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Random-fuzzy variable
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<p>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 <a href="/facts/Systematic_error/q7pa7bRt">systematic error</a> and if there is, how much? Hence, systematic uncertainty could be considered as a contribution of a fuzzy nature. </p><p>This systematic error can be approximately modeled based on our past data about the measuring instrument and the process. </p><p>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. </p><p><a href="/facts/Lotfi_A._Zadeh/WojTlG4Y">L.A.Zadeh</a> 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. </p><p>Random-fuzzy variable (RFV) is a <a href="/facts/Type-2_fuzzy_sets_and_systems/LsqLRemx">type 2 fuzzy variable</a>, 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. </p>