Fuzzy real algebra: Some results |
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Authors: | Didier Dubois Henri Prade |
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Affiliation: | School of Electrical Engineering, Purdue University, West Lafayette, IN 47905, U.S.A.;Stanford Artificial Intelligence Lab., Stanford University, 94305, U.S.A. |
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Abstract: | In this paper, the possibility to perform easily most of the extended n-ary operations on fuzzy subsets of the real line is shown. A general algorithm is given. These results are particularized for usual operations such as addition, subtraction, multiplication, division, ‘max’ and ‘min’ operations for normalized convex fuzzy subsets of the real line, i.e. fuzzy numbers. A three parameters representation for fuzzy numbers is shown to be very convenient to perform usual operations. Lastly, interpretative comments about fuzzy real algebra are given and possible applications pointed out. |
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Keywords: | Fuzzy numbers Extension principle Fuzzy tolerance analysis |
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