Journal
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
Volume 53, Issue 5, Pages 805-836Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ijar.2012.02.001
Keywords
Fuzzy number; Trapezoidal fuzzy number; Approximation; Ambiguity
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Funding
- Romanian National Authority for Scientific Research, CNCS-UEFISCDI [PN-II-ID-PCE-2011-3-0861]
- Sectoral Operational Programme for Human Resources Development
- European Social Fund [POSDRU/107/1.5/S/76841]
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The ambiguity was introduced to simplify the task of representing and handling of fuzzy numbers. We find the nearest real interval, nearest triangular (symmetric) fuzzy number, nearest trapezoidal (symmetric) fuzzy number of a fuzzy number, with respect to average Euclidean distance, preserving the ambiguity. A simpler and elementary method, to avoid the Karush-Kuhn-Tucker theorem and the laborious calculus associated with it and to prove the continuity is used. We give algorithms for calculus and several examples.The approximations are discussed in relation to data aggregation. (C) 2012 Elsevier Inc. All rights reserved.
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