模糊Bonferroni平均算子及在多准则群决策中的应用

在进行信息集成时，有时需要考虑输入变量之间的相互影响,而Bonferroni平均（Bonferroni mean, BM）算子正好具有这种优点。为了集成三角模糊数，提出模糊Bonferroni平均（fuzzy Bonferroni mean, FBM）算子，讨论它的几种特殊情形。在此基础上，提出模糊加权Bonferroni平均（fuzzy weighted Bonferroni mean, FWBM）算子和组合模糊加权Bonferroni平均（combined fuzzy weighted Bonferroni mean, C-FWBM）算子，同时研究它们的一些性质。针对决策信息以三角模糊数给出的决策问题，提出一种基于FWBM算子和C-FWBM算子的多准则决策方法。最后举例说明其在模糊多准则群决策中的应用，结果表明该方法是可行的。

Fuzzy Bonferroni mean operator and its application to multi-criteria group decision making

The advantage of the Bonferroni mean operator is its capability to capture the interrelationship between input arguments in information fusion.In order to aggregate triangular fuzzy numbers,the fuzzy Bonferroni mean(FBM) operator is developed and its some special cases are discussed.Based on this,the fuzzy weighted Bonferroni mean(FWBM) operator and the combined fuzzy weighted Bonferroni mean(C-FWBM) operator are proposed.Meanwhile,some desirable properties of these operators are investigated.With respect to multi-criteria group decision making in which the decision making information is given by triangular fuzzy numbers,a new decision making method is proposed based on FWBM operator and C-FWBM operator.Finally an illustrative example is given to use these operators in the range of fuzzy multi-criteria group decision-making.The results show that the proposed method is feasible.