Lexicographic use of Sugeno integrals and monotonicity conditions

Abstract

The Sugeno integral is very useful but its sensitivity is low. In order to overcome this disadvantage, the author proposes the lexicographic order induced by Sugeno integrals, which is called the LS order. It is an extension of useful orderings such as the ordinary lexicographic order, the leximax (the lexicographic maximax rule), and the leximin (the lexicographic maximin rule). Concerning the sensitivity of orderings, the author discusses three monotonicity conditions: the ordinary monotonicity condition (M), the weak Pareto principle (WP), and the strong Pareto principle (SP). As well known, the Sugeno integral always satisfies (M). The author shows that it satisfies (WP) under a special condition, and that it never satisfies (SP). In addition, he shows necessary and sufficient conditions for an LS order to satisfy (WP) and (SP). By using these conditions one can design LS orders satisfying desired monotonicity conditions.