Hamming distance of generalised L-R intuitionistic fuzzy number and its application

This paper proposes a distance measure for generalised L-R intuitionistic fuzzy number (GLRIFN) which is Hamming distance, aiming to enhance the theoretical and practical tools available for decision-making under uncertainty. The properties of the Hamming distance of generalised L-R intuitionistic fuzzy number are also discussed in this study. GLRIFN extends traditional L-R intuitionistic fuzzy number by incorporating confidence level for both membership and non-membership functions, making them more reliable in the evaluation process. To demonstrate the practical utility of the proposed measure, it is applied within the Generalised L-R Intuitionistic Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (GLRIF-TOPSIS), a multi-criteria decision-making (MCDM) method. A real-world case study on river water pollution classification is conducted, wherein the proposed model effectively evaluates the pollution levels of different rivers by capturing the nuances of imprecise, vague, and conflicting environmental data. The results show that the River 5 J is the cleanest river, while the River 1 J is the most polluted river. The integration of the Hamming distance with GLRIF-TOPSIS offers a structured and adaptable decision-making framework, capable of addressing complex multi-criteria problems across domains characterised by high levels of ambiguity. This contribution not only enriches the existing body of fuzzy set theory but also opens avenues for further applications in environmental assessment and other areas that require robust fuzzy modeling.