Made available in DSpace on 2015-03-03T15:47:46Z (GMT). No. of bitstreams: 1 ClaudioACO_DISSERT.pdf: 456086 bytes, checksum: 05ce54b27a831e1c5708083e2231bc35 (MD5) Previous issue date: 2012-02-13 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / In order to make this document self-contained, we first present all the necessary theory as a background. Then we study several definitions that extended the classic bi-implication in to the domain of well stablished fuzzy logics, namely, into the [0; 1] interval. Those approaches of the fuzzy bi-implication can be summarized as follows: two axiomatized definitions, which we proved that represent the same class of functions, four defining standard (two of them proposed by us), which varied by the number of different compound operators and what restrictions they had to satisfy. We proved that those defining standard represent only two classes of functions, having one as a proper subclass of the other, yet being both a subclass of the class represented by the axiomatized definitions. Since those three clases satisfy some contraints that we judge unnecessary, we proposed a new defining standard free of those restrictions and that represents a class of functions that intersects with the class represented by the axiomatized definitions. By this dissertation we are aiming to settle the groundwork for future research on this operator. / A fim de tornar este documento auto-suficiente, n?s apresentamos toda a teoria necess?ria como arcabou?o te?rico. Em seguida, estudamos v?rias defini??es que estenderam a bi-implica??o cl?ssica para o dom?nio da bem estabelecida l?gica difusa, ou seja, no intervalo [0; 1]. Essas abordagens da bi-implica??o difusa podem ser resumidas da seguinte forma: duas defini??es axiomatizadas, que demonstramos que representam a mesma classe de fun??es, quatro padr?es definit?rios (dois deles proposto por n?s), que variam com o n?mero de diferentes operadores que as comp?em e quais restri??es que tinham para satisfazer. N?s demonstramos que esses padr?es definit?rios representam apenas duas classes de fun??es, tendo uma como uma subclasse pr?pria da outra, mas sendo ambas subclasses da classe representada pelas defini??es axiomatizadas. Uma vez que esses tr?s clases satisfazer algumas restri??es que julgamos desnecess?rias, propusemos um novo padr?o definit?rio sem essas restri??es e que representa uma classe de fun??es que se interseta com a classe representada pelas defini??es axiomatizadas. Nesta disserta??o estamos pretendendo estabelecer as bases para futuras pesquisas sobre este operador