scholarly journals FUZZY ROBUST ESTIMATES OF LOCATION AND SCALE PARAMETERS OF A FUZZY RANDOM VARIABLE

2021 ◽  
Vol 2 ◽  
pp. 181-186
Author(s):  
Oleg Uzhga Rebrov ◽  
Galina Kuleshova
Keyword(s):  
Extreme Values ◽  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Arithmetic Mean ◽  
Data Uncertainty ◽  
Absolute Deviation ◽  
Scale Parameters ◽  
Robust Estimates ◽  
Fuzzy Random

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. 

scholarly journals On Distribution Characteristics of a Fuzzy Random Variable

2018 ◽  
Vol 47 (2) ◽  
pp. 53-67 ◽  
Author(s):  
Jalal Chachi
Keyword(s):  
Probability Theory ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Distribution Characteristics ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

In this paper, rst a new notion of fuzzy random variables is introduced. Then, usingclassical techniques in Probability Theory, some aspects and results associated to a randomvariable (including expectation, variance, covariance, correlation coecient, etc.) will beextended to this new environment. Furthermore, within this framework, we can use thetools of general Probability Theory to dene fuzzy cumulative distribution function of afuzzy random variable.

PERCEPTION-BASED ESTIMATIONS OF FUZZY RANDOM VARIABLES: LINEARITY AND CONVEXITY

2008 ◽  
Vol 16 (supp01) ◽  
pp. 71-87 ◽  
Author(s):  
YUJI YOSHIDA
Keyword(s):  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Fuzzy Random Variables ◽  
Engineering Economics ◽  
Random Events ◽  
Fuzzy Random

A set of perceived random events is given by a fuzzy random variable, and an estimation of real random variables is represented by a functional on real random variables. The perception-based extension of estimation regarding random events is introduced, extending the functional to a functional of fuzzy random variables. This paper discusses some conditions and various properties of the extended estimations, for example, monotonicity, continuity, linearity, sub-additivity/super-additivity, convexity/concavity. Several examples of the perception-based extended estimations are investigated. This paper analyzes the general cases, where the estimations do not have monotone properties, from the viewpoint of convexity/concavity. The results can be applicable to other estimations in engineering, economics and so on.

scholarly journals Several Limit Theorems on Fuzzy Quantum Space

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 438
Author(s):  
Viliam Ďuriš ◽  
Renáta Bartková ◽  
Anna Tirpáková
Keyword(s):  
Financial Markets ◽  
Incomplete Data ◽  
Extreme Values ◽  
Random Variables ◽  
Consumer Electronics ◽  
Financial Risks ◽  
Quantum Space ◽  
Fuzzy Random Variables ◽  
Scientific Disciplines ◽  
Fuzzy Random

The probability theory using fuzzy random variables has applications in several scientific disciplines. These are mainly technical in scope, such as in the automotive industry and in consumer electronics, for example, in washing machines, televisions, and microwaves. The theory is gradually entering the domain of finance where people work with incomplete data. We often find that events in the financial markets cannot be described precisely, and this is where we can use fuzzy random variables. By proving the validity of the theorem on extreme values of fuzzy quantum space in our article, we see possible applications for estimating financial risks with incomplete data.

The Compatibility Assessment between Voltage Sags and Equipment Tolerance Based on Fuzzy-Random Method

2012 ◽  
Vol 588-589 ◽  
pp. 458-462
Author(s):  
Zhi Jian Yuan ◽  
Yan Li
Keyword(s):  
Engineering Application ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Assessment Model ◽  
Voltage Sags ◽  
Equipment Failure ◽  
Failure Event ◽  
Cut Set ◽  
The Impact ◽  
Fuzzy Random

The impact of voltage sags on equipment is usually described by equipment failure probability.It is generally difficult to assess and predict the probability because of the uncertainty of both the nature of voltage sags and the VTL (VTL) of equipment. By defining the equipment failure event caused by voltage sags as a fuzzy-random event, a fuzzy-random assessment model incorporating those uncertainty is developed. The model is able to convert the probability problem of a fuzzy-random variable to that of a common random variable by using λ-cut set. It is thus valuable in theoretical analysis and engineering application. The validity of the developed model is verified by Monte Carlo stochastic simulation using personal computers (PCs)as test equipment.

scholarly journals On the Generalization Performance of a Regression Model with Imprecise Elements

2017 ◽  
Vol 25 (05) ◽  
pp. 723-740 ◽  
Author(s):  
Maria Brigida Ferraro
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Prediction Error ◽  
Random Element ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Generalization Performance ◽  
Bootstrap Procedure ◽  
Link Functions ◽  
Fuzzy Random

A linear regression model for imprecise random variables is considered. The imprecision of a random element has been formalized by means of the LR fuzzy random variable, characterized by a center, a left and a right spread. In order to avoid the non-negativity conditions the spreads are transformed by means of two invertible functions. To analyze the generalization performance of that model an appropriate prediction error is introduced, and it is estimated by means of a bootstrap procedure. Furthermore, since the choice of response transformations could affect the inferential procedures, a computational proposal is introduced for choosing from a family of parametric link functions, the Box-Cox family, the transformation parameters that minimize the prediction error of the model.

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