A hybrid construction method based on weight functions to obtain interval‐valued fuzzy relations
Pelayo Quirós, Pedro Alonso, Irene Dı́az, Aránzazu Jurío, Susana Montes · Mathematical Methods in the Applied Sciences · 2015
Interval‐valued fuzzy sets are an extension of fuzzy sets and are helpful when there is not enough information to define a membership function. This paper studies the behavior of a construction method for an interval‐valued fuzzy relation built from a fuzzy relation. The behavior of this construction method is analyzed depending on the used t‐norms and t‐conorms, showing that different combinations of them produce a big variation in the results. Furthermore, a hybrid construction method that considers weight functions and a smoothing procedure is also introduced. Among the different applications of this method, the detection of edges in images is one of the most challenging. Thus, the performance of the proposal in detecting image edges is tested, showing that the hybrid approach that combines weights and a smoothing procedure provides better results than the non‐weighted methods. Copyright © 2015 John Wiley & Sons, Ltd.