Restudy of Intuitionistic Fuzzy Relations

The notions of kernel and closure of intuitionistic fuzzy relations are proposed, and fourteen-sets theorem of intuitionistic fuzzy relations is proved. First, we propose the notions of anti-reflexive kernel, symmetric kernel, reflexive closure and symmetric closure of intuitionistic fuzzy relations by intuitionistic fuzzy anti-reflexive relations, symmetric relations and reflexive relations. Second, their accurate formulae and some properties are respectively obtained by utilizing some properties of intuitionistic fuzzy relations. Last, we conclude that fourteen different intuitionistic fuzzy relations can be constructed at most by using these properties via symmetric kernel operator, symmetric closure operator and complement operator from an intuitionistic fuzzy relation.