Overlap function-based amongness spaces

Overlap functions are typical aggregation functions with rich theoretical connotations and have many applications in other theoretical branches. In this paper, we will choose an overlap function to model the conjunction to introduce two kinds of fuzzy amongnesses. Precisely, we will propose the concepts of O-fuzzifying amongnesses and (closed, stratified, perfect) pointwise amongnesses via an overlap function O. Then, we will establish the relationship between O-fuzzifying amongnesses and (closed, stratified, perfect) pointwise amongnesses. These results not only provide a theoretical application of overlap functions, but also demonstrate the relationship between different fuzzifications of amongnesses.