Random-fuzzy variable

Random-fuzzy variable

In measurements, the measurement obtained can suffer from two types of uncertainties. The first is the random uncertainty which is due to the noise in the process and the measurement. The second contribution is due to the systematic uncertainty which may be present in the measuring instrument. Systematic errors, if detected, can be easily compensated as they are usually constant throughout the measurement process as long as the measuring instrument and the measurement process are not changed. But it can not be accurately known while using the instrument if there is a systematic error and if there is, how much? Hence, systematic uncertainty could be considered as a contribution of a fuzzy nature.

Comment
enIn measurements, the measurement obtained can suffer from two types of uncertainties. The first is the random uncertainty which is due to the noise in the process and the measurement. The second contribution is due to the systematic uncertainty which may be present in the measuring instrument. Systematic errors, if detected, can be easily compensated as they are usually constant throughout the measurement process as long as the measuring instrument and the measurement process are not changed. But it can not be accurately known while using the instrument if there is a systematic error and if there is, how much? Hence, systematic uncertainty could be considered as a contribution of a fuzzy nature.
Depiction
Construction of an RFV.png
Normal distribution in probability and possibility.png
Random-Fuzzy Variable.png
Triangular distribution in probability and possibility.png
Uniform distribution in probability and possibility.png
Has abstract
enIn measurements, the measurement obtained can suffer from two types of uncertainties. The first is the random uncertainty which is due to the noise in the process and the measurement. The second contribution is due to the systematic uncertainty which may be present in the measuring instrument. Systematic errors, if detected, can be easily compensated as they are usually constant throughout the measurement process as long as the measuring instrument and the measurement process are not changed. But it can not be accurately known while using the instrument if there is a systematic error and if there is, how much? Hence, systematic uncertainty could be considered as a contribution of a fuzzy nature. This systematic error can be approximately modeled based on our past data about the measuring instrument and the process. Statistical methods can be used to calculate the total uncertainty from both systematic and random contributions in a measurement. But, the computational complexity is very high and hence, are not desirable. L.A.Zadeh introduced the concepts of fuzzy variables and fuzzy sets. Fuzzy variables are based on the theory of possibility and hence are possibility distributions. This makes them suitable to handle any type of uncertainty, i.e., both systematic and random contributions to the total uncertainty. Random-fuzzy variable (RFV) is a type 2 fuzzy variable, defined using the mathematical possibility theory, used to represent the entire information associated to a measurement result. It has an internal possibility distribution and an external possibility distribution called membership functions. The internal distribution is the uncertainty contributions due to the systematic uncertainty and the bounds of the RFV are because of the random contributions. The external distribution gives the uncertainty bounds from all contributions.
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Random-fuzzy variable
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enRandom-fuzzy variable
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Category:Fuzzy logic
Category:Metrology
Central limit theorem
Dempster–Shafer theory
File:Construction of an RFV.png
File:Normal distribution in probability and possibility.png
File:Random-Fuzzy Variable.png
File:Triangular distribution in probability and possibility.png
File:Uniform distribution in probability and possibility.png
Fuzzy set
Gamma distribution
Lotfi A. Zadeh
Observational error
Possibility theory
Probability distribution
Probability theory
Random error
Systematic error
T-norm
Type-2 fuzzy sets and systems
Uniform distribution (continuous)
SameAs
9mSoo
Q65028338
Variabel acak-buram
Subject
Category:Fuzzy logic
Category:Metrology
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