Equality. Two fuzzy sets A and B are equal if they have the same membership funetion within a universe of diseourse U. [Pg.328]

Fuzzy sets and fuzzy logic. Fuzzy sets differ from the normal crisp sets in the fact that their elements have partial membership (represented by a value between 0 an 1) in the set. Fuzzy logic differs from the binary logic by the fact that the truth values are represented by fuzzy sets. [Pg.99]

All the three techniques mentioned above may make use of fuzzy sets and fuzzy logic (for fuzzy classification, fuzzy rules or fuzzy matching) but this does not effect the discussion of the applicability to NDT problems in the next section. [Pg.99]

To know about fuzzy sets and fuzzy logic [Pg.439]

Figure 9-25. Membership function for the fuzzy set of numbers close to 3. |

Fuzzy logic and fuzzy set theory are applied to various problems in chemistry. The applications range from component identification and spectral Hbrary search to fuzzy pattern recognition or calibrations of analytical methods. [Pg.466]

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]

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]

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]

Let the fuzzy set medium temperature be called fuzzy set M. If an element u of the universe of discourse U lies within fuzzy set M, it will have a value of between 0 and 1. This is expressed mathematically as [Pg.327]

When the universe of discourse is discrete and finite, fuzzy set M may be expressed as [Pg.327]

Let A and B be two fuzzy sets within a universe of diseourse U with membership funetions /ta and /tb respeetively. The following fuzzy set operations ean be defined as [Pg.328]

Union The union of two fuzzy sets A and B eorresponds to the Boolean OR funetion and is given by [Pg.328]

Find the union and interseetion of fuzzy set low temperature L and medium temperature M shown in Figure 10.4. Find also the eomplement of fuzzy set M. Using equation (10.2) the fuzzy sets for = 11 are [Pg.328]

Fuzzifieation is the proeess of mapping inputs to the FLC into fuzzy set membership values in the various input universes of diseourse. Deeisions need to be made regarding [Pg.331]

The number and shape of fuzzy sets in a partieular universe of diseourse is a tradeoff between preeision of eontrol aetion and real-time eomputational eomplexity. In this example, seven triangular sets will be used. [Pg.331]

Figure 10.9 assumes that the output window contains seven fuzzy sets with the same linguistic labels as the input fuzzy sets. If the universe of discourse for the control signal u(t) is 9, then the output window is as shown in Figure 10.10. [Pg.332]

In Figure 10.8 and equation (10.20) the fuzzy sets that were hit in the error input window when e(t) = 2.5 were PS and PM. In the rate of change input window when ce = -0.2, the fuzzy sets to be hit were NS and Z. From Figure 10.9, the relevant rules that correspond to these hits are [Pg.333]

Figure 10.38 shows an input window with three triangular fuzzy sets NB, Z and PB. Each set is positioned in its regime of operation by the centre parameter c so that, for example, NB can only operate on the negative side of the universe of discourse. The width of each set is controlled by parameter ri . [Pg.372]

© 2019 chempedia.info