PROCEEDINGS ARTICLE | December 30, 2003
Proc. SPIE. 5200, Applications and Science of Neural Networks, Fuzzy Systems, and Evolutionary Computation VI
KEYWORDS: Superposition, Diffraction, Holography, Logic, Transparency, Medical diagnostics, Data processing, Artificial intelligence, Fuzzy logic, Standards development
In this paper we consider linguistic model as an algebraic model and restrict our consideration to the semantics only. The concept allows “natural-like” language to be used by human-teacher to describe for machine the way of the problem solving, which is based on human’s knowledge and experience. Such imprecision words as “big”, “very big”, “not very big”, etc can be used for human’s knowledge representation. Technically, the problem is to match metric scale, used by the technical device, with the linguistic scale, intuitively formed by the person. We develop an algebraic description of 4-f Fourier-holography setup by using triangular norms based approach. In the model we use the Fourier-duality of the t-norms and t-conorms, which is implemented by 4-f Fourier-holography setup. We demonstrate the setup is described adequately by De-Morgan’s law for involution. Fourier-duality of the t-norms and t-conorms leads to fuzzy-valued logic. We consider General Modus Ponens rule implementation to define the semantical operators, which are adequate to the setup. We consider scales, formed in both +1 and -1 orders of diffraction. We use representation of linguistic labels by fuzzy numbers to form the scale and discuss the dependence of the scale grading on the holographic recording medium operator. To implement reasoning with multi-parametric input variable we use Lorentz function to approximate linguistic labels. We use an example of medical diagnostics for experimental illustration of reasoning on the linguistic scale.
