TRANSITIVE OPENING OF FUZZY SIMILARITY RELATION
Guannan Deng · Journal of Beijing Normal University · 2010
The transitive closure of fuzzy similarity relation R is the smallest fuzzy equivalent relation that contains R.From a symmetrical point of view,it is natural to ask for the largest fuzzy equivalence relation being contained by R,that is transitive opening.Focus on transitive opening,some of its basic properties were proposed,existence and non-uniqueness of transitive opening were proved.In addition,relationship between transitive opening and transitive closure were compared,localizations of transitive opening and transitive closure in fuzzy clustering were indicated.