Note the symbol + is not an addition in the normal algebraie sense, but in fuzzy arithmetie denotes a union operation. [Pg.328]

An overview over different applications of fuzzy set theory and fuzzy logic is given in [15] (see also Chapter IX, Section 1.5 in the Handbook). [Pg.466]

If a spectrum lacks certain Lines or contains extra lines from additional unknown components, or if the true line positions are blurred, fuzzy set theory can improve the matching. [Pg.466]

APPLICATION OF FUZZY SETS THEORY TO SOLVING TASKS OF MULTICOMPONENT QUALITATIVE ANALYSIS [Pg.48]

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. [Pg.48]

Fuzzy logic control systems 10.2.1 Fuzzy set theory [Pg.326]

The central concept of fuzzy set theory is that the membership function /i, like probability theory, can have a value of between 0 and 1. In Figure 10.3, the membership function /i has a linear relationship with the x-axis, called the universe of discourse U. This produces a triangular shaped fuzzy set. [Pg.327]

Bayesian probability theory and methods that are based on fuzzy-set theory. The principles of both theories are explained in Chapter 16 and Chapter 19, respectively. Both approaches have advantages and disadvantages for the use in expert systems and it must be emphasized that none of the methods, developed up to now are satisfactory [7,11]. [Pg.640]

Fragment Reduced to an Environment that is Limited (FREL) 516 Frequency 215 Fr ejacque number 55 Friedel-Crafts alkylation 193 Frontier Molecular Orital (FMO) theory 179 Functional group 188, 192, 403 Fuzzy logic 465, 479 Fuzzy set 465 [Pg.639]

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