Degree of monotonicity in aggregation process

In this paper we introduce a fuzzy order relation notion in the description of aggregation process. Namely, we use the fuzzy order relation to define the degree of monotonicity, which is equal to 1 for a monotone function with respect to a crisp order relation. In that case, integration of fuzzy order relation allows us to generalize the notion of monotonicity and we try to investigate the benefits of using fuzzy relations instead of a crisp relation. Further we illustrate this definition by examples and study the properties of aggregation functions which have a certain degree of monotonicity.