The linguistic gradient of a fuzzy logic rule-base

We introduce the linguistic gradient operator, a novel concept in fuzzy systems theory. A multiple-input, single-output fuzzy rule-base of the Mamdani type is modeled in a linguistic state space. The consequents of the rules are treated as a function, whose domain is the linguistic state space representing the rule antecedents. The linguistic gradient operator operates on the consequent function, and produces an n-dimensional vector pointing in the direction of the greatest local increase in the rule consequents. Thus, the linguistic gradient shows how a given rule relates to its neighbors in linguistic space. An example demonstrates that the linguistic gradient vector is a linguistic analogue of the classical gradient vector.