The objective of this manuscript is to present some aggregation operators for aggregating the different complex intuitionistic fuzzy (CIF) sets by considering the dependency between the pairs of its membership degrees. In the existing studies of fuzzy and its extensions, the uncertainties present in the data are handled with the help of degrees of membership that are the subset of real numbers, which may lose some useful information and hence consequently affect the decision results. A modification to these, complex intuitionistic fuzzy set handles the uncertainties with the degrees whose ranges are extended from real subset to the complex subset with unit disc and hence handle the two‐dimensional information in a single set. Thus, motivated by this, we developed some new power aggregation operators, namely, CIF power averaging, CIF weighted power averaging, CIF ordered weighted power averaging, CIF power geometric, CIF weighted power geometric, and CIF ordered weighted power geometric. Also, some of the desirable properties of these are investigated. Further, based on these operators, a multicriteria decision‐making approach is presented under the CIF set environment. An illustrative example related to the selection of the best alternative(s) is considered to demonstrate the efficiency of the proposed approach and is validated it by comparing their results with the several existing approaches results.
The objective of this manuscript is to present the concept of the complex intervalvalued intuitionistic fuzzy (CIVIF) set, their algebraic operations and their corresponding aggregation operators, which can better represent the time-periodic problems and two-dimensional information in a single set. The proposed CIVIF set includes the characteristics of both complex intuitionistic fuzzy set, as well as the interval-valued intuitionistic fuzzy sets. Some of the basic operational laws and their properties have been investigated in details. Also, we have developed some new weighted and ordered weighted averaging and geometric aggregation operators with complex interval-valued intuitionistic fuzzy information. The proposed operations are the generalization of the operations of interval-valued intuitionistic fuzzy, complex fuzzy and complex intuitionistic fuzzy theories. Furthermore, a group decision-making method is established based on these operators. Finally, an illustrative example is used to illustrate the applicability and validity of the proposed approach and compare the results with the existing methods to show the effectiveness of it.
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