Triangular fuzzy Bonferroni mean operators and their application to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making( MADM) problems with triangular fuzzy information. Motivated by the ideal of Bonferroni mean, we develop the aggregation techniques called the triangular fuzzy Bonferroni mean (TFBM) operator for aggregating the triangular fuzzy information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define the triangular fuzzy weighted Bonferroni mean (TFWBM) operator, based on which we develop the procedure for multiple attribute decision making under the triangular fuzzy environments. Finally, a practical example for evaluating the modernization development of Chinese traditional medicine industry is given to verify the developed approach and to demonstrate its practicality and effectiveness.