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

Manuel Marin, David Defour, Federico Milano
DALI and Universite Montpellier 2, LIRMM, France
hal-01140485, (8 April 2015)

   title={An efficient midpoint-radius representation format to deal with symmetric fuzzy numbers},

   author={Marin, Manuel and Defour, David and Milano, Federico},


   school={DALI-UPVD/LIRMM, UCD}


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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 alpha-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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