Summary: Initially, an axiomatic definition of fuzzy implication has been recalled. Next, several important fuzzy implications and their properties have been described. Then, the idea of approximate reasoning using generalized modus ponens and fuzzy implication are considered. After reviewing well-known fuzzy systems, a new Artificial Neural network Based on Logical Interpretation of if-then Rules (ANBLIR) is introduced. The elimination of non-informative part of final fuzzy set before defuzzification plays the pivotal role in this system. The application of ANBLIR to recognition of non-insulin-dependent diabetes mellitus in Pima Indians is shown.