FRACTAL GEOMETRY: A TOOL FOR FUZZY REASONING |
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| Authors: | MIROSLAV PUNČOCHÁŘ JIŘÍ DRAHOŠ |
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| Affiliation: | Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic , Prague 6, 16502, Czech Republic |
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| Abstract: | Abstract A new procedure for construction of a fuzzy number is given, based on the covering of points by consequently contracting intervals. The approach leads to the membership function in the form of Devil's staircase, a borderline fractal finding many applications in the modern physics. The alternative definition of subsethood based on the self-similarity of the sets is also given. |
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| Keywords: | Cantor discontinuum Devil's staircase geometry of fuzzy sets membership function self-similarity fuzzy subsethood |
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