Evaluation of inconsistency in a 2-way fuzzy adaptive system using shadowed sets

Our objective in this paper is to evaluate inconsistency for our proposed 2-way fuzzy adaptive system that makes use of intuitionistic fuzzy sets. Uncertainty is modeled as the width of the interval introduced by the independent assignment of membership and nonmembership functions of the intuitionistic fuzzy sets. There is only a consistency constraint in this assignment, violation of which gives rise to inconsistency in the system. The inconsistency model using this fact is reduced through training. There are two phases of training for our proposed 2-way adaptive fuzzy system. The first phase is to reduce inconsistency introduced by the inconsistent assignment of membership and nonmembership functions. The resultant system is a consistent 2-way fuzzy adaptive system. The evaluation of the degree of reduction of inconsistency is carried out at the end of phase I training by forming the shadowed set patterns of the membership and nonmembership functions after training. The shadowed set patterns are first mapped into types of inconsistencies which are further classified according to the global index of fuzziness generated out of the output membership and nonmembership functions. It is seen that the system is able to reduce inconsistency very efficiently