A new family of Bonferroni mean-type pre-aggregation operators

摘要

The concept of pre-aggregation functions, which was oriented as an elementary attempt to outstretch the notion of monotonicity in aggregation functions, has enlarged the class of operators for information accumulation by considering directional monotonicity with respect to a vector. This consideration propels us to focus on the systematic investigation of the theoretical framework of different forms of pre-aggregation functions, particularly Bonferroni mean-type. In this regard, we propose the construction methodology of Bonferroni mean-type (BM-type) pre-aggregation functions by befitting suitable functions to provide a descriptive configuration, which is quite interpretable and understandable. Firstly, a construction method of BM-type pre-aggregation function has been propounded by utilizing a bivariate function M. Its properties are inspected in detail. To enrich its capacity, the proposed BM-type pre-aggregation function has been customized by utilizing two functions, namely M and M^∗, respectively. Several illustrative examples have been presented in this regard.