Reasoning with truth values on compacted fuzzy chained rules

In this paper, we consider the problem of executing a fuzzy knowledge base (FKB) with rule chaining, The inference process used as starting point is the one based on forward reasoning functions which, obtained from the compositional rule of inference, permits performing the execution of rules in the truth space, This way the process is totally independent from the universes of discourse in which the different variables are defined, allowing a homogeneous treatment for all the variables in the FKB. The execution of the rules is interpreted as the "propagation" of linguistic truth values of the linguistic truth-variable that reflect the linguistic degree of fulfillment of each of the propositions in the rules, This execution process is analyzed in two fields of application: control systems, where it is customary to assume t-norm operators as implication functions, and the aggregation process is implemented through the maximum operator and expert systems applications, where other implication functions may be needed and t-norm operators are generally used as aggregation operators. For both of these situations, we present a compaction mechanism which allows a noticeable part of the operations to be performed a priori, thus achieving an important computation time saving. Besides, a parameterization for both processes is used, allowing the FKB execution process to be performed through simple operations involving single numerical values (and this way no possibility distributions are directly involved). Through this double mechanism, the computational load of the inference process in FKBs with chaining is considerably reduced.