Aggregation with T-norms and LexiT-orderings and their connections with the Leximin principle

Abstract

We analyze the impact of applying families of T-norm and LexiT-ordering aggregation functions in the context of egalitarian reasoning. We compare both of them with the minimum and lexicographic minimum aggregation functions, which are well-known functions used in the aggregation approach in the decision making problem. For this task, we consider three logical properties in the Social Choice theory and Economics: Hammond Equity, Strong Pareto and Anonymity. It is known that lexicographic minimum satisfies all of these properties. We present in this paper some conditions to T-norms and LexiT-orderings satisfy these logical properties or restrictions of them.