Title: Estimation of the fuzzy variance by different approximations of the fuzzy product
Authors: Redina Berkachy - Applied Statistics And Modelling, University of Fribourg (Switzerland) [presenting]
Laurent Donze - University of Fribourg (Switzerland)
Abstract: Fuzzy statistical methods appear to be well suited to situations where the data we are collecting are exposed to fuzziness and uncertainty. Calculating for instance analytically or numerically the fuzzy variance could be advantageous. Yet, this task is not simple, especially regarding the difficulties in measuring the multiplication of two fuzzy sets. These computational problems are not evident to overcome. Therefore, an approximation of this product is needed. In the aim of computing the fuzzy variance, we propose different approximations of this product including the one using a particular method called the signed distance. However, using some of our approximations, another computational complexity arises since we get non-positive fuzzy numbers due to the difference between two fuzzy sets. This implies a result given by a fuzzy number violating the principles of the n-uples notations. In order to solve this problem, we use the shifting (translation) techniques. In addition, we give a comparison between these approximations in the purpose of displaying their characteristics. Finally, we illustrate our approach by numerical examples. We highlight that one should be prudent when choosing an estimation of the fuzzy variance.