On linguistic representation of quantitative dependencies

A description of quantitative dependencies by a novel type of fuzzy rules like 'If X is SMALL then Y is QUICKLY INCREASING' is considered. The use of such rules for representation of perception based and numerical information about dependencies between variables is discussed. These rules are based on a granulation of directions of function change or slope values. Perception based information given by rules is represented by a fuzzy function Y(X). A method of solution of a fuzzy equation Y(X) = B is considered. A linguistic representation of given numerical information about dependencies between variables X and Y is based on a fuzzy partition of the domain of X on fuzzy intervals, on a linear approximations of data on these intervals and on a linguistic retranslation of results. A genetic algorithm is used for obtaining fuzzy partitions. In conclusion, the possible applications of proposed methods in petroleum industry are discussed.