Fuzzy modeling of measurement data acquired from physical sensors (original) (raw)
Related papers
Modeling the Measurement Uncertainty with Fuzzy Approach
There are several types of uncertainty in a material characterization arisen from different sources of measurement errors, such as methodological, instrumental, and personal. As a reason of the uncertainty in material models, it is plausible to consider model parameters in an interval instead of a singleton. The probability theory is widely known method used for the consideration of uncertainties by means of a certain distribution function and confidence level concept. In this study, fuzzy logic is considered within a material characterization model to deal with the uncertainty coming from random measurement errors. Data points are treated using fuzzy numbers instead of single values to cover random measurement errors. In this context, an illustrative example, prepared with core strength-rebound hammer data obtained from a concrete structure, is solved and evaluated in detail. Results revealed that there is a potential for fuzzy logic to characterize the uncertainty in a material model arisen from measurement errors.
The Random-Fuzzy Variables: A New Approach to the Expression of Uncertainty in Measurement
IEEE Transactions on Instrumentation and Measurement, 2004
The good measurement practice requires that the measurement uncertainty is estimated and provided together with the measurement result. The practice today, which is reflected in the reference standard provided by the IEC-ISO "Guide to the expression of uncertainty in measurement," adopts a statistical approach for the expression and estimation of the uncertainty, since the probability theory is the most known and used mathematical tool to deal with distributions of values. However, the probability theory is not the only tool to deal with distributions of values and is not the most suitable one when the values do not distribute in a totally random way. In this case, a more general theory, the theory of the evidence, should be considered. This paper recalls the fundamentals of the theory of the evidence and frames the random-fuzzy variables within this theory, showing how they can usefully be employed to represent the result of a measurement together with its associated uncertainty. The mathematics is defined on the random-fuzzy variables, so that the uncertainty can be processed, and simple examples are given.
IEEE Transactions on Instrumentation and Measurement, 2000
Random-fuzzy variables (RFVs) are mathematical variables defined within the theory of evidence. Their importance in measurement activities is due to the fact that they can be employed for the representation of measurement results, together with the associated uncertainty, whether its nature is random effects, systematic effects, or unknown effects. Of course, their importance and usability also depend on the fact that they can be employed for processing measurement results. This paper proposes suitable mathematics and related calculus for processing RFVs, which consider the different nature and the different behavior of the uncertainty effects. The proposed approach yields to process measurement algorithms directly in terms of RFVs so that the final measurement result (and all associated available information) is provided as an RFV.
Instrumentation and Measurement Ieee Transactions on, 2007
Random-fuzzy variables (RFVs) are mathematical variables defined within the theory of evidence. Their importance in measurement activities is due to the fact that they can be employed for the representation of measurement results, together with the associated uncertainty, whether its nature is random effects, systematic effects, or unknown effects. Of course, their importance and usability also depend on the fact that they can be employed for processing measurement results. This paper proposes suitable mathematics and related calculus for processing RFVs, which consider the different nature and the different behavior of the uncertainty effects. The proposed approach yields to process measurement algorithms directly in terms of RFVs so that the final measurement result (and all associated available information) is provided as an RFV.
Fuzzy Logic for Stochastic Modeling
Advances in Soft Computing, 2006
Exploring the growing interest in extending the theory of probability and statistics to allow for more flexible modeling of uncertainty, ignorance, and fuzziness, the properties of fuzzy modeling are investigated for statistical signals, which benefit from the properties of fuzzy modeling. There is relatively research in the area, making explicit identification of statistical/stochastic fuzzy modeling properties, where statistical/stochastic signals are in play. This research makes explicit comparative investigations and positions fuzzy modeling in the statistical signal processing domain, next to nonlinear dynamic system modeling.
Fuzzy Randomness -Towards a new Modeling of Uncertainty
In the paper a new concept of modeling uncertainty is presented, based on the theory of fuzzy random variables. By this means, a super-ordinate uncertainty model is made available which includes the models developed so far, based on random variables and fuzzy variables as special cases.
The construction of random-fuzzy variables from the available relevant metrological information
IEEE Transactions on Instrumentation and Measurement, 2000
Approaches other than the probabilistic approach recommended by the Guide to the Expression of Uncertainty in Measurement (GUM) have been proposed during the recent past for uncertainty expression and estimation. The approach based on random-fuzzy variables (RFVs) appears to be the most promising approach since it is based on the theory of evidence, which encompasses probability theory as a particular case. The correctness of the final uncertainty estimation quite directly depends on the way the RFVs are built, which depends on the available relevant metrological information. After briefly recalling the fundamentals of the RFV approach, this paper discusses how the available relevant information should be exploited to attain correct results.
The two scopes of fuzzy probability theory
The aim of this work is to compare between what seems to be entirely different two highly developing "fuzzy probability" theories. The first theory had been developed firstly by statisticians and the other separately by physicists. We start by indicating the needs to develop such theories and what helped to develop each, then we will establish the basis of the two theories and illustrate that each indeed extends classical probability theory. Moreover, we will try to see whether or not any of the two theory can be embedded into the other.
Modeling uncertainty with fuzzy logic: with recent theory and applications
2009
The objective of this book is to present an uncertainty modeling approach using a new type of fuzzy system model via" Fuzzy Functions". Since most researchers on fuzzy systems are more familiar with the standard fuzzy rule bases and their inference system structures, many standard tools of fuzzy system modeling approaches are reviewed to demonstrate the novelty of the structurally different fuzzy functions, before we introduced the new methodologies.
Overview on the development of fuzzy random variables
Fuzzy Sets and Systems, 2006
This paper presents a backward analysis on the interpretation, modelling and impact of the concept of fuzzy random variable. After some preliminaries, the situations modelled by means of fuzzy random variables as well as the main approaches to model them are explained. We also summarize briefly some of the probabilistic studies concerning this concept as well as some statistical applications.