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Fuzzy Logic with Engineering Applications, 4th Edition by Timothy J. Ross

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10Fuzzy Classification and Pattern Recognition

From causes which appear similar, we expect similar effects. This is the sum total of all our experimental conclusions.

David Hume, Scottish philosopher, Enquiry Concerning Human Understanding, 1748

There is structure in nature. Much of this structure is known to us and is quite beautiful. Consider the natural sphericity of rain drops and bubbles; why do balloons take this shape? How about the elegant beauty of crystals, rhombic solids with rectangular, pentagonal, or hexagonal cross sections? Why do these naturally beautiful, geometric shapes exist? What causes the natural repetition of the mounds of sand dunes? Some phenomena we cannot see directly; for example, the elliptical shape of the magnetic field around the earth, or we can see only when certain atmospheric conditions exist, such as the beautiful and circular appearance of a rainbow or the repetitive patterns of the aurora borealis in the night sky near the North Pole. Some patterns, such as the helical appearance of DNA or the cylindrical shape of some bacteria, have only appeared to us since the advent of extremely powerful electron microscopes. Consider the geometry and colorful patterns of a butterfly’s wings; why do these patterns exist in our physical world? The answers to some of these questions are still unknown; many others have been discovered through increased understanding of physics, chemistry, and biology.

Just as there is structure in nature, we believe ...

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