The Tellez-Molina-Villa algorithm

The Tellez-Molina-Villa (TMV) algorithm is a new defuzzification method for interval type-2 fuzzy systems. It is based on found the mean trajectory of any interval type-2 fuzzy set. With the mean trajectory we pretend to find the type-1 reduced fuzzy set of the interval type-2 fuzzy set. With this algorithm we try to find the generalized centroid of any interval type-2 fuzzy set. Also, we try to increase the type-2 fuzzy logic system accuracy. In general we found from 5 defuzzification methods that try to extract a crisp value from an interval type-2 fuzzy set as a representative value. First is necessary to obtain a type-1 fuzzy set from the type-2 fuzzy set, second from this reduced fuzzy set obtain a single crisp value. This crisp value represents lot of information, so that is necessary to do these steps carefully because we can obtain misinformation from the type-2 fuzzy inference system. In this paper we present some result from the new algorithm, and in order to compare the TMV algorithm we present comparative results with 5 type-2 defuzzification methods. From the obtained results we demonstrated that the TMV approach performs better that the Nie-Tan method. In fact, we can say that the TMV algorithm has at least equivalent results than Karnik-Mendel algorithm that in our opinion is one of the best defuzzification methods, but with the difference that the TMV algorithm is based on the mean trajectory of an interval type-2 fuzz set.