Central tendency for symmetric random fuzzy numbers

Abstract

Random fuzzy numbers are becoming a valuable tool to model and handle fuzzyvalued data generated through a random process. Recent studies have been devoted to introduce measures of the central tendency of random fuzzy numbers showing a more robust behaviour than the so-called Aumann-type mean value. This paper aims to deepen in the (rather comparative) analysis of these centrality measures and the Aumann-type mean by examining the situation of symmetric random fuzzy numbers. Similarities and differences with the real-valued case are pointed out and theoretical conclusions are accompanied with some illustrative examples.

Fuzzy Robust Estimates of Location and Scale Parameters of a Fuzzy Random Variable

“…The fuzzy median is devoid of this synonym drawback and can be used as a fuzzy robust estimator of the location parameter of a fuzzy random variable. The theoretical foundations of fuzzy medians are discussed in [12,13].…”

“…A detailed analysis of these differences is provided in [7]. Various aspects of the theory and practice of fuzzy random variables can be found in [8][9][10][11][12]. According to the authors of formal definitions, the first type of such variables is called fuzzy random variables in Kwakernaak's sense, the second type is called fuzzy random variables in Puri /Ralescu's sense.…”

M-Estimates of Location for the Robust Central Tendency of Fuzzy Data

“…, x n ) be a sample of independent observations from a random fuzzy number X : Ω → F * c (R) on a probability space (Ω, A, P ). Then, the sample x n is said to be symmetric about c ∈ R (see Sinova et al [30]) if and only if x n − c and c − x n (or, equivalently, 2c − x n and x n ) include exactly the same fuzzy data. We then have the following result: In addition to these properties, it is also of importance to investigate the consistency of sample M-estimators as well as their robustness.…”

An analysis of the median of a fuzzy random variable based on Zadeh’s extension principle

“…Thus, in the real-valued case a wellknown result is that the median of a symmetric random variable coincides with the point the variable is symmetric about whenever it is unique. Sinova et al [16] have proved that the 1-norm median shows a suitable central tendency behaviour since it leads to a fuzzy number which is symmetric about the symmetry point. This property is also shared by Grzegorzewski's population fuzzy median.…”