Threshold fuzzy

Approximate transferability of fuzzy density fragments is a key feature of the method, where the fuzzy fragments are custom-made in order to reproduce interfragment interactions. By increasing the size of the interaction shell about each fuzzy density fragment, the error of transferred fragment densities can be reduced below any positive threshold. One tool for this purpose is the Adjustable Density... 

A different approach to threshold selection is based on fuzzy logic [14], By adopting this approach, the value that represents the crisp discriminant between faults and disturbances is replaced by a fuzzy set, characterized by a membership function. Hence, a yes-no decision is replaced by a continuous indication of the faulty level. 

This approach, however, can be generalized for any threshold value a, and one may consider the fuzzy molecular body as being viewed at various density thresholds, for the whole range of possible densities. An infinite family of formal bodies is obtained, and all these formal bodies, collectively, represent the actual molecular body. For each threshold value a, the formal, threshold-dependent molecular body is the density domain DD(a,K), defined as the collection of all those points r of the 3D space where the electronic density is greater than or equal to the threshold a,... 

With minor modifications, the fuzzy electron density membership function formalism of molecular families can also be applied to a family of functional groups within a molecule. Consider a molecule X and some electron density threshold a within the functional group range of density. Consider the functional groups appearing as separate density domains... 

The mapping of T from the subdomain of temperatures onto the interval [0, 1] is the membership or compatibility function fx T). The form of this function is subject to some relatively nonarbitrary constraints to be consistent with one s primitive notions of hotness, fx T) should increase monotonically and smoothly with T, and it should be roughly sigmoidal in shape. However, since a whole family of curves will fit this description, the choice of numerical values for the parameters of fi(T) will to a considerable extent be an arbitrary one. Therefore, the threshold criteria, which are given by fi(T), are themselves fuzzy. 

Consider a set of molecules A,B,C,... with electron densities p (r), pg(r), pc(r)> and level sets G (fl),Gg(fl),Gc(a),respectively, for each density threshold value a. By choosing an appropriate definition for fuzzy membership function describing the fuzzy assignment of points r of the three-dimensional space to each molecule, such as the membership function /x (r) = p. (r)/p of Eq. (20) or = 1 - exp(- rpj(r)) of Eq. (21), the density-scaled fuzzy Hausdorff-type metric f p(A,B) applies... 

FIGURE 1 The fuzzy body of the electron density of a bovine insulin molecule is represented by three molecular isodensity contour surfaces (MlDCOs), for the density thresholds of 0.1, 0.01, and 0.001 a.u. (atomic unit), respectively, as computed using the MEDLA method. Bovine insulin was among the proteins selected for the first ab initio quality electron density computations for macromolecules. ... 

In what follows we show that a fuzzy partition P = A, A2 describes real clusters if and only if for each class / ,/= 1,2, there exists an x such that Aj(x) > and R(P) > t, where t is an appropriate threshold in the interval (0.5,1). We may interpret t as our confidence limit that the detected clusters are real. We consider now a data set X = x x, x, x and a fuzzy partition P = [A, A2 of X having the memberships specified as follows ... 

Key concerns about use of name as the primary means of identification of an individual is that it can have many variations that are difficult to be computationally analyzed so as to declare that two or more records belong to the same individual. Fuzzy logic can be used for searching to increase the matching threshold. 

When applied to our macromolecular sets, we observed no interpenetration for most complexes kept in their crystalline configuration only a few showed some steric clashes - 20 with one bump, nine with two bumps and one with three bumps. Some fuzziness was thus introduced through tolerated interpenetrations. If the number of clashes is less than the tolerance threshold, no bump is considered in the steric penalty score. We decided to set this number to three, according to the results above. To obtain a penalty score that is expressible as per cent, we... 

Lim YW, Lee SU (1990) On the color image segmentation algorithm based tm the thresholding and the fuzzy c-means technique. Pattern Recogn 23(9) 935-952... 

The fuzzy C-mean (FCM) approach (Udupa and Samarasekera 1996 Bezdek 1948) is able to make unsupervised classification of data in a number of clusters by identifying different tissues in an image without the use of an explicit threshold. The FCM algorithm performs a classification of image data by computing a measure of membership, called fuzzy membership, at each pixel for a specified number of classes. The fuzzy membership function, con-... 

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