MCDM model using Jaccard and cosine similarity-driven aggregation operators in (n, m)-rung orthopair fuzzy environment: a case study on government medical facilities in Indian states

This paper introduces a new Multiple Criteria Decision Making (MCDM) method based on the (n, m)-rung orthopair fuzzy sets (n, m-ROFSs) framework, enhanced with Jaccard and cosine similarity measures. This innovative approach effectively captures complex nuances and uncertainties in decision-making processes. The method involves several key contributions likewise, the proposal of new Jaccard (JSM) and cosine similarity measures (CSM) within the n, m-ROFSs environment, a novel weight determination method, and a new MCDM method tailored for n, m-ROFSs. The robustness of the method is demonstrated through a detailed examination of its mathematical properties and the development of a new aggregation operator, followed by sensitivity and comparison analyses. The practical utility of the proposed MCDM method is illustrated by evaluating and ranking the ten most densely populated states in India based on government-provided medical facilities. This study highlights the effectiveness and real-world applicability of the developed approach.