Weak monotonicity of Lehmer and Gini means

作者：Beliakov Gleb; Spirkova Jana^*

来源：Fuzzy Sets and Systems, 2016, 299: 26-40.

DOI：10.1016/j.fss.2015.11.0060165

• Mixture function
• Weak monotonicity
• Lehmer mean
• Gini mean

We analyzedirectional monotonicity of several mixture functions in the direction (1, 1 ..., 1), called weak monotonicity. Our particular focus is on power weighting functions and the special cases of Lehmer and Gini means. We establish limits on the number of arguments of these means for which they are weakly monotone. These bounds significantly improve the earlier results and hence increase the range of applicability of Gini and Lehmer means. We also discuss the case of affine weighting functions and find the smallest constant which ensures weak monotonicity of such mixture functions.

• 出版日期2016-9-15
• 单位迪肯大学