The rank order of the neutrosophic triplets (T, I, F) may change after normalization

This paper examines the effects of normalization on the ranking order of single-valued neutrosophic triplets. Neutrosophic triplets are often normalized so that their sum equals one. However, we demonstrate that the ranking order of these triplets, when determined by score, accuracy, and certainty functions, can change upon normalization. Through formal proofs and illustrative counter-examples, we show that inequalities between unnormalized triplets do not always hold after normalization, affecting ranking stability. These findings highlight the importance of considering normalization's impact when using neutrosophic triplets for decision-making and uncertainty modeling.

Keywords:

neutrosophic set , Ranking Functions , Score function , Accuracy function , Decision-making , Rank Order Consistency