• Oleg Uzhga Rebrov Rezekne Academy of Technologies (LV)
  • Galina Kuleshova Dept. of Modelling and Simulation, Riga Technical University (LV)




fuzzy median, fuzzy median of absolute deviations from the fuzzy median, fuzzy random variable, random variable


A random variable is a variable whose components are random values. To characterise a random variable, the arithmetic mean is widely used as an estimate of the location parameter, and variation as an estimate of the scale parameter. The disadvantage of the arithmetic mean is that it is sensitive to extreme values, outliers in the data. Due to that, to characterise random variables, robust estimates of the location and scale parameters are widely used: the median and median absolute deviation from the median. In real situations, the components of a random variable cannot always be estimated in a deterministic way. One way to model the initial data uncertainty is to use fuzzy estimates of the components of a random variable. Such variables are called fuzzy random variables. In this paper, we examine fuzzy robust estimates of location and scale parameters of a fuzzy random variable: fuzzy median and fuzzy median of the deviations of fuzzy component values from the fuzzy median.



Download data is not yet available.


F. R. Hampel, E.M. Ronchetti, P. J. Rousseeuwand W. A. Stahel, Linear Networks and Systems. New York, John Wiley&Sons, 1986.

P. J. Huber. Robust Statistics. New York, John Wiley&Sons, 1981.

O.Uzhga-Rebrov, Managing Uncertainties. Part 2. Modern Methods of Probabilistic Reasoning, Rezekne, RA Izdevniecība, 2007. Ужга-Ребров О. И. Управление неопределённостями. Часть 2. Современные методы вероятностного вывода. Rēzekne, RA izdevniecība, 2007.

H. Kwakernaak,“Fuzzy Random Variables – I. Definitions and Theorems”, Information Sciences, 15, 1978, pp. 1 – 29.

H. Kwakernaak, “Fuzzy Random Variables –II. Definitions and Examples for the Discrete Case”, Information Sciences, 17, pp. 253-278, 1979.

M. L. Puri. and D. A. Ralescu ,“Fuzzy random variables”, J. Math. Anal. Appl., 114,pp. 409 – 422, 1986.

A. F. Shapiro, Implementing Fuzzy Random Variables – Some Preliminary Observations. ARC Proceedings, August 1-4, 2012.

A. Colubi, R. Coppi, P. D′Urso and M. A. Gil, “Statistics with fuzzy random variables”. METRON – International Journal of Statistics,Vol. LXV, No. 3, pp. 277 – 303, 2007.

R. Coppi, M. A. Gil and H.A.L. Kiers, “The fuzzy approach to statistical analysis”,Computational Statistics & Data Analysis. Vol. 51, Issue 1, pp. 1 – 14, 2006.

P. D′Urso and M. A. Gil,”Fuzzy Statistical Analysis: Methods and Applications”,METRON, 71, pp. 197-199, 2013.

M.A. Gil, M. López-Díaz and D.A. Ralescu, “Overview of the Development of Fuzzy Random Variables”.Fuzzy Sets and Systems, 157, (19), pp. 2546 – 2557, 2005.

B. Sinova, M.R. Casalsand M.A. Gil,” Central tendency for symmetric random fuzzy numbers”, Information Sciences, 278, pp. 599 – 613, 2014.

B. Sinova, M. A. Gil, A.Colubi, and S. van Aelst. “The median of random fuzzy number. The 1-norm distance approach”. Fuzzy Sets and Systems, 200, 2012, pp. 99 – 115.

I. Couso, S. Montes and P.Gil,“The necessity of the strong -cuts of a fuzzy sets”, Int. Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 9, No. 2, pp. 249 – 262. 2001.




How to Cite

O. Uzhga Rebrov and G. Kuleshova, “FUZZY ROBUST ESTIMATES OF LOCATION AND SCALE PARAMETERS OF A FUZZY RANDOM VARIABLE”, ETR, vol. 2, pp. 181–186, Jun. 2021, doi: 10.17770/etr2021vol2.6566.