The sustainability assessment framework aims to identify the most sustainable product, or process, or system from a set of alternate options. An appropriate sustainability assessment framework simultaneously handles multi-dimensional sustainable parameters to incorporate aspects such as minimizing the land acquisition, depleting the fossil fuels and materials consumption, reducing the environmental harness, etc. Various multi-criteria decision-making methods such as The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Euclidean Distance Method, etc., are applied to identify the most sustainable option. These assessment methods incorporate precise indicator scores to ascertain the most sustainable option. However, in most applications, sustainable indicator scores are not precise. Imprecise values of parameters may be represented as an interval number with a lower and an upper bound. This paper proposes a generalized framework of sustainability assessment method incorporating interval indicator scores to identify the appropriate option. The significant steps of sustainability assessment methods have been explored from the physical point of view towards sustainability. These steps are extended to an interval scale for retrospective parameters. An extended normalization function and an extended aggregation function are recommended in the proposed method. The proposed framework signifies the appropriate sustainability assessment method and helps to identify the most sustainable system among the systems with imprecise indicator scores. The applicability of the proposed method is illustrated by the sustainability assessment example of deciding the most sustainable electricity generation system. Furthermore, the significance of the proposed approach is discussed.