As with the S&P 500 or the Wilshire 5000 for traded companies, or even more recently the Sandhill Index for Venture Capital in non traded operations, indexes are helpful to benchmark the performance of a company.
There is an impressive activity worldwide in privatization matters, in sectors as water, gas, power, telecoms, airports, ports, banks, prisons, health, education, railways or toll roads for example. It is easy to understand that the use for benchmarking this information could be high in order to compare sectors (about 12 ) in different countries (about 40 active ones), that is more than 500 combinations of markets.
The instrument used to establish the algorithm base of this article is the Experton, a perfect tool set up by Kauffman to capture the opinion of experts on a matter. Gil Aluja in Spain (proposed once for the Nobel Economy prize) has been the developper of such an instrument to the economic world.
Richard Onses started using the Fuzzy Logics for its Doctorate Thesis in Economy about Determinatin of the Uncertainty in South American Investments with Fuzzy Logic Mathematics. This instrument started in 1965 with the discovery by Zadeh (Berkeley, basically in order to calculate the movement of an electron in the atom) of the Fuzzy Logic concept, then Sambuc (Aplication of diagnostic in Tyroidian Pathology) introduced the concept of Phi-Logic, an then Féron and Hirota the probabilistic Sets. Kaufman mixed it with the Moore works on intervals of confidence, creating the Experton. Richard Onses added to this experton a third dimension, that is the Experton of Order 2 (Sous Ensemble Aléatoire Flou de Type 2 (Experton) et d´Ordre 2).
The fact is that the algorithm is useful to determine for each country and each company a certain number of caracteristics, which are evaluated with ranges of confidence by experts. Then the expert opinions (Subsets) are combined (Probabilistic sets) and may be added and combined as numbers (each fuzzy number is equal to thousands of combinations). Theses Expertons have inside all the fuzziness of a brain evaluation, also named grey numbers: a rose may be red, very red , more pink than red, etc…The second order experton is used then to allow the operations keeping the fussiness until the very last moment when it is decide to shut of the process and eliminate the entropy getting a final classification between all the elements (companies, countries..).
Fuzzy Logic is an instrument that allows very quick decisions as it works with ranges. For example, it is used in the guidance system of the Tomawak style missiles to compare a route with the profile given by the camera on board. Something basically fuzzy may give in fact a very precise decision.
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