A New Distance Measure for Trapezoidal Fuzzy Numbers

Abstract EN

We propose a new distance measure for the space ofall trapezoidal fuzzy numbers using centroid point and left/rightspread of trapezoidal fuzzy numbers.

Moreover, the metricproperties of suggested distance measure are investigated.

Indeed,we show that for two arbitrary trapezoidal fuzzy numbers if thedistance between centroid points and also the distance between leftspreads and right spreads go to zero, then two given fuzzy numbersare equal.

Consequently, we complete discussion about therelation between fuzzy number and its centroid which is the firstlydiscussed by Hadi-Vencheh and Allame (2010).

To the best of our knowledge, this is first time in the literature that such metric is applied by centroid point.