The aggregation of multiple three-way decision spaces

Based on the theory of three-way decisions proposed by Yao, Hu established three-way decision spaces on fuzzy lattices and partially ordered sets. At the same time, multiple three-way decision spaces and its corresponding three-way decisions were also established. How to choose a method for the transformation from multiple three-way decision spaces to a single three-way decision space? This is one of the main problems on multiple three-way decision spaces. In connection with the transformation question on multiple three-way decision spaces, this paper gives out an aggregation method from multiple three-way decision spaces to a single three-way decision space through an axiomatic complement-preserving aggregation function. These aggregation methods in the partially set [0,1] contain the weighted average three-way decisions, max-min average three-way decisions and median three-way decisions etc. These methods are generalized to three-way decisions over two groups of multiple three-way decision spaces. At last we illustrate aggregation methods of multiple three-way decision spaces through a practical example.