Linguistic intuitionistic fuzzy set (LIFS) is an efficient theory to represent the data in form of membership degrees in a qualitative rather than the quantitative aspects. But in sometimes, it is preferable by the decision‐maker to give their preferences in terms of interval numbers rather than real numbers. To address this, the present manuscript extends the theory of LIFS to linguistic interval‐valued intuitionistic fuzzy set (LIVIFS) by expressing the degrees of membership and non‐membership by the interval‐valued linguistic terms. Under this environment, some measures of distances have been proposed to measuring the uncertainties in the data. The characteristics and their desirable relations have also been stated. Further, based on these measures, an extended technique for order preference by similarity to ideal solution method has been presented under the LIVIFS environment by different pairs of decision‐makers and their corresponding priority levels. The study has been validated through a numerical example.