Some q-Rung Picture Fuzzy Dombi Hamy Mean Operators with Their Application to Project Assessment

Abstract

The recently proposed q-rung picture fuzzy set (q-RPFSs) can describe complex fuzzy and uncertain information effectively. The Hamy mean (HM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this study, we extend HM to q-rung picture fuzzy environment, propose novel q-rung picture fuzzy aggregation operators, and demonstrate their application to multi-attribute group decision-making (MAGDM). First of all, on the basis of Dombi t-norm and t-conorm (DTT), we propose novel operational rules of q-rung picture fuzzy numbers (q-RPFNs). Second, we propose some new aggregation operators of q-RPFNs based on the newly-developed operations, i.e., the q-rung picture fuzzy Dombi Hamy mean (q-RPFDHM) operator, the q-rung picture fuzzy Dombi weighted Hamy mean (q-RPFDWHM) operator, the q-rung picture fuzzy Dombi dual Hamy mean (q-RPFDDHM) operator, and the q-rung picture fuzzy Dombi weighted dual Hamy mean (q-RPFDWDHM) operator. Properties of these operators are also discussed. Third, a new q-rung picture fuzzy MAGDM method is proposed with the help of the proposed operators. Finally, a best project selection example is provided to demonstrate the practicality and effectiveness of the new method. The superiorities of the proposed method are illustrated through comparative analysis.

Group Decision Algorithm for Aged Healthcare Product Purchase Under q-Rung Picture Normal Fuzzy Environment Using Heronian Mean Operator

“…Li et al [55] developed a MADM method based on q-Rung Picture Linguistic sets (q-RPtLS). He et al [56] presented q-rung picture fuzzy Dombi Hamy mean operators, Liu et al [57] proposed T-Spherical fuzzy Power Muirhead mean operator by combining IFSs, PFSs, q-ROFSs, and PtFSs for MADM.…”

“…For this reason, in order to make a reasonable comparison with the existing methods, the Bonferroni mean operator involved in the method proposed by Liu and Liu [62] is applied to the q-RPtNoF environment for information aggregation, and the parameters of Bonferroni mean operator are p = q = 2, then the best alternative is still A 3 . Similarly, the Dombi Hamy Mean operator ( = 2) in the method proposed by He et al [56] is applied to the q-RPtNoF environment to get the ranking of alternatives, the best alternative is still A 3 , which is the same as the best choice based on our method. It indicates the rationality of the operators proposed in this paper.…”

“…Compared with PtFS proposed by Cuong and Kreinovich [48] and Cuong [49], the q-RPtNoFSs takes into account the normal distribution of attribute information, further characterizes human social activities and natural phenomena, and is closer to human decision-making thinking. Compared with the q-Rung Picture Linguistic proposed by Li et al [55] and q-RPtF Dombi Hamy Mean Operators proposed by He et al [56] and T-Spherical Fuzzy Power Muirhead Mean Operators proposed by Liu et al [57], the operators proposed in this paper take into account the opinions of heterogeneous groups and describe the correlation between different groups and attributes. In addition, in this paper, the preferences of different groups of opinions are considered, and the information aggregator is proposed to obtain different decision results according to different parameters, so the method in this paper has greater flexibility.…”

Some picture fuzzy Bonferroni mean operators with their application to multicriteria decision making

“…Wei 11 proposed picture fuzzy aggregation operators: picture fuzzy weighted averaging (PFWA) operator, picture fuzzy weighted geometric (PFWG) operator, picture fuzzy hybrid average (PFHA) operator, picture fuzzy hybrid geometric (PFHG) operator, picture fuzzy ordered weighted averaging (PFOWA) operator, and picture fuzzy ordered weighted geometric (PFOWG) operator. For other researches on PFS, the readers are referred to recent works 12–21 …”

“…For other researches on PFS, the readers are referred to recent works. [12][13][14][15][16][17][18][19][20][21] The large diversity of possible correlations between the criterions in multicriteria decision making (MCDM) problems motivates excellent interest in purposing aggregation functions that can be used to model these possible relationships. Bonferroni mean (BM), which reflects the correlations of input arguments, was originally presented by Bonferroni 22 and then interpreted by Yager 23 as joined averaging and "anding" operator, which allows replacing the average operator by other means, such as Choquet integral 24 and ordered weighted average operator.…”