Joint Random-Fuzzy Variables: A Tool for Propagating Uncertainty Through Nonlinear Measurement Functions

A still open issue, in uncertainty evaluation, is asymmetrical distributions of the values that can be attributed to the measurand. This problem generally becomes not negligible when the measurement function is highly nonlinear. In this case, the law of uncertainty propagation suggested by the Guide to the Expression of Uncertainty in Measurement is not correct any longer, and only Monte Carlo simulations can be used to obtain such distributions. This paper shows how this problem can be solved in a quite immediate way when measurement results are expressed in terms of random-fuzzy variables. Under this approach, nonrandom contributions to uncertainty can also be considered. An experimental example is reported and the results compared with those obtained by means of Monte Carlo simulations, showing the effectiveness of the proposed approach.

[1]  Bernadette Bouchon Fuzzy inferences and conditional possibility distributions , 1987 .

[2]  Alessandro Ferrero,et al.  Uncertainty propagation through non-linear measurement functions by means of joint Random-Fuzzy Variables , 2015, 2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings.

[3]  Alessandro Ferrero,et al.  A Metrological Comparison Between Different Methods for Harmonic Pollution Metering , 2012, IEEE Transactions on Instrumentation and Measurement.

[4]  Michał K. Urbański,et al.  Fuzzy approach to the theory of measurement inexactness , 2003 .

[5]  Alessandro Ferrero,et al.  The construction of random-fuzzy variables from the available relevant metrological information , 2008, IEEE Transactions on Instrumentation and Measurement.

[6]  Rogelio Luck,et al.  Evaluation of parameter effects in estimating non-linear uncertainty propagation , 2007 .

[7]  Didier Dubois,et al.  Joint propagation of probability and possibility in risk analysis: Towards a formal framework , 2007, Int. J. Approx. Reason..

[8]  Alessandro Ferrero,et al.  A distributed system for electric power quality measurement , 2002, IEEE Trans. Instrum. Meas..

[9]  Alessandro Ferrero,et al.  The evaluation of uncertainty contributions due to uncompensated systematic effects , 2013, 2013 IEEE International Instrumentation and Measurement Technology Conference (I2MTC).

[10]  G. Mauris,et al.  A fuzzy approach for the expression of uncertainty in measurement , 2001 .

[11]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[12]  Alessandro Ferrero,et al.  Fuzzy Metrology-Sound Approach to the Identification of Sources Injecting Periodic Disturbances in Electric Networks , 2011, IEEE Transactions on Instrumentation and Measurement.

[13]  Alessandro Ferrero,et al.  The Construction of Joint Possibility Distributions of Random Contributions to Uncertainty , 2014, IEEE Transactions on Instrumentation and Measurement.

[14]  M. J. Frank,et al.  Associative Functions: Triangular Norms And Copulas , 2006 .

[15]  L. Zadeh Fuzzy sets as a basis for a theory of possibility , 1999 .

[16]  Alessandro Ferrero,et al.  Processing Dependent Systematic Contributions to Measurement Uncertainty , 2013, IEEE Transactions on Instrumentation and Measurement.

[17]  Simona Salicone,et al.  Measurement Uncertainty: An Approach Via the Mathematical Theory of Evidence , 2006 .

[18]  Alessandro Ferrero,et al.  Uncertainty: Only One Mathematical Approach to Its Evaluation and Expression? , 2012, IEEE Transactions on Instrumentation and Measurement.

[19]  Lamia Berrah,et al.  Fuzzy handling of measurement errors in instrumentation , 2000, IEEE Trans. Instrum. Meas..

[20]  Márcio A. F. Martins,et al.  Generalized expressions of second and third order for the evaluation of standard measurement uncertainty , 2011 .

[21]  Alessandro Ferrero,et al.  The random-fuzzy variables: a new approach to the expression of uncertainty in measurement , 2004, IEEE Transactions on Instrumentation and Measurement.

[22]  Radko Mesiar,et al.  Triangular norms. Position paper II: general constructions and parameterized families , 2004, Fuzzy Sets Syst..

[23]  Alessandro Ferrero,et al.  Conditional Random-Fuzzy Variables Representing Measurement Results , 2015, IEEE Transactions on Instrumentation and Measurement.