Abstract
Intuitionistic fuzzy sets is one of the successful extensions of the fuzzy set to deal with the data, where the information is vague, imprecise, or insufficient during the decision-making process. The objective of the manuscript is to present generalized intuitionistic fuzzy sets and their corresponding operations. For it, we first presented an idea of the generalized IFSs and their corresponding operational laws. Furthermore, some new arithmetic and geometric mean operations are defined to aggregate the different preferences of the decision makers during the process. Various relations related to these operations are investigated in detail. Finally, a decision-making approach has been presented under the GIFSs environment and illustrated with a numerical example.
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