Complex Fuzzy Power Aggregation Operators

Abstract

A complex fuzzy set is an extension of the fuzzy set, of which membership grades take complex values in the complex unit disk. We present two complex fuzzy power aggregation operators including complex fuzzy weighted power (CFWP) and complex fuzzy ordered weighted power (CFOWP) operators. We then study two geometric properties which include rotational invariance and reflectional invariance for these complex fuzzy aggregation operators. We also apply the new proposed aggregation operators to decision making and illustrate an example to show the validity of the new approach.

Analyzing the effect of different types of pollution with bipolar complex fuzzy power Bonferroni mean operators

“…The introduced PBM operators (BCFPBM, BCFWPBM, BCFPGBM, and BCFWPGBM) and a DM procedure in the environment of the BCFS are more effective than other prevailing operators. We now take prevailing theories, including the CF power and DM procedure defined by Hu et al (2019), sin trigonometric AOs and the DM procedure in the environment of the BF set defined by Riaz et al (2022), Hamacher AOs and the DM procedure in the environment of the BF set established by Wei et al (2018), PBM AOs and the DM procedure in the setting of the interval-valued intuitionistic FS (IVIFS) introduced by Liu and Li (2017), and BM AOs and the DM procedure for the BCFS introduced by Mahmood et al (2022b). We consider the data provided in Table 1 and aggregate it with the assistance of these prevailing theories and the operators and the DM procedure introduced in this article.…”

“…The results indicate that existing theories, for example, Hu et al ( 2019), Riaz et al (2022), Wei et al (2018), and Liu and Li (2017), cannot solve the DM issue because the data form the structure of the BCFS. Hu et al (2019) can merely solve the data in the model of CFS and cannot tackle the negative aspects, while Riaz et al (2022) and Wei et al (2018) merely resolve the information in the setting of the BFS and cannot overcome the second dimension, and Liu and Li (2017) merely resolve the information in the model of IVIFS and cannot address the second dimension and negative aspects. Furthermore, the results show that BM AO (BCF Bonferroni mean AO) (Mahmood et al, 2022b) for the BCFS and the DM approach handle the data and give us the result that M BCFS−4 is the finest choice, but anyone can say that this decision or selection is biased and not fair because of the weight vector that the decision analyst provides to each attribute on his own choice, for example, in this case, we take the weight vector (0.08, 0.06, 0.06, 0.8) and u v 2.…”

“…Akram and Bashir (2021) described ordered, weighted, quadratic, and averaging operators based on the CFS. Hu et al (2019) proposed CF power AOs. Mahmood and Ur Rehman (2022a) provided one of the most modified models of the FS because the FS lacks the ability to tackle negative aspects of human beings, as well as information involving the second dimension, and called it a bipolar complex fuzzy set (BCFS).…”

Trident Fuzzy Aggregation Operators on Right and Left Apex-Base Angles in Parallel Computing

“…Further, a fuzzy optimum solution through pascal's triangle graded mean and harmonization of a square fuzzy changeover likelihood relative matrix is proposed by [10] [11] which paves the way for trapezoidal trident fuzzy number. Then, a novel mixture prototype named the multifaceted cubic fuzzy set was introduced by [12], and also the multifaceted cubic fuzzy biased averaging, geometric operators, and its properties are introduced through complex power aggregation operators.…”

Bipolar Complex Fuzzy Hamacher Aggregation Operators and Their Applications in Multi-Attribute Decision Making

“…Bi et al [37] interpreted CF geometric aggregation operators. The CF power aggregation operators were given by Hu et al [38]. Bi et al [39] described CF arithmetic aggregation operators.…”