Backward-chaining with fuzzy `if. . . then. . .´ rules

The authors consider the issue of backward-chaining when using fuzzy if-then rules. Usually, forward-chaining is used to induce new information, given a set of rules and a set of data. However, backward-chaining is more efficient when one wants to check whether a given fact holds. A mathematical formulation of the problem in the case of finite and continuous universes of discourse is given, and a method is outlined to solve the problem. An interpretation is given of the different possible solutions, and the problem of the choice of a particular solution is considered. As the method is very sensitive to the given goal, in the case in which no solution can be found the extent to which it is possible to modify the initial problem to find an approximate solution is examined. Some results relative to finite sets are generalized to the case of continuous sets