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The objective of this manuscript is to present the concept of the complex interval-valued 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.
Garg et al. (Wed,) studied this question.