Construction of fuzzy logic by optical techniques

Alexander V. Pavlov

doi:10.1117/12.373661

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29 December 1999 Construction of fuzzy logic by optical techniques

Alexander V. Pavlov

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Proceedings Volume 4016, Photonics, Devices, and Systems; (1999) https://doi.org/10.1117/12.373661
Event: Photonics Prague '99, 1999, Prague, Czech Republic

Abstract

Our main interest is to establish connections between Optics and Fuzzy Set Theory. We formulate the t-norms based algebraic description of both geometrical and Fourier- approximations of optics. Geometrical optics implements probabilistic operators under the linear approximation of negative recording process. For real recording media not Zadeh's, but Sugeno negation is more appropriate approximation. It gives dual to the product t-norm family of t-conforms, parameterized by the recording medium and developing process properties. Fourier-optics allows Fourier-duality to be used in addition to N-duality. Fourier-holography setup implements semiring with product t- norm and F-dual family of t-conorms - sum-product convolutions, parameterized by holographic recording medium operator. Implication operator, implemented by Fourier- holography technique, is defined. Experimental realization of General Modus Ponenes rule by holographic fuzzy interference engine is presented.

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Alexander V. Pavlov "Construction of fuzzy logic by optical techniques", Proc. SPIE 4016, Photonics, Devices, and Systems, (29 December 1999); https://doi.org/10.1117/12.373661

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