Aggregation of I-transitive fuzzy relations and fuzzy preference relations

To make a better application of I-transitive fuzzy relations and fuzzy preference relations in uncertainty reasoning and decision-making according to the practical requirement, it is meaningful to investigates the preservation of well-known properties when some I-transitive and fuzzy preference relations are aggregated, respectively. Therefore, this paper firstly characterizes the aggregation functions in order to preserve some properties of I-transitive fuzzy relations. Further, two aggregation functions are constructed to preserve some relevant properties of fuzzy preference relations. Especially, focused on the T–S consistency, we further investigate the retainment of some T–S consistent fuzzy preference relations aggregated.