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In this paper, it is aimed to express more accurately the intuitionistic fuzzy values expressed by the decision-makers for intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets. For this purpose, virtual intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets are proposed by defining the concepts of virtual lower and upper intuitionistic fuzzy approaches. Moreover, the basic set operations for this hybrid set type are examined together with their associated properties. In addition, a decision-making algorithm focusing on virtual intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets is constructed. Finally, an analysis of the obtained results was made. [ABSTRACT FROM AUTHOR]

In this paper, fuzzy parametrized intuitionistic fuzzy soft (briefly FPIFS-) set theory, which is a generalization of virtual fuzzy parametrized intuitionistic fuzzy soft (briefly VFPIFS-) sets proposed for uncertainty problems, is given and some important properties of it are examined. In addition, an uncertainty problem was exemplified and the best object was selected by giving a decision-making approach for VFPIFS-sets. Finally, a comparative analysis was done for both mathematical models. [ABSTRACT FROM AUTHOR]