An investigation of the effects of fuzzy resolution on control inference using explicit relationships

The number of partitions or fuzzy states that exist in a fuzzy variable determines the resolution of that variable. This paper investigates the effect of fuzzy resolution on the control action that is derived from a fuzzy-control rulebase. First, it is shown that some explicit relationships could be derived for the inference from a fuzzy rulebase in terms of input variables and known geometry of the membership functions. These relationships are established for a generic, single-input-single-output (SISO) fuzzy control rulebase that employs uniform triangular membership functions. Specifically, a formula for control action u is derived in terms of incremental input variable and corresponding membership grades and fuzzy resolution. The result is then extended to include global variations of the input variable. It is argued that the resulting equations could be used to demonstrate the applicability of fuzzy control rules in a wide variety of control situations. Also some useful properties that arise from these equations are identified