and the wavelength discriminator in (b).

Fig. 6
Fig. 6

Spectral response of a typical PSD. If the controller uses wavelengths beneath the peak value (900 nm), then increasing the wavelength will increase the response, whereas use of the higher wavelengths results in the opposite characteristics.

Fig. 7
Fig. 7

Four-input optical inference engine, with two 2-D channels. Each channel propagates with a different polarization, and thus interaction between the channels is prevented.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

T(x, y)=exp-ik2f (x2+y2)expiknΔ0,
U(x0, y0)=expikziλzexpik2z(x-x0)2+(y-y0)2U(x, y)dxd,
knδ=2πm,
δ=mλ,
upx=uxexpiαx.
Upη=upxexp-i2πxvdx=Uv-a2π,
PTE=Ptotal coxθ, PTM=Ptotal sinθ,P=power, θ = rotation angle.

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