A Novel Approach for Multi-Criteria Decision-Making Problem with Linguistic q-Rung Orthopair Fuzzy Attribute Weight Information

Linguistic q-Rung orthopair fuzzy set is a new extension of the linguistic Pythagorean fuzzy set, which effectively represents the fuzzy and uncertain decision-making information based on qualitative modeling. However, its operational rules are unable to process pure linguistic exponential calculations, in which the exponents are represented using linguistic q-Rung orthopair fuzzy values and the bases are represented as linguistic terms or interval linguistic numbers. This greatly restricts its application in decision making under complex environments. As the complement of the existing linguistic q-Rung orthopair fuzzy operational rules, this paper defines linguistic q-Rung orthopair fuzzy calculation rules, including division, subtraction, and exponent operations. Based on theorem-based proofs, the relevant properties of the calculation rules have been analyzed, such as commutative law, distributive law, symmetry, and so on. Moreover, in order to facilitate the application of linguistic q-Rung orthopair fuzzy theory, this paper introduces the concept of dual linguistic q-Rung orthopair fuzzy value. Building on this foundation, a series of weighted aggregation operators for the calculations involving linguistic q-Rung orthopair fuzzy values and dual linguistic q-Rung orthopair fuzzy values have been designed. In conclusion, a novel pure linguistic multi criteria decision-making methodology is introduced in this work. The validity and utility of the proposed method are demonstrated via a real-world application in the decision process of energy resource exploitation.