【正文】 example, squares membership functions。 since the membership values are always less than 1, this narrows the membership function. Extremely cubes the values to give greater narrowing, while somewhat broadens the function by taking the square root. In practice, the fuzzy rule sets usually have several antecedents that are bined using fuzzy operators, such as AND, OR, and NOT, though again the definitions tend to vary: AND, in one popular definition, simply uses the minimum weight of all the antecedents, while OR uses the maximum value. There is also a NOT operator that subtracts a membership function from 1 to give the plementary function. There are several ways to define the result of a rule, but one of the most mon and simplest is the maxmin inference method, in which the output membership function is given the truth value generated by the premise. Rules can be solved in parallel in hardware, or sequentially in software. The results of all the rules that have fired are defuzzified to a crisp value by one of several methods. There are dozens in theory, each with various advantages and drawbacks. The centroid method is very popular, in which the center of mass of the result provides the crisp value. Another approach is the height method, which takes the value of the biggest contributor. The centroid method favors the rule with the output of greatest area, while the height method obviously favors the rule with the greatest output value. The diagram below demonstrates maxmin inferring and centroid defuzzification for a system with input variables x, y, and z and an output variable n. Note that mu is standard fuzzylogic nomenclature for truth value: Fuzzy control system design is based on empirical methods, basically a methodical approach to trialanderror. The general process is as follows: the system39。s operational specifications and inputs and outputs. the fuzzy sets for the inputs. the rule set. the defuzzification method. through test suite to validate system, adjust details as required. document and release to production.Logical interpretation of fuzzy controlIn spite of the appearance there are several difficulties to give a rigorous logical interpretation of the IFTHEN rules. As an example, interpret a rule as IF (temperature is cold) THEN (heater is high) by the first order formula Cold(x)→High(y) and assume that r is an input such that Cold(r) is false. Then the formula Cold(r)→High(t) is true for any t and therefore any t gives a correct control given r. Obviously, if we consider systems of rules in which the class antecedent define a partition such a paradoxical phenomenon does not arise. In any case it is sometimes unsatisfactory to consider two variables x and y in a rule without some kind of functional dependence. A rigorous logical justification of fuzzy control is given in H225。jek39。s book ,where fuzzy control is represented as a theory of H225。jek39。s basic logic. Also in Gerla 2005 a logical approach to fuzzy control is proposed based on the following idea. Denote by f the fuzzy function associated with the fuzzy control system, ., given the input r, s(y) = f(r,y) is the fuzzy set of possible outputs. Then given a possible output 39。t39。, we interpret f(r,t) as the truth degree of the claim t is a good answer given r. More formally, any system of IFTHEN rules can be translate into a fuzzy program in such a way that the fuzzy function f is the interpretation of a vague predicate Good(x,y) in the associated least fuzzy Herbrand model. In such a way fuzzy control bees a chapter of fuzzy logic programming. The learning process bees a question belonging to inductive logic theory.