Improved Karnik-Mendel algorithm: Eliminating the need for sorting

In this paper a novel type reducer for interval type-2 fuzzy systems is proposed. Type reduction of interval type-2 fuzzy systems requires the solution of two nonlinear constrained optimization problems. Existing exact solutions to these problems (Karnik-Mendel algorithms and their variants) require sorting which is known to be computationally very expensive. In this research, these optimization problems are reformulated and novel improved solutions to these problem are proposed which do not require sorting any more. Simulation results show that the results obtained using the proposed methods are exactly the same as that of enhanced Karnik-Mendel algorithms with at least 9% less computational time when the number of rules of fuzzy system is bigger than ten. For more number of rules, it is even possible that the proposed methods converge 37% faster than enhanced Karnik-Mendel algorithms. In addition, it is shown that the computational time required by the proposed methods grow linearly as the number of the rules increases.