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Fuzzy sets application

M. Otto, Anal. Chem., 62, 797A (1990). Fuzzy Sets Applications to Analytical Chemistry. [Pg.330]

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]

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]

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

Zadeh [1975] extended the classical set theory to the so-called fuzzy set theory, introducing membership functions that can take on any value between 0 and 1. As illustrated by the intersection of the (hard) reference data set (A) and the fuzzed test data set (C), the intersection (E) shows an agreement of about 80%. Details on application of fuzzy set theory in analytical chemistry can be found in Blaffert [1984], Otto and Bandemer [ 1986a,b] and Otto et al. [1992],... [Pg.64]

Zadeh LA (1975) Fuzzy sets and their applications to cognitive and decision processes. Academic Press, New York... [Pg.68]

The application of both of these hedges concentrates the region to which the hedge applies. Nonzero membership of the fuzzy set "very low pH" covers the same overall range of pH as membership of the group "low pH," even with the hedge in place, but the effect of the hedge is to reduce membership in the "low pH" set for those pHs that also have some membership in the "medium pH" set. The effect of "very very" is even more marked, as we would expect. [Pg.249]

Distances in these spaces should be based upon an Zj or city-block metric (see Eq. 2.18) and not the Z2 or Euclidean metric typically used in many applications. The reasons for this are the same as those discussed in Subheading 2.2.1. for binary vectors. Set-based similarity measures can be adapted from those based on bit vectors using an ansatz borrowed from fuzzy set theory (41,42). For example, the Tanimoto similarity coefficient becomes... [Pg.17]

Klir, G. J. and Yuan, B. (1995) Fuzzy sets and fuzzy logic theory and applications. Prentice Hall PTR, Upper Saddle River, NJ. [Pg.47]

G.L. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logics-Theory and Application, Prentice Hall, New York, 1995. [Pg.100]

Evans GW, Karwowski W, Wilhelm MR (1986) An introduction to fuzzy set methodologies for industrial and systems engineering. In Evans GW, Karwowski W, Wilhelm MR, eds. Applications of fuzzy set methodologies in industrial engineering. New York, NY, Elsevier, pp. 3-11. [Pg.88]

Dubois, D. and Prade, H. (1980) Fuzzy Sets and Systems Theory and Applications, Academic Press, San Diego, CA, USA. [Pg.179]

The early recognition that quantum mechanical uncertainty [94] of electronic arrangement and motion within a molecule [95,96] has a special role in chemistry has been fundamental in the development of quantum chemistry. In general, the uncertainty itself can be represented by fuzzy set methods, applied in a wide range of disciplines [97-103], and both general quantum mechanical [104-108] and quantum chemical applications [40,52,109-111] have led to novel descriptions of physical and chemical properties. [Pg.188]

In each particular application of classical set theory as well as fuzzy set theory, all the sets of concern (classical or fuzzy) are subsets of a fixed set, which consists of all objects relevant to the applications. This set is called a uniuersal set and it is always denoted in this chapter by X. To distinguish classical (nonfuzzy) sets from fuzzy sets, the former are referred to as crisp sets. [Pg.34]

As an example, several possible membership functions that are reasonable for defining the set of real numbers that are close to 3 are shown in Fig. 1. Which of these functions captures best the concept close to 3 depends on the context within which the concept is applied. It turns out, however, that most current applications of fuzzy set theory are not overly sensitive to changes in shapes of the membership functions employed. Since triangular shapes (function A in Fig. 1) and trapezoidal shapes (Fig. [Pg.36]

The problem of constructing membership functions in the contexts of various applications is not a problem of fuzzy set theory per se. It is a problem of knowledge acquisition, which is a subject of a relatively new field referred to as knowledge engineering. [Pg.37]

When fuzzy sets are defined on universal sets that are Cartesian products of two or more sets, they are called fuzzy relations. For any Cartesian product of n sets, the relations are called n-dimensional. From the standpoint of fuzzy relations, ordinary fuzzy sets may be viewed as degenerate, one-dimensional relations. All concepts and operations applicable to fuzzy sets are applicable to fuzzy relations as well. However, fuzzy relations involve additional concepts and operations that emerge from their multidimensionality. [Pg.41]

Responses of opponents of fuzzy set theory to these examples of very successful applications of fuzzy set theory have been of two kinds. In the first kind of response, the examples are accepted as legitimate applications of fuzzy set theory, but it is maintained that some traditional methodology (classical control theory, Bayesian methodology, classical logic, etc.) would solve the problems even better. An example of this kind of response is the following excerpt from a personal letter I received from Anthony Garrett, one of my professional acquaintances and a devoted Bayesian, after I informed him about the fuzzy helicopter control ... [Pg.58]

P. Diamond and P. Kloeden, Metric Spaces of Fuzzy Sets Theory and Application. World Scientific, Singapore, 1994. [Pg.62]

Fuzzy set methods have been developed for a variety of applications, initially mostly in engineering and technology. However, many applications in the natural sciences quickly followed. " The Heisenberg relationship and many other aspects of quantum mechanics can be interpreted in terms of fuzzy sets. " A straightforward extension of these ideas to some of the elementary concepts of chemistry suggests the following rather... [Pg.139]

Both the unsealed fuzzy Hausdorff-type metric g A,B) and the scaled fuzzy Hausdorff-type metric f(A,B) have been shown in the preceding text to fulfill the conditions for proper metric if the mutual locations of fuzzy sets A, B, and C are fixed. However, in some applications, various translated, rotated, or reflected versions of these fuzzy sets can be regarded as equivalent. For example, the inherent dissimilarities between... [Pg.152]

Note that if a fuzzy set A has the fuzzy symmetry element / ()3) corresponding to the symmetry operator R at the fuzzy level j8 of the fuzzy Hausdorff-type similarity measure then the application of R on 4 generates a set R indistinguishable from set A at the fuzzy level (i. For the fuzzy set A the application of symmetry operator R of fuzzy symmetry element R(p ) present at the fuzzy level is completed by a formal recognition of the indistinguishability of set R/1 and set A at the given fuzzy level. This additional step, for which the sufficient and necessary condition is the presence of fuzzy symmetry element Ri ) at the fuzzy level /S, involves operator setting the membership functions of elements of the fuzzy set R/1 equal to those of fuzzy set A. [Pg.157]

The discontinuous symmetry changes and the binary nature of the presence or absence of symmetry elements hinders the application of point group symmetry methods for general molecular structures. In the syntopy approach, based on fuzzy set theory, the discrete concept of point symmetry is replaced by a continuous concept and is applicable to cases of almost symmetric or quasisymmetric molecular arrangements. When replacing symmetry with syntopy, some of the advantages of the group... [Pg.164]

A fuzzy set generalization of nuclear point symmetry in terms of these two syntopy models is applicable to all nuclear arrangements. Using appropriate membership functions, syntopy provides a measure of symmetry resemblance of actual, general nuclear configurations to ideal, fully symmetric nuclear configurations. [Pg.166]

In many applications of continuum mechanics the center of mass of objects has special significance. It appears advantageous to use an analogous concept in fuzzy set theory, taking the value of membership function at each point x of a fuzzy set A in the role of mass density and the integral defined in Eq. (100) as the total mass of the fuzzy set A. This is easily accomplished if the underlying set X can be interpreted as a Euclidean space with a well-defined Cartesian coordinate system. In this case, the center of mass c( ) of fuzzy set A is defined as... [Pg.183]

Although the treatment subsequently described is applicable for any reference point c of A for any fuzzy set A, the choice of reference point as the center of mass c(A) of fuzzy set A is usually advantageous in chemical applications, where the electronic density center ciA ) or c( (p., ) of molecule A can be selected. [Pg.184]

For crisp continuum sets and fuzzy sets, the crisp and fuzzy versions of the SNSM metric, as well as the crisp and fuzzy versions of the Hausdorff metric, provide generalizations of the ZPA approach. The generalization we shall describe requires a computational technique applicable for generating a crisp average of a family... [Pg.188]

Following the principles of the ZPA approach, these symmetry deficiency measures are generalizations of the folding-unfolding approach, equally applicable to crisp continuum sets and fuzzy sets, for example, to entire electron density distributions of molecules and various molecular fragments representing fuzzy functional groups. [Pg.195]


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See also in sourсe #XX -- [ Pg.2 , Pg.1095 ]




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