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Selection of α for α-Hull and formulation of fuzzy α-Hull in Ir2

A decade ago, Edelsbrunner et. al. introduced the concept of α-hulls for finding the shape of a planar set. But it still suffers from a major deficiency i.e., the single parameter α must be fine-tuned. The present article initially proposes a selection criterion of α for α-hulls in R2. Then the concept of α-hulls is extended to define the fuzzy α-hulls. The effectiveness of the fuzzy α-hulls and the proposed selection criterion of α is demonstrated on some artificially generated data sets. The convergence (with sample size) of both the crisp and fuzzy α-hulls, based on the proposed selection criterion of α, to the original pattern class has also been verified.