A novel idea of linguistic interval-valued intuitionistic neutrosophic fuzzy numbers (LIVINFNs) and operational laws of the numbers are introduced in this paper. LIVINF TOPSIS method is developed and application of the developed TOPSIS method to a multi-attribute group decision making (MAGDM) problem in a LIVINF environment is discussed. Finally, a numerical example is presented to validate this new approach in group decision making problems.
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