Truncated pi-functions in Approximation of Multi-shaped Polygons

TL;DRAbstract

The studies of data, which result in sampled information in the form of finite fuzzy sets, give rise to the creation of polygons consisting of finite numbers of points tied together. Since the polygons are not formalized by some mathematical expressions, it would be desirable to find continuous functions approximating them rather thoroughly in spite of their irregular shapes. An approximation by the standard curves is sometimes too rough to be a reliable source of a further analysis of the polygons. To improve the accuracy of approximating we test a continuous function, which is composed of joined pi-class functions with seven parameters. The function, called by us “the sampled, truncated pi”, is very sensitive for each little deviation in the polygon’s shape, which allows us to classify it exactly without large errors usually accompanying a process of standard approximation.

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