Mathematical Approach to Vagueness

From 1920, when Lukasiewicz established the 3-valued logic, many other versions have been made, with the purpose of improving or generalizing the precedent system. Fuzzy Logic departs from the multi-valued logic point of view, with real truth values in the closed unit interval. Our paper deals, basically, with analogies and differences between fuzzy and rough characters. Therefore, it belongs to a relatively new field: Fuzzy/Rough Mathematical Analysis. The Fuzzy Theory was initiated by Lofti A. Zadeh, in 1965, and the Rough Theory by Zdzislaw Pawlak, in 1981-82. As general purpose, to obtain a way to model flexible restrictions constructed from vague pieces of information. From then, great advances have followed, not only in theoretical aspects, but in applications. We attempt to give a clear vision of the foundations and applications of such very related, but essentially different, theories. Mathematics Subject Classification: 03E72, 94D05, 93C41, 68727