Black-box (functional) test cases are identified from functional requirements of the tested system, which is viewed as a mathematical function mapping its inputs onto its outputs. While the number of possible black-box tests for any non-trivial program is extremely large, the testers can run only a limited number of test cases under their resource limitations. An effective set of test cases is the one that has a high probability of detecting faults presenting ina computer program.In this paper, we introduce a new, computationally intelligent approach to automated generation of effective test cases based on a novel, Fuzzy-Based Age Extension of Genetic Algorithms (FAexGA). The basic idea is to eliminate "bad" test cases that are unlikely to expose any error, while increasing the number of "good" test cases that have a high probability of producing an erroneous output. The promising performance of the FAexGA-based approach is demonstrated on testing a complex Boolean expression.