Potential fuzziness

Any formal models of the conduct of research work and success are often soft or fuzzy in nature, and so may be distrusted by those used to hard evidence. There is a particular distrust of opaque, black box solutions, and numerate managers rightly demand to see the detailed assumptions made in any decision analysis. The most controversial assumptions tend to be those about project future costs, chance of success, and potential value within drug... 

Most AI methods used in science lie within one of three areas evolutionary methods, neural networks and related methods, and knowledge-based systems. Additional methods, such as automated reasoning, hybrid systems, fuzzy logic, and case-based reasoning, are also of scientific interest, but this review will focus on the methods that seem to offer the greatest near-term potential in science. 

In order to prepare the final multi-class predictor map, the input weighted layers are fused using various Fuzzy operators (Fig. 5). Figure 6 is a reclassified final Fuzzy map, predicting the high potential areas for further drilling at East-Kahang. To validate the accuracy of the Fuzzy model, the projected Cu values of the completed drill holes are overlain on the final predictive map. The results show... 

Fig. 6. Fuzzy potential priority map at East-Kahagn deposit.

SCIL sorbents are a rapidly emerging alternative in LC that are poised to address the critical need for novel and more universal separation strategies. These novel sorbent materials present unique potential separation capabilities applicable to a broad range of compounds (e.g., polar organics and biomolecules/biopolymers). Specific feafures of fhese sorbents which allow for this unique separation capability include the presence of a fuzzy ion with a delocalized charge which can promote interactions with neutral aromatic species, a scaffold for introducing additional functionality, and ion-exchange capability with potentially tunable hydrophobicity. 

Artificial neural networks (ANNs) emulate some human brain characteristics, such as the ability to derive conclusions from fuzzy input data, the capacity to memorise patterns and a high potential to relate facts (samples). If we examine carefully those human (animal) abilities, they share a common basis they cannot be expressed through a classical well-defined algorithm rather, they are based on a common characteristic experience. Humans can solve situations according to their accumulated experience, rather on a conscious and strict reasoning procedure. 

This is, of course, a very Terra-centric categorization, but so far we only have the unitary example of Earth from which to draw examples. Furfaro et al. (2007) have developed a fuzzy-logic-based scheme that goes more toward the fundamentals of coupled physical/biological planetary systems, but still it takes a restricted view oriented toward Mars- and Earth-like planets. It is entirely possible that Earth has a thin biospheric veneer compared to potentially more massive biospheres on worlds with deep ice-covered oceans such as Europa we just don t know. 

Fuzzy clustering methods that have recently become popular are distinct from traditional clustering techniques in that molecules are permitted to belong to multiple clusters or have fractional membership in all clusters. A potential advantage of such classification schemes is that more than one similarity relationship can be established by cluster analysis. 

A molecule contains a nuclear distribution and an electronic distribution there is nothing else in a molecule. The nuclear arrangement is fully reflected in the electronic density distribution, consequently, the electronic density and its changes are sufficient to derive all information on all molecular properties. Molecular bodies are the fuzzy bodies of electronic charge density distributions consequently, the shape and shape changes of these fuzzy bodies potentially describe all molecular properties. Modern computational methods of quantum chemistry provide practical means to describe molecular electron distributions, and sufficiently accurate quantum chemical representations of the fuzzy molecular bodies are of importance for many reasons. A detailed analysis and understanding of "static" molecular properties such as "equilibrium" structure, and the more important dynamic properties such as vibrations, conformational changes and chemical reactions are hardly possible without a description of the molecule itself that implies a description of molecular bodies. 

To accomplish the above two major developments were made in the CAE programs. One development was the application of fuzzy logic in expert software to examine mold-filling simulations for potential... 

When a molecule takes part in a reaction, it is properties at the molecular level which determine its chemical behaviour. Such intrinsic properties cannot be measured directly, however. What can be measured are macroscopic molecular properties which are likely to be manifestations of the intrinsic properties. It is therefore reasonable to assume that we can use macroscopic properties as probes on intrinsic properties. Through physical chemical models it is sometimes possible to relate macroscopic properties to intrinsic properties. For instance 13C NMR shifts can be used to estimate electron densities on different carbon atoms in a molecule. It is reasonable to expect that macroscopic observable properties which depend on the same intrinsic property will be more or less correlated to each other. It is also likely that observed properties which depend on different intrinsic properties will not be strongly correlated. A few examples illustrate this In a homologous series of compounds, the melting points and the boiling points are correlated. They depend on the strengths of intermolecular forces. To some extent such forces are due to van der Waals interactions, and hence, it is reasonable to assume a correlation also to the molar mass. Another example is furnished by the rather fuzzy concept nucleophilicity . What is usually meant by this term is the ability to donate electron density to an electron-deficient site. A number of measurable properties are related to this intrinsic property, e.g. refractive index, basicity as measured by pK, ionization potential, HOMO-LUMO energies, n — n ... 

In discussing and drawing pictures of orbitals, there s potential for confusion in that you might think that if you were small enough to look at an atom directly, you would actually see these fuzzy shapes. Not so. Orbitals represent possible locations of electrons, not a physical thing. This idea is similar to drawing the orbits of the planets around the Sun. We draw those lines to represent the paths of planets, but those lines don t really exist in space. In the same way, atomic orbitals don t exist as physical things but rather are mathematical representations of where we are likely to find electrons. 

As is well known, fuzzy sets are holistic concepts, each representing a potentially infinite family of nested crisp sets (a-cuts), each defined for a particular number (a) in the unit interval. When we operate on fuzzy sets, we operate in fact simultaneously on all crisp sets in the associated families. This is quite powerful, both conceptually and computationally. 

Here the research statistics got fuzzy and perhaps a little creative to demonstrate the hypothesis that psilocybin therapy was effective in reducing the crime rate. In their paper published in Psychotherapy Theory, Research and Practice (Leary et al. 1965), the researchers broke the numbers down into types of return due to parole violations and due to new crimes. They found that, compared to a 50/50 incidence in the prison population as a whole, only 7% of project participants were returned for new crimes, with 52% returned for parole violations. One and one half years after termination of the program the rate of new crimes has been reduced from 28% to 7%, although if parole violations are counted the overall return rate has not changed. It is proposed that these results warrant further research into the potentials of the methods used, especially since no other method of reducing the crime rate exists. (Leary et al. 1965 Doblin 1998). 

---