Some Results on Fuzzy Theory

The apparition of Fuzzy Logic has had a double repercussion on scientific research, and has provoked two types of reactions. From a theoretical point of view, it is indeed a very useful generalization of the classical Set Theory proposed by Boole and Cantor, in this way making possible our analysis of uncertainty. But unfortunately, in his first steps it had to avoid the assaults of routine minds from the often too rigid mathematical field. This situation improved later, especially in nations with less deep-rooted prejudices. And by contrast, the new theory has obtained a strong rooting in nations with new and increasing scientific potential, such as China, Japan, and South Korea. More recently it has also become rooted in European countries, such Hungary, Spain, and Romania, mainly due to its successful technical applications. We analyze some essential aspects of this new and powerful tool of Mathematical Analysis.