An efficient midpoint-radius representation format to deal with symmetric fuzzy numbers

Manuel Marin 1, 2 David Defour 1 Federico Milano 2
1 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : This paper proposes a novel representation for symmetric fuzzy numbers that uses the midpoint-radius approach instead of the conventional lower-upper representation. A theoretical analysis based on the α-cut concept shows that the proposed format requires half the amount of operations and memory than the traditional one. Also, a novel technique involving radius increments is introduced, to mitigate floating-point rounding errors when using the proposed representation. We describe the implementation of all these features into a fuzzy arithmetic library, specifically tuned to run on Graphic Processing Units (GPU). The results of a series of tests using compute-bound and memory-bound benchmarks, show that the proposed format provides a performance gain of two to twenty over the traditional one. Finally, several implementation issues regarding GPU are discussed in light of these results.
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Manuel Marin, David Defour, Federico Milano. An efficient midpoint-radius representation format to deal with symmetric fuzzy numbers. [Research Report] DALI - UPVD/LIRMM, UCD. 2015. ⟨hal-01140485⟩

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