Application Of Bonferroni Mean Operators Under Two Types Of Fuzzy Environment In Multi-attribute Decision Making

This paper mainly considers the problem of the application of Bonferroni mean operator in multi-attribute decision making under two fuzzy environments.The main contents are as follows:First part,combining the concepts of hesitant fuzzy sets and generalized inter-valued trapezoidal fuzzy sets,the concept of generalized hesitant intervalued trapezoidal fuzzy sets is proposed,and the distance,scoring function,sorting method and algorithm of generalized hesitant inter-valued trapezoidal fuzzy elements are defined;The Bonferroni mean operator and the geometry Bonferroni mean operator are extended to the generalized hesitant inter-valued trapezoidal fuzzy environment,and the generalized hesitant inter-valued trapezoidal fuzzy Bonferroni mean operator and the generalized hesitant inter-valued trapezoidal fuzzy geometry Bonferroni mean operator are proposed,and then studied the related properties and some special cases of two types of operators.For the case where the attribute weights are known,the generalized hesitant inter-valued trapezoidal fuzzy weighted Bonferroni mean operator and the generalized hesitant inter-valued trapezoidal fuzzy weighted geometry Bonferroni mean operator are studied;Finally,a multi-attribute group decision-making method based on the GHIVTr FWBM operator and the GHIVTr FWGBM operator is proposed,and the validity and feasibility of the two types of operators are verified by numerical examples.The second part,combining the hesitant normal fuzzy set and the Bonferroni mean operator,first the hesitant normal fuzzy Bonferroni mean operator and the hesitant normal fuzzy geometry Bonferroni mean operator are proposed.Some properties and special cases of the two types of operators are studied.For the case where the attribute weights are unknown,the hesitant normal fuzzy weighted Bonferroni mean operator and the hesitant normal fuzzy weighted geometric Bonferroni mean operator are proposed;finally,the multi-attribute decision-making method of the HNFWBM operator and the HNFWGBM operator are proposed,and using numerical examples to verify the feasibility and effectiveness of these two operators.