Fuzzy matching

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. 

In this work a fuzzy matching procedure is suggested which takes the foregoing uncertainties into account at least in principle. The approach is based on a soft definition of a surface that is defined in terms of membership functions (see Fig. 8) These functions are and, .(r) and they measure to what extent a given space point belongs to the surface and the bulk of a molecule, respectively. The matching of two molecules A and B can then be calculated in many different ways. In a first attempt we used the intersection of two fuzzy sets... 

Term weighting, fuzzy matches to words, and stemming words are other ways to improve the relevant ordering of the resulting documents... 

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. 

The principle of applying fuzzy logic to matching of spectra is that, given a sample spectrum and a collection of reference spectra, in a first step the reference spectra are unified and fuzzed, i.e., around each characteristic line at a certain wavenumber k, a certain fuzzy interval [/ o - Ak, + Afe] is laid. The resulting fuzzy set is then intersected with the crisp sample spectrum. A membership function analogous to the one in Figure 9-25 is applied. If a line of the sample spec-... 

Using these operators, fuzzy inference mechanisms are then developed to manipulate rules that include fuzzy values. The largest difference between fuzzy inference and ordinary inference is that fuzzy inference aUows partial match of input and produces an interpolated output. This technology is useml in control also. See Ref. 94. 

At first, only two conflict objectives are considered the minimal utility consumption and the maximal flexibility to all source-stream temperatures. And then the third objective, the minimal number of matches, would be appended. Results of two-phase fuzzy optimization with preference intervals of [2550, 12750] or [2550, 8850] for utility, [0, 150], [40, 90] or [40, 70] for flexibility, and [4, 7] for unit numbers, along with either or not considering restrictions on heat loads at extreme operating points, are listed in Table 4. The resulting HEN structures are also depicted in Fig. 2. Notably, the reduced range of flexibility, [40, 90], implies that the required minimum tolerance for temperature deviation is at least 40 K and a tolerance of maximum temperature deviation for 90 K... 

Figure 7.12 Bioisosteric replacement of 2-methylpropionic acid in 7.6. These fragments were suggested by SQUIRRELnovo based on shape matching (mesh) and pharmacophore point scoring (LIQUID fuzzy pharmacophore method). All bioisosteres have been proven to exhibit the desired bioactivity as building-blocks for PPAR agonists.

IV. MATCHING OF MOLECULAR SURFACES WITH FUZZY LOGIC STRATEGIES... 

When an ISNet is matched to its cluster center, it may output a number of topological mappings as illustrated in Fig. 7. The best mapping will be used for the fuzzy graph similarity calculation. 

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