Affiliations: [a] School of Management Science and Engineering, Shandong University of Finance andEconomics, Jinan Shandong, China
| [b] Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
Correspondence:
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Corresponding author. Peide Liu, School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan Shandong 250014, China. E-mail: peide.liu@gmail.com.
Abstract: This article puts forward an innovative notion of complex picture fuzzy set (CPFS) which is particularly an extension and a generalization of picture fuzzy sets (PFSs) by the addition of phase term in the description of PFSs. The uniqueness of CPFS lies in the capability to manage the uncertainty and periodicity, simultaneously, due to the presence of phase term which broadens the range of CPFS from a real plane to the complex plane of unit disk. We describe and verify the fundamental operations and properties of CPFSs. We introduce the aggregation operators, namely; complex picture fuzzy power averaging and complex picture fuzzy power geometric operators in CPFSs environment, based on weighted and ordered weighted averaging and geometric operators. We construct multi-criteria decision making (MCDM) problem, using these operators and describe a numerical example to illustrate the validity and competence of this article. Finally, we discuss the advantages of this generalized concept of aggregation technique and analyze a comparative study to demonstrate the superiority and consistency of our model.
Keywords: Complex picture fuzzy set, power aggregation operators, multi-criteria decision making
