A novel approach for generalizing weighted averages for trapezoidal interval type-2 fuzzy sets

Interval type-2 fuzzy sets are used to deal with the uncertain information present when more than one fuzzy observation can be made about the same entity. They found numerous applications in engineering recommendation systems, fuzzy control and modeling, pattern recognition and other. The paper presents a novel approach for generalizing weighted averages on purpose of processing uncertainty expressible by trapezoidal interval type-2 fuzzy sets. A family of new aggregation operators is presented, that can process data types specific for perceptual computing, and thus can be used as an engine for computing with words. It has time complexity θ(n). Some software realization details are discussed. The new engine family has been compared to novel weighted averages both analytically and empirically. Their similarities and differences are pointed out and rationalized. It has been discussed how simplified versions of the new engine resemble to some known type-reduction algorithms. Conclusions and open questions are summarized.