Application For Two Kinds Of Bonferroni Mean Operators In Multiple Attribute Decision Making

With respect to the hesitant trapezoidal fuzzy multi-attribute decision mak-ing problems(HTrFMADM),we consider the interrelationships among arguments and combine Bonferroni mean and geometric Bonferroni mean with the hesitan-t trapezoidal fuzzy sets(HTrFS),then the hesitant trapezoidal fuzzy Bonferroni mean operator(HTrFBM)and the hesitant trapezoidal fuzzy geometric Bonfer-roni mean operator(HTrFGBM)are defined,the properties of the operators are discussed by the hesitant trapezoidal fuzzy operational laws.Considering the attribute play defferent roles in HTrFMADM,we investigate the weighted hesi-tant trapezoidal fuzzy Bonferroni inean(WHTrFBM)and the weighted hesitant trapezoidal fuzzy geometric Bonferroni mean operator(WHTrFGBM).In addi-tion,an approach is proposed based on WHTrFBM and WHTrFGBM.Finally,an illustrative example of HTrFMADM problems is uesd to demonstrated the effectiveness of the proposed operators.With respect to the hesitant normal fuzzy multi-attribute decision making problems(HNFMADM)which with no weight of arguments,we consider the in-terrelationships among arguments,combine Bonferroni mean and power operator and combine Bonferroni geometric mean and power geometric operator with the hesitant normal fuzzy sets(HNFS),then the hesitant normal fuzzy power Bonfer-roni mean operator(HNFPBM)and the hesitant normal fuzzy power geometric Bonferroni mean operator(HNFPGBM)are defined,the properties of the opera-tor are discussed by the hesitant normal fuzzy operational laws.In addition,an approach is proposed based on HNFPBM and HNFPGBM.Finally,an illustra-tive example of HNFMADM problems is used to demonstrated the effectiveness of the proposed operator.