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A hybrid construction method based on weight functions to obtain interval‐valued fuzzy relations
Author(s) -
Quirós Pelayo,
Alonso Pedro,
Díaz Irene,
Jurío Aránzazu,
Montes Susana
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3443
Subject(s) - mathematics , smoothing , extension (predicate logic) , fuzzy logic , interval (graph theory) , relation (database) , fuzzy set , membership function , function (biology) , algorithm , fuzzy number , mathematical optimization , weight function , fuzzy set operations , data mining , artificial intelligence , computer science , statistics , combinatorics , evolutionary biology , biology , programming language
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.