Generalized Fuzzy Bonferroni Harmonic Mean Operators and Their Applications in Group Decision Making

Abstract

The Bonferroni mean (BM) operator is an important aggregation technique which reflects the correlations of aggregated arguments. Based on the BM and harmonic mean operators, H. Sun and M. Sun (2012) developed the fuzzy Bonferroni harmonic mean (FBHM) and fuzzy ordered Bonferroni harmonic mean (FOBHM) operators. In this paper, we study desirable properties of these operators and extend them, by considering the correlations of any three aggregated arguments instead of any two, to develop generalized fuzzy weighted Bonferroni harmonic mean (GFWBHM) operator and generalized fuzzy ordered weighted Bonferroni harmonic mean (GFOWBHM) operator. In particular, all these operators can be reduced to aggregate interval or real numbers. Then based on the GFWBHM and GFOWBHM operators, we present an approach to multiple attribute group decision making and illustrate it with a practical example.