Our objective in this paper is to model and reduce inconsistency in expert knowledge for our proposed 2-way adaptive fuzzy system that makes use of intuitionistic fuzzy sets. Intuitionistic fuzzy sets model an interval valued distribution of information in the adaptive control architecture with the necessity at the lower bound as the degree of membership functions and the possibility at the upper bound as the complement of the degree of nonmembership functions. Uncertainty is modelled as the width of this interval. A width of zero is at the basis of a deterministic control. The use of intuitionistic fuzzy sets brings a flexibility in the system since it is possible to assign control upper bounds (nonmembership functions) independently from control lower bounds (the membership functions). There is only a consistency constraint on this assignment, which is that the sum of the two functions should be less than or equal to unity. However, in many control problems, this inequality constraint is not satisfied giving rise to inconsistency. The proposed 2-way adaptive fuzzy system is subject to training for the adjustment of parameters. The training of adaptive fuzzy systems was originally applied to supports of rule propositions with single distribution such that they can be termed 1-way adaptive. The novelty in our approach is due to the additional training required for the adjustment of the parameters of the nonmembership functions. Moreover, our proposed system is subject to two phases of training. The first phase of training is necessary in order to obtain a consistent 2-way adaptive fuzzy control system by reducing optimally any inherent inconsistencies. The purpose of the second phase is to reduce the uncertainty defined as the width introduced by the independent assignments of membership and nonmembership functions. The resultant system is a one-way fuzzy adaptive system without inconsistency and without uncertainty.
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