APPROXIMATE REASONING BY LINEAR RULE INTERPOLATION AND GENERAL APPROXIMATION

The problem of sparse fuzzy rule bases is introduced Because of the hi gh computational complexity of the original compositional rule of infe rence (CRI) method, it is strongly suggested that the number of rules in a final fuzzy knowledge base is drastically reduced. Various method s of analogical reasoning available in the literature are reviewed. Th e mapping style interpretation of fuzzy rules leads to the idea of app roximating the fuzzy mapping by using classical approximation techniqu es. Graduality, measurability, and distance in the fuzzy sense are int roduced. These notions enable the introduction of the concept of simil arity between two fuzzy terms, by their closeness derived from their d istance. The fundamental equation of linear rule interpolation is give n, its solution gives the final formulas used for interpolating pairs of rules by their alpha-cuts, using the resolution principle. The meth od is extended to multiple dimensional variable spaces, by the normali zation of all dimensions. Finally, some further methods are shown that generalize the previous idea, where. various approximation techniques are used for the alpha-cuts and so, various approximations of the fuz zy mapping R: X --> Y.