Aggregation of fuzzy metrics and its application in image segmentation

This paper proposes a novel method for the construction of a fuzzy metrics and demonstrates application in image segmentation. Some new properties of t-norms, t-conorms, aggregation functions, and fuzzy metrics are proved, which provides the procedures for constructing a new fuzzy metric. We prove that by applying some types of t-norms, t-conorms and aggregation functions on the sequence of fuzzy metrics, a new fuzzy metric could be obtained. The application of the fuzzy metric constructed in this way is illustrated in image segmentation by using the \textsf{FCM} algorithm. For the purpose of constructing a new fuzzy metric, an extended aggregation function called generalized quasi-arithmetic mean is considered.