Natural fuzziness

The formal "bodies" of molecules do not have boundaries and the actual shape of molecules is determined by the fuzzy electron distribution. Realistic models describing molecular shapes and chemical bonding must reflect this natural fuzziness [27]. 

Handling natural fuzziness experimental data underlie certain fuzziness that is addressed by Fuzzy Logic and similar techniques. 

Accuracy checks are generally performed by comparing measured data with data from certified reference materials. When measured data are not accurate because of relative or systematic errors, or a lack of precision (noise), the comparison between measured data and reference values cannot lead to any useful conclusion in an expert system. To process larger sets of potential source data for knowledge bases, a method must be used that takes inaccuracies as well as natural fuzziness of experimental data into account — ideally automatically and without the help of an expert. 

Some of the fundamental relations of fuzzy set theory and the actual formulation of fuzzy set methods [59-63] appear ideally suitable for the description of the fuzzy, low-density electron distributions [64. A molecular electron density exhibits a natural fuzziness, in part due to the quantum mechanical uncertainty relation. Evidently, a molecular electron distribution, when considered as a formal molecular body, is inherently fuzzy without any well-dehned boundaries. A molecule does not end abruptly, since the electron density is gradually decreasing with distance from the nearest nucleus, and becomes zero, in the strict sense, at infinity. In fact, the same consideration has been the motivation for the compactihcation technique described in the proof of the holographic electron density theorem. For a correct description of molecules, the models used for electron densities must exhibit the natural fuzziness of quantum chemical electron distributions [64. ... 

The properties of fuzzy logic make it suitable for application within the conducted research presented in the work at hand. The cause-and-effect chain between an SCI and revenues is determined by the value driver customer satisfaction and, thus, is of a qualitative nature. Fuzzy logic makes it possible to utilize practical knowledge, which is based in this context in marketing, sales and logistics, to gain a quantifiable relationship. Thus, the technique of fuzzy logic is employed in a model for the determination of an SCTs revenue contribution. ... 

The way the chemist knows that she has methylamine and not ammonium chloride is that she compares the look of the two types of crystals. Ammonium chloride crystals that come from this reaction are white, tiny and fuzzy. The methylamine hydrochloride crystals are longer, more crystalline in nature and are a lot more sparkly. The chemist leaves the methylamine crystals in the Buchner funnel of the vacuum filtration apparatus and returns the filtrate to the distillation set up so it can be reduced one last time to afford a second crop. The combined methylamine hydrochloride filter cake is washed with a little chloroform, scraped into a beaker of hot ethanol and chilled. The methylamine hydrochloride that recrystallizes in the cold ethanol is vacuum filtered to afford clean, happy product (yield=50%). 

The second aspect is more fundamental. It is related to the very nature of chemistry (quantum chemistry is physics). Chemistry deals with fuzzy objects, like solvent or substituent effects, that are of paramount importance in tautomerism. These effects can be modeled using LFER (Linear Free Energy Relationships), like the famous Hammett and Taft equations, with considerable success. Quantum calculations apply to individual molecules and perturbations remain relatively difficult to consider (an exception is general solvation using an Onsager-type approach). However, preliminary attempts have been made to treat families of compounds in a variational way [81AQ(C)105]. 

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... 

Some types of knowledge-based systems may make judgments based on data that contain uncertainty we shall learn more of this in the next chapter when we encounter fuzzy systems. Even when the information that the system reasons with is unambiguous, the system s conclusions may come as a surprise to a nonexpert. If the user doubts whether the ES has reasoned correctly, it is natural for them to seek reassurance that the line of reasoning used is robust, so the ES must be able to do more than merely provide advice, it should be able to explain how it has reached a particular conclusion. 

Naturally, this advice is of no use at all, but fortunately there is help at hand in the form of fuzzy logic, which provides a way to reason from vague information. 

Suppose that we have defined a membership function for the "Low pH" set. Most acid solutions would be, to some degree, members of this fuzzy set. We may want to be able to qualify the description by adding modifiers, such as "very," "slightly," or "extremely" whose use allows us to retain close ties to natural language. The qualifiers that modify the shape of a fuzzy set are known as hedges. We can see the effect of the hedges "very" and "very very" in Figure 8.11. 

Van Regenmortel, M. FI. V. (1998), From absolute to exquisite specificity. Reflections on the fuzzy nature of species, specificity and antigenic sites , J. Immunol. Meth., 216, 37-48. 

Evaluation of the concept of mental illness suggests that there are other aspects of its definition that create variability. Lilienfeld and Marino (1995) stated that there has always been great difficulty in establishing the boundary between mental illness and normalcy. These authors suggested that we need to accept this fuzzy boundary as a necessary condition of mental illness. They argued that mental illnesses should be considered open concepts (Meehl, 1977) or Roschian concepts (Rosch, 1973). A Roschian concept is essentially the same as the open concept we have already defined. It is a mental construction used to categorize natural entities that are characterized by fuzzy boundaries. Lilienfeld and Marino argued that this conception of... 

If the virus is treated with proteolytic enzymes the fuzzy layer formed by the viral spikes is removed (Osterrieth, 1965 Compans, 1971 Gahm-berg et al, 1972 Sefton and Gaffney, 1974 Utermann and Simons, 1974). Remnants of both El and E2 are left in the bilayer. These have a hydrophobic amino acid composition, and are soluble in lipid solvents such as chloroform-methanol. The amphiphilic nature of the spike protein is also evident from its capacity to bind Triton X-100 (0.6 g/g protein) which binds to the hydrophobic part to form a water-soluble protein-detergent complex (Simons et al., 1973a). The ability of amphiphilic proteins to bind Triton can be used to separate them from hydrophilic proteins using an extraction procedure recendy described... 

DE Quadros, T.F.P., Koppe, J.C., Strieder, A.J., Costa, J.F.C.L. 2006. Minerai-Potentiai Mapping A Comparison of Weights-of-Evidence and Fuzzy Methods. Natural Resources Research, 15, 49-65. 

Early efforts in what could be termed polymer informatics go back to an ACS symposium on polymer nomenclature in the late 1960s [46-51]. Papers in this symposium were mainly concerned with issues of polymer nomenclature and aspects of information retrieval. A first set of seminal papers only appeared about a decade later, as a consequence of another ACS symposium on the retrieval of polymer information in 1978 [52-59]. Collectively, the papers resulting from the 1978 symposium set out the challenges still faced by polymer informatics today the fuzzy nature of polymers and the variety of different types of descriptions and representations of polymers arising as a consequence, the problem of information... 

The little man, or homunculus, as it was sometimes called, was imaginative, of course—the mind sometimes creates such illusions when examining an object too small or fuzzy to be clearly seen. The notion that the microscopic world consisted of familiar objects reduced to a small scale was also incorrect. As scientists probed the nature of particles, they realized that the behavior of small objects does not necessarily mimic larger ones. This discovery opened up new vistas in science as well as technology, including the subject of this chapter—technology on the scale of atoms and molecules. 

O Dowd CD, Facchini MC, Cavalli F, Cebumis D, Mircea M, Decesari S, Fuzzi S, Yoon YJ, Putaud J-P (2004) Biogenically Driven Organic Contribution to Marine Aerosol. Nature 431 676... 

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