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.
Highlights
Multiple attribute group decision making (MAGDM) is the common phenomenon in modern life, which is to select the optimal alternative(s) from several alternatives or to get their ranking by aggregating the performances of each alternative under several attributes, in which the aggregation techniques play an important role
We have extended the generalized weighted Bonferroni mean (GWBM) operator to the triangular fuzzy environment and developed the fuzzy harmonic aggregation operators including the fuzzy weighted Bonferroni harmonic mean (FWBHM) and generalized fuzzy weighted Bonferroni harmonic mean (GFWBHM) operators
Based on the these operators and Yager’s ordered weighted averaging (OWA) operator, we have developed the fuzzy ordered weighted Bonferroni harmonic mean (FOWBHM)
Summary
Multiple attribute group decision making (MAGDM) is the common phenomenon in modern life, which is to select the optimal alternative(s) from several alternatives or to get their ranking by aggregating the performances of each alternative under several attributes, in which the aggregation techniques play an important role. Beliakov et al [14] presented a composed aggregation technique called the generalized Bonferroni mean (GBM) operator, which models the average of the conjunctive expressions and the average of remaining They extended the BM operator by considering the correlations of any three aggregated arguments instead of any two. 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. All these operators can be reduced to aggregate interval or real numbers.
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