Pattern recognition based on fuzzy observations for spectroscopic quality control and chromatographic fingerprinting

Otto, M. Alexander; Bandemer, Hans

doi:10.1016/s0003-2670(00)86467-3

Cited by 34 publications

(8 citation statements)

References 8 publications

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“…Different schemes of reasoning can be applied, for example the theory of approximate reasoning as further developed by Yager [13]. Approximate reasoning has been already explored in analytical chemistry for reasoning about missing data/information in a data base on pHindicators [14] and is used at present for building an interpretation system in IR-spectroscopy. The concept of fuzzy theory is also used for data analysis in analytical chemistry.…”

Section: Applicationsmentioning

confidence: 99%

Fuzzy Type-2 Applications to Analytical Chemistry

Shabaninia

Torabi²

2013

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Section: Applicationsmentioning

confidence: 99%

Fuzzy Type-2 Applications to Analytical Chemistry

Shabaninia

Torabi²

2013

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“…We may now characterize the objects in X with respect to the classes of proprieties 5¿, i = 1,.... n. The value xj of the object k with respect to the class 5, is defined as d % = X B¡(yk) xik, i = 1,..., n\j = 1, ...,p (17) <t=i Thus, from the original p d-dimensional objects we have computed p new n-dimensional objects, which correspond to the classes of characteristics B¡s i = 12 .... n Let us now consider the set X = {X'L ..., XP} of the modified objects. We define the fuzzy set C on X, given by c(x,) = c(Ay= i,...,p With the generalized fuzzy n-means algorithm we will determine a fuzzy partition P' = {A\,..., A'} of the class C, by using the objects given by the relation (17). The process continues until two successive partitions of objects (or of characteristics) are close enough to each other.…”

Section: Simultaneous Fuzzy N-means Algorithmmentioning

confidence: 99%

“…53. With the generalized fuzzy n-means algorithm we determine a fuzzy n-partition P(,+1) of the class C by using the characteristics defined in (17).…”

Section: Simultaneous Fuzzy N-means Algorithmmentioning

confidence: 99%

“…Let us denote the final partitions obtained above by P = (Ai,..., An} and Q = {B\.....B"}. If we will try to build the fuzzy partitions corresponding to the fuzzy sets A, and B" i = 1, ..., n, with the help of this algorithm, when computing for the first time the fuzzy partition of objects, instead the original objects we may use the objects defined in the relation (17) and determined before the end of the algorithm that produced the fuzzy partitions P and Q. Now we will present the procedure of hierarchical classclassification.…”

Section: Simultaneous Fuzzy N-means Algorithmmentioning

confidence: 99%

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Fuzzy hierarchical cross-classification of Greek muds

Dumitrescu¹,

Pop²,

Sârbu³

1995

J. Chem. Inf. Comput. Sci.

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In this paper we analyze the set of Greek muds from eight different locations given in ref 16 using a divisive fuzzy hierarchical cross-classification algorithm. We consider the fuzzy clustering algorithms are capable to eliminate the disfunctionalities of the hard clustering algorithms as well as to provide information obtained from a metrical analysis of the data. The fuzzy hierarchical cross-classification algorithm presented here produces not only a fuzzy partition of the muds in discussion but also a fuzzy partition of the 23 chemical and mineralogical characteristics, so that to each class of muds we may associate the class of characteristics that contributed to the separation of the class of muds.

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“…By doing this, each number manipulated also carries information on its spread. Important applications of fuzzy theory so far have been library searching [ 19 ], pattern classification [ 20 ], and calibration with linear and non-linear signal/analyte dependencies in the presence of errors in x and y [ 21 ]. In the future, the incorporation of fuzzy information in expert systems will undoubtedly play a major role.…”

Section: Fuzzy Theory In Analytical Chemistrymentioning

confidence: 99%

Chemometrics in Europe - Selected results

Wegscheider¹

1988

J. RES. NATL. BUR. STAN.

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to recalculate the concentration profiles. This process (truncation, normalization and pseudoinverse followed by pseudoinverse) was repeated until no further refinement occurred.The concentration profiles and spectra of the three unknown components of stearyl alcohol in carbon tetrachloride obtained in this manner were found to make chemical sense.This EFA procedure, unlike others, was successful in extracting concentration profiles from situations where one component profile was completely encompassed underneath another component profile.References [I] Malinowski, E. R., and Howery, D. G., Factor Analysis in Chemistry, Wiley Interscience, New York (1980). [2] Gemperline, P. G., J. Chem. Inf. Comput. Sci. 24, 206 (1984).[3] Vandeginste, B. G. M., Derks, W., and Kateman, G., Anal.Chim. Acta 173, 253 (1985). [4] Gampp, H., Macder, M., Meyer, C. J., and Zuberbuhler, A.D., Talanta 32, 1133Talanta 32, (1985.[5] Malinowski, F. R., J. Chemometrics 1, 33 (1987).[6] Wold, S., Technometrics 20, 397 (1978). Chemometrics in Europe:Selected Results Wolfhard WegscheiderInstitute for Analytical Chemistry Mikro-and Radiochemistry Technical University Graz, A-8010 Graz, AustriaChemometrics is a very international branch of science, perhaps more so than chemistry at large, and it is therefore appropriate to question the suitability of the topic to be presented. It is, however, the author's opinion that the profile of European chemometric research has a couple of distinct features that may originate more in the structure of the educational system than in the actual research topics. The profile as it will be presented is the one perceived by the author, and therefore comprises a very subjective selection of individual contributions to the field. Obviously, this is not the place to offer a review on chemometrics, let alone one that is restricted to a continent.The definition of chemometrics [I] comprises three distinct areas characterized by the key words "optimal measurements," "maximum chemical information" and, for analytical chemistry something that sounds like the synopsis of the other two: "optimal way [to obtain] relevant information." Information TheoryEckschlager and Stepanek [2][3][4][5] where q and p are the prior and posterior distribution of the analyte concentration for the specific cases of a rectangular prior distribution in (x,,x 2 ) and a Gaussian posterior with a standard deviation s determined from /A independent results. The penalty for an inaccurate analysis is considerable and can be expressed as (2) I (r;q,p)= I (q 11P)_nA with d the difference between obtained value and the true value of x. The concept has also been extended to multicomponent analysis and multimethod characterization.In the latter case, correlations between the information provided by the different methods need to be accounted for. Given the cost of and time needed for an analysis, information efficiency can be deduced in a straightforward manner [2]. Recently, work was published [5] suggesting the incorporation of various relevance co...

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Pattern recognition based on fuzzy observations for spectroscopic quality control and chromatographic fingerprinting

Cited by 34 publications

References 8 publications

Fuzzy Type-2 Applications to Analytical Chemistry

Fuzzy Type-2 Applications to Analytical Chemistry

Fuzzy hierarchical cross-classification of Greek muds

Chemometrics in Europe - Selected results

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