Pythagorean Fuzzy Bonferroni Mean Research Articles

Triangular Pythagorean fuzzy Bonferroni mean operators in multiple attribute decision making and applications to college English smart classroom teaching quality evaluation

At the stage of college education, English is a very important subject, which is directly related to the enhancement of college students’ English literacy and the improvement of their English level. From the perspective of mobile internet, the construction and application of college English intelligent classroom teaching mode can promote the reform and improvement of traditional English teaching mode. By giving full play to students’ subjectivity, English teaching can be carried out in a modern teaching classroom environment, which is conducive to strengthening students’ comprehensive English ability, which is also very important and meaningful for building an efficient college English classroom. The college English smart classroom (CESC) teaching quality evaluation is a classical multiple attribute decision making (MADM). In this paper, we define the triangular Pythagorean fuzzy set (TPFS) and investigate the multiple attribute decision making problems under it. Accordingly, we take advantage of traditional Bonferroni mean (BM) operator to develop some triangular Pythagorean fuzzy information operators: triangular Pythagorean fuzzy Bonferroni mean (TPFBM) operator and triangular Pythagorean fuzzy weighted Bonferroni mean (TPFWBM) operator. The dominating natures of these operators are researched. Accordingly, the TPFWBM operator is built for triangular Pythagorean fuzzy MADM. Ultimately, a practical example for CESC teaching quality evaluation is took advantage of to validate the developed approach.

Dual hesitant Pythagorean fuzzy Bonferroni mean operators in multi-attribute decision making

Dual hesitant Pythagorean fuzzy Bonferroni mean operators in multi-attribute decision making

Pythagorean Fuzzy Bonferroni Mean with Weighted Interaction Operator and Its Application in Fusion of Online Multidimensional Ratings

Aiming at the aggregation problem of online multi-attribute interactive ratings, a decision-making method based on Pythagorean Fuzzy Bonferroni mean with weighted interaction (PFWIBM) operator is developed by mining the advantages of ratings driven decision-making and the quantitative advantages of Pythagorean fuzzy sets on linguistic ratings. First, the shortcomings of existing operators in criterion interactive representation are analyzed, and the improved Bonferroni mean with weighted interaction and its dual operator are defined, which are used to aggregate the membership information and non-membership information under the Pythagorean fuzzy environment, respectively, and then the PFWIBM operator is constructed. Second, a generation method of interaction coefficients embedded in the PFWIBM operator is designed by combining expert knowledge and user ratings to overcome the limitations of the method of relying on subjective setting parameter values. Third, based on the proposed operator and the transformation relationship between Pythagorean fuzzy sets and linguistic ratings, an online multi-dimensional rating aggregation decision-making approach for solving product raking problems is developed. Finally, the proposed method is applied to a passenger car ranking example to show the feasibility of the method, and through some comparative analysis, the advantages of the proposed operator are clarified, and the influence of operator parameters on the decision-making results is analyzed.

Models for multiple attribute decision making with some interval-valued 2-tuple linguistic Pythagorean fuzzy Bonferroni mean operators

Models for multiple attribute decision making with some interval-valued 2-tuple linguistic Pythagorean fuzzy Bonferroni mean operators

The linear assignment method for multicriteria group decision making based on interval-valued Pythagorean fuzzy Bonferroni mean

The interval-valued Pythagorean fuzzy sets can easily handle uncertain information more flexibly in the process of decision making. Considering the interrelationship among the input arguments, we extend the Bonferroni mean and the geometric Bonferroni mean to the interval-valued Pythagorean fuzzy environment and solve its practical application problems. First, we develop the interval-valued Pythagorean fuzzy Bonferroni mean and the weighted interval-valued Pythagorean fuzzy Bonferroni mean (WIVPFBM) operators. The properties of these aggregation operators are investigated. Then, we also develop the interval-valued Pythagorean fuzzy geometric Bonferroni mean and the weighted interval-valued Pythagorean fuzzy geometric Bonferroni mean (WIVPFGBM) operators and analyze their properties. Third, we utilize the WIVPFBM and WIVPFGBM operators to fuse the information in the interval-valued Pythagorean fuzzy multicriteria group decision making (IVPFMCGDM) problem, which can obtain much more information in the process of group decision making. With the aid of the linear assignment method, we present its extension and further design a new algorithm for the application of IVPFMCGDM. Finally, an example is given to elaborate our proposed algorithm and validate its excellent performance.

Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading

Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading

Models for Safety Assessment of Construction Project With Some 2-Tuple Linguistic Pythagorean Fuzzy Bonferroni Mean Operators

For this paper, to consider both Bonferroni mean (BM) operator and two-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs), we combine the weighted BM (WBM) operator, the generalized WBM (GWBM) operator, and the dual GWBM operator with 2TLPFNs to propose the two-tuple linguistic Pythagorean WBM (2TLPFWBM) operator, the 2TLPFWGBM operator, the generalized 2TLPFWBM (G2TLPFWBM) operator, the generalized 2TLPFWGBM operator, the dual G2TLPFWBM operator, and the dual G2TLPFWGBM operator. Then, some MADM procedures are developed based on these operators. At last, an applicable example for a safety assessment of construction project is given.

Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making

The Pythagorean fuzzy set as an extension of the intuitionistic fuzzy set characterized by membership and nonmembership degrees has been introduced recently. Accordingly, the square sum of the membership and nonmembership degrees is a maximum of one. The Pythagorean fuzzy set has been previously applied to multiattribute group decision-making. This study develops a few aggregation operators for fusing the Pythagorean fuzzy information, and a novel approach to decision-making is introduced based on the proposed operators. First, we extend the generalized Bonferroni mean to the Pythagorean fuzzy environment and introduce the generalized Pythagorean fuzzy Bonferroni mean and the generalized Pythagorean fuzzy Bonferroni geometric mean. Second, a new generalization of the Bonferroni mean, namely, the dual generalized Bonferroni mean, is proposed by considering the shortcomings of the generalized Bonferroni mean. Furthermore, we investigate the dual generalized Bonferroni mean in the Pythagorean fuzzy sets and introduce the dual generalized Pythagorean fuzzy Bonferroni mean and dual generalized Pythagorean fuzzy Bonferroni geometric mean. Third, a novel approach to multiattribute group decision-making based on proposed operators is proposed. Lastly, a numerical instance is provided to illustrate the validity of the new approach.