Fuzzy Concepts

Sustainable development is a fuzzy concept. As a concept, however, it meets the needs of the present without compromising the needs of future generations (Morse, 1998). From a business perspective, sustainable development is often separated into three interdependent areas economic, environmental, and social. 

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 ... 

Aromatic molecules play a central role in organic chemistry and, although a somewhat fuzzy concept that eludes definition in terms of clear-cut experimental... 

Aromaticity is one of a number of remarkably important but fuzzy concepts in chemistry that does not lend itself easily to widely applicable clear-cut definitions. One of the more recent attempts to summarise what chemists with dilferent backgrounds see in this term was made by Schleyer. Valence bond theory has been, since Kekule s times, a major source of qualitative and quantitative interpretations of aromaticity, and it is surprising that it has not been mentioned, even once, in Schleyer s editorial. Of course, this omission does not diminish the importance that VB methods have had and still have in providing easy-to-understand ideas about aromatic behaviour which are often markedly superior to those coming from other theoretical sources. In order to justify this claim from a current perspective, in this section we look at the recent VB studies of the aromaticity of a series of benzenelike rings, and of clamped benzenes. 

The ranking of chiral systems such as the foregoing by their structures and associated properties is intuitively obvious, and is arrived at independently of any theory that accounts for these properties. For this reason we are led to the conclusion that chirality in a real system is a primitive fuzzy concept. ... 

Fig. 8 Fuzzy rules for controlling a fan heater based on fuzzy concepts of room temperature (COLD, COOL, WARM, HOT).

Congenericity is a fuzzy concept related to the structures of the molecules of the studied dataset. With respect to some defined molecular structural characteristics, chemical analogues can be considered congeneric compounds, their structural differences being the interesting part of the study. Mono-substituted benzenes, polychlorobiphe-nyls, triazines, and poly-aromatic hydrocarbons are all examples of congeneric datasets. 

Branching of a graph is a fuzzy concept which can be based on the presence in the graph of vertices with degrees equal to three or higher. 

For example, we say that an atom is "happy" when it has a full octet of elecctrons. In casual conversation, this gets a point across, but it is not appropriate in rigorous scientific terms, for example, on exams. Under more formal conditons, we are expected to use the specific terms of science because they are well defined and do not permit sloppy or fuzzy concepts. 

The idler performance is a fuzzy concept which follows fuzzy comprehensive evaluation method and the performance level factor set can be established. Factor sets are composed by the elements which affect the values of the variable factors. Components quality, manufacturing process and key performance are three factors which are selected for evaluation system of idler performance level. 

The simplest expression for describing the essence of structural changes occurring in a reaction is the record of the reaction skeleton graph (RSG) including all the bonds altered by a specific reaction together with the atoms involved. The concept of RSG roughly equivalent to the traditional more or less fuzzy concept of reaction site, or... 

Chen, T. and Wang, M., 1999. Forecasting methods using fuzzy concepts. Fuzzy Sets and Systems, 105(3), 339-352. 

Actually, we are not really sure whether it is metastable or unstable. The reaction between water and anhydrite to form gypsum is probably very, very slow at 25 °C, but much faster at slightly higher temperatures. This is an example of the discussion in 4.9.1. Metastable is a rather fuzzy concept in geology, but crystal clear in thermodynamics. 

Although human wonder and mind are the sources of fuzziness, they also serve overcoming problems with human experience, which can be regarded as expert views. The fuzzy concepts in understanding complex problems are dependent on observations, experiences and conscious expert views. When problems are solved, there is always fuzziness attached to them, which paves ways for future developments. Hence, the scientific solutions cannot be taken as absolute truths in positivistic manner. 

The fuzzy concepts in problem nnderstandings that emerge out of life complexity as it unfolds cannot be resolved at the same level of knowledge that one has when these problems appear. Only when our consciousness is expanded to a higher level than the tension fades away and the problems, being seen in a new light, are no longer problems. When problems dissolve, one can say that the fuzziness related to them has been transcended. 

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