Decision Analysis by Advanced Fuzzy Systems

Human beings live in a world that shows a multitude of phenomena, which can vary continuously Think of colours that can be characterized by wavelengths or frequencies of the real valued electromagnetic spectrum. The development of language has produced an inestimable tool to fmd one’s way in this cosmos of phenomena. For instance, a language offers different words such as red, yellow, green or blue to distinguish colours. Each of these words is used to label an infinite set of different pure colours that belong to a certain interval of the frequency spectrum. Thus, words allow us to handle the huge cosmos of phenomena by dividing it into suitable ‘granules’ where the words can be considered as the labels of the granules (Zadeh, 1997). To continue the example of the colours, it is interesting to note that the language of certain peoples who live in a mainly green environment contains dozens of words to distinguish slightly different kinds of green but no word that summarizes all these green colours. Obviously in the development of languages, the precision of the words that correspond to the granules adapts constantly to changing needs.