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The objective of this manuscript is to present the concept of interval-valued <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-rung orthopair 2-tuple linguistic set (IV<inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-RO2TLSs) and their basic operations. As a generalization of the sets, interval-valued <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-rung orthopair fuzzy set is a more profitable way to express the uncertainties in the data while 2-tuple linguistic set deals with the qualitative aspects of the information. By utilizing both these features, we propose a concept of IV<inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-RO2TLSs and studies their properties. For it, firstly, we define the basic operational laws between the pairs of the sets and define the score, accuracy and basic operations. Secondly, based on the operational laws, we develop some weighted averaging and geometric aggregation operators for IV<inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-RO2TLSs and characterize their desirable properties. Thirdly, a novel approach is developed to solve multi-attribute decision making (MADM) problem with interval-valued <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-rung orthopair 2-tuple linguistic information. Finally, several numerical examples are provided with some comparative study to validate the approach.

Interval-Valued $q$ -Rung Orthopair 2-Tuple Linguistic Aggregation Operators and Their Applications to Decision Making Process