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We present a communication which deals with some new methods to solve multiple attribute decision-making (MADM) problems based on Fermatean neutrosophic normal number (FNNN). Fermatean neutrosophic sets based on further generalization of neutrosophic and Pythagorean neutrosophic sets. To develop some Fermatean neutrosophic normal aggregation operators. The notion of FNNN holds for commutative and associative laws. There are many aggregation operators that have been defined up to date, but we concentration of this article is to introduce a new concept of Fermatean neutrosophic normal weighted averaging (FNNWA), Fermatean neutrosophic normal weighted geometric(FNNWG), generalized Fermatean neutrosophic normal weighted averaging(GFNNWA) and generalized Fermatean neutrosophic normal weighted geometric(GFNNWG). Also, we obtain an algorithm that deals with the MADM problems based on these operators. We interact applicability of the euclidean and hamming distance measures which are further extended in real life example. Finally, some important properties of these sets under algebraic operations are to be elaborated in this communication.