*Number of sub-sets:* Ranges of process measurements and outputs will be divided into subsets. Specifying the number of subsets is part of the design. The example in the ‘Fuzzification function’ graphic used only three conditions: low, normal, and high. But this may not provide sufficient resolution. Taken further, the family of subsets m

ight include very low, low, normal, high, and very high. Even more subsets could be used.

Variables, such as errors, that can be both positive and negative will need subsets for both signs, and one for zero as well. The number of subsets does not have to be symmetrical around zero, if measurements deviate from set point more in one direction than the other.

If the number of subsets is inadequate, and they do not overlap, then it will be possible for small variations to exist without generating a response from the control system. This creates a situation equivalent to hysteresis in final actuators and can result in constant cycling by the control system. When this occurs in a process with multiple interactions, oscillations in one variable can be passed into many other variables in the system.

*Ruleset structure:* Defining more subsets provides more resolution for decision-making, but the number of logical possibilities increases according to the rules of combinations and permutations. For example, if temperature and flow rate each have five subsets, so that each single value has a degree of membership in five subsets, then there are 25 possible combinations which the rule structure may need to address. Add another variable with five subsets, and the number of possible situations requiring rules increases to 125.

On the output side, the range for control output signals also will be divided into subsets. If each of three control outputs is divided in