In this paper, we investigate the multiple attribute decision making problems with picture fuzzy information. Then, we utilize arithmetic and geometric operations to develop some picture fuzzy aggregation operators: picture fuzzy weighted average (PFWA) operator, picture fuzzy weighted geometric (PFWG) operator, picture fuzzy ordered weighted average (PFOWA) operator, picture fuzzy ordered weighted geometric (PFOWG) operator, picture fuzzy hybrid average (PFHA) operator and picture fuzzy hybrid geometric (PFHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the picture fuzzy multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Picture fuzzy aggregation operators and their application to multiple attribute decision making

Archimedean ${t}$ -conorm and ${t}$ -norm provide the general operational rules for intuitionistic fuzzy numbers (IFNs). The aggregation operators based on them can generalize most of the existing aggregation operators. At the same time, the Heronian mean (HM) has a significant advantage of considering interrelationships between the attributes. Therefore, it is very necessary to extend the HM based on IFNs and to construct intuitionistic fuzzy HM operators based on the Archimedean ${t}$ -conorm and ${t}$ -norm. In this paper, we first discuss intuitionistic fuzzy operational rules based on the Archimedean ${t}$ -conorm and ${t}$ -norm. Then, we propose the intuitionistic fuzzy Archimedean Heronian aggregation (IFAHA) operator and the intuitionistic fuzzy weight Archimedean Heronian aggregation (IFWAHA) operator. We also further discuss some properties and some special cases of these new operators. Moreover, we also propose a new multiple attribute group decision making (MAGDM) method based on the proposed IFAHA operator and the proposed IFWAHA operator. Finally, we use an illustrative example to show the MAGDM processes and to illustrate the effectiveness of the developed method.

Group Decision Making Based on Heronian Aggregation Operators of Intuitionistic Fuzzy Numbers

Sustainable supplier selection: A novel integrated fuzzy best worst method (F-BWM) and fuzzy CoCoSo with Bonferroni (CoCoSo’B) multi-criteria model

The power Bonferroni mean (PBM) operator can relieve the influence of unreasonable aggregation values and also capture the interrelationship among the input arguments, which is an important generalization of power average operator and Bonferroni mean operator, and Pythagorean fuzzy set is an effective mathematical method to handle imprecise and uncertain information. In this paper, we extend PBM operator to integrate Pythagorean fuzzy numbers (PFNs) based on the interaction operational laws of PFNs, and propose Pythagorean fuzzy interaction PBM operator and weighted Pythagorean fuzzy interaction PBM operator. These new Pythagorean fuzzy interaction PBM operators can capture the interactions between the membership and nonmembership function of PFNs and retain the main merits of the PBM operator. Then, we analyze some desirable properties and particular cases of the presented operators. Further, a new multiple attribute decision making method based on the proposed method has been presented. Finally, a numerical example concerning the evaluation of online payment service providers is provided to illustrate the validity and merits of the new method by comparing it with the existing methods.

https://onlinelibrary.wiley.com/doi/epdf/10.1002/int.22204

Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making

Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods

The Bonferroni mean (BM) was originally presented by Bonferroni and had been generalized by many researchers for its capacity to capture the interrelationship between input arguments. Nevertheless, the existing intuitionistic fuzzy BMs only consider the effects of membership function or nonmembership function of different intuitionistic fuzzy sets (IFSs). As complements to the existing generalizations of BM under intuitionistic fuzzy environment, this paper also considers the interactions between the membership function and nonmembership function of different IFSs and develops the intuitionistic fuzzy interaction BM and the weighted intuitionistic fuzzy interaction BM. We investigate the properties of these new extensions of BM and discuss their special cases. Furthermore, the detailed steps of multiple attribute decision making with the presented operators under intuitionistic fuzzy environment are investigated and an example is illustrated to show the validity and feasibility of the new approach.

Huayou Chen

Papers

Intuitionistic fuzzy interaction bonferroni means and its application to multiple attribute decision making.