Gradual Complex Numbers, local order and local aggregations
Gradual Numbers, Gradual Complex Numbers, Machine Learning, Aggregation Operator, Local Order
Aggregations are functions that have the ability to combine multiple objects into a single object of the same nature. Minimum, maximum, weighted average and arithmetic mean, are examples of aggregations frequently used in everyday life which have several possibilities for applications. However, when working with aggregations, such as those mentioned above, the objects in question are always real numbers. There are almost no studies in the literature that portray these aggregations when objects are complex numbers. This is due to the fact that to introduce some aggregations, the objects involved need to be provided with a total order relation. The Graduated Complex Numbers (NCG), proposed by the author, was recently applied in the performance evaluation of classification algorithms. The method required the comparison of complex graduated numbers to achieve that the notion of local order is proposed and consequently the concept of local aggregation is developed. Two applications of such approach are provided.