Experimental data fuzziness

Figure 3.8 Comparison of theory and experiments (water-air horizontal flow at 25°C and 1 atm pressure with diameter of 2.5 cm). Solid lines theory. (From Dukler, 1978. Copyright 1978 by National Council of Canada. Reprinted with permission.) Fuzzy lines experimental data. (From Mand-hane et al., 1974. Copyright 1974 by Elsevier Science Ltd., Kidlington, UK. Reprinted with permission.)...

As an illustration of this statement, Figure 15 to Figure 17 detail the faults detected by fuzzy module Qin-pR, module Qin-Qgas-pR and module Qin-Qgas-CH4 when analyzing the experimental data described in Figure 14. These... 

The dynamic behavior of liquid-crystalline polymers in concentrated solution is strongly affected by the collision of polymer chains. We treat the interchain collision effect by modelling the stiff polymer chain by what we refer to as the fuzzy cylinder [19]. This model allows the translational and rotational (self-)diffusion coefficients as well as the stress of the solution to be formulated without resort to the hypothetical tube model (Sect. 6). The results of formulation are compared with experimental data in Sects. 7-9. 

In this article, we have surveyed typical properties of isotropic and liquid crystal solutions of liquid-crystalline stiff-chain polymers. It had already been shown that dilute solution properties of these polymers can be successfully described by the wormlike chain (or wormlike cylinder) model. We have here concerned ourselves with the properties of their concentrated solutions, with the main interest in the applicability of two molecular theories to them. They are the scaled particle theory for static properties and the fuzzy cylinder model theory for dynamical properties, both formulated on the wormlike cylinder model. In most cases, the calculated results were shown to describe representative experimental data successfully in terms of the parameters equal or close to those derived from dilute solution data. 

Van der Waals treatment makes no mention of three or more molecules interacting at the same time, and a billiard-ball-type of excluded volume is quite unreasonable for the fuzzy electron clouds required by quantum mechanics. Nevertheless, it still finds extensive use as a first correction to the ideal gas law. The equation is called semiempirical, in that, although it is based on physical arguments, it contains two constants, specific for each molecule, which must be evaluated by comparison with experimental data. Values for some of these constants are listed in Table 1. The numbers in such tables may vary somewhat, depending on the pressure and temperature regime in which the fitting to experimental data has been performed. Predictions of the van der Waals equation will be more accurate close to the conditions under which the constants have been determined. 

The simplest method of accounting for variability consists in identifying the parameters, experimental data, and model output with an average or reference individual [45], One shortcoming of this approach is that although general model behavior is representative, much of the actual population may not be well described. Methods attempting to explicitly account for variability and uncertainty include Monte Carlo simulations [18,46,48], Bayesian population methods [49-51,53,56], the use of fuzzy sets [44,52], and other probability based methods [43], Monte Carlo simulations, which model the parameter variability in terms of probability distributions, are the most common methods. Each individual is characterized by a set of parameters whose values are drawn from a... 

Handling natural fuzziness experimental data underlie certain fuzziness that is addressed by Fuzzy Logic and similar techniques. 

However, we have to face the fact that most data come from experimental observations. The results from these observations rarely underlie a linear and straightforward model experimental data exhibit certain fuzziness, usually as a result of the... 

Accuracy checks are generally performed by comparing measured data with data from certified reference materials. When measured data are not accurate because of relative or systematic errors, or a lack of precision (noise), the comparison between measured data and reference values cannot lead to any useful conclusion in an expert system. To process larger sets of potential source data for knowledge bases, a method must be used that takes inaccuracies as well as natural fuzziness of experimental data into account — ideally automatically and without the help of an expert. 

The general principle in fuzzy logic is that a reference value Xq is associated with a fuzzy interval dx, and experimental data within an interval of Xq dx are identified as reference data. Since natural, or experimental, data are always inaccurate, and the representation of knowledge is quite like that in fuzzy logic, expert systems have to use fuzzy logic or some techniques similar to fuzzy logic [33]. In a computer system based on the fuzzy logic approach, fuzzy intervals for reference values are defined a priori. 

Jin et al. applied fuzzy control and artificial neural networks for fed-batch cultivation of recombinant saccharomyces cerevisiae to improve productivity and product yield of P-galactosidase. Experimental data have shown that by application of fuzzy control and neural network estimators, the productivity was 2.7-fold higher than in the case of exponential feeding. 

Artificial Intelligence in Chemistry Chemical Engineering Expert Systems Chemometrics Multivariate View on Chemical Problems Electrostatic Potentials Chemical Applications Environmental Chemistry QSAR Experimental Data Evaluation and Quality Control Fuzzy Methods in Chemistry Infrared Data Correlations with Chemical Structure Infrared Spectra Interpretation by the Characteristic Frequency Approach Machine Learning Techniques in Chemistry NMR Data Correlation with Chemical Structure Protein Modeling Protein Structure Prediction in ID, 2D, and 3D Quality Control, Data Analysis Quantitative Structure-Activity Relationships in Drug Design Quantitative Structure-Property Relationships (QSPR) Shape Analysis Spectroscopic Databases Structure Determination by Computer-based Spectrum Interpretation. 

Data collected by modern analytical instalments are usually presented by the multidimensional arrays. To perform the detection/identification of the supposed component or to verify the authenticity of a product, it is necessary to estimate the similarity of the analyte to the reference. The similarity is commonly estimated with the use of the distance between the multidimensional arrays corresponding to the compared objects. To exclude within the limits of the possible the influence of the random errors and the nonreproductivity of the experimental conditions and to make the comparison of samples more robust, it is possible to handle the arrays with the use of the fuzzy set theory apparatus. 

The rules that the fuzzy system uses are expressed in terms such as a "high" or a "medium" pH, while the experimental input data are numerical quantities. The first stage in applying these rules is to transform the input data into a degree of membership for each variable in each class through the use of membership functions. 

This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

In many experimental cases, a certain degree of interference occurs among the measures, which gives rise to possible collections of results however, the situation is even more complex if the input data are subjected to uncertainty or imprecision (Kaufmann and Gupta, 1991). Fuzzy logic is the only mathematical application that can properly solve problems with imprecision in input data. 

The second requirement is a suitable similarity measure for the comparison of patterns. Once the patterns are defined and the quality of the experimental base data is good, pattern-recognition methods are valuable. Nevertheless, if patterns change irregularly and cannot be explicitly defined, the similarity measure no longer describes the difference between query and experimental pattern even if a fuzzy logic approach is implemented. 

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