Application of novel similarity measures in electric vehicle charging station site selection based on q-rung orthopair hesitant fuzzy rough sets under quantitative information

Similarity measures provide a viable approach for evaluating the degree of similarity between two collections. They serve as effective procedures for addressing decision-making issues influenced by cognitive processes. This manuscript presents the innovative notions of cosine similarity and weighted cosine similarity measures based on q-rung orthopair hesitant fuzzy rough sets and discusses some relevant properties of the aforementioned measures. These measures are an enhancement of several existing ones that can handle ambiguous and imprecise information with a broader range. Decision makers can determine the most desirable alternative by evaluating the differences between each option and the portrayed standard. Moreover, we present an exemplary illustration for the assessment of an optimal location for electric vehicle charging station in order to illustrate the applicability and advantages of the established similarity measures. Furthermore, assess and determine whether a geographical area has a good, moderate or hazardous air quality index (AQI). The AQI is one of the primary aspects of the environment which is affected by air pollution. Air pollution is one of the extensive worldwide problems, and currently it is well accepted to be harmful to human health. To emphasise the authenticity and the viability of the suggested approach, the findings obtained through cosine and weighted cosine similarity measures are compared. It is pertinent to observe that the computation from novel similarity measures is consistent and provides the same ranking order. We validate the efficacy of the proposed similarity measures through a comparative analysis with established approaches, contrasting their rankings with those demonstrated in existing literature. The results illustrate that the novel similarity measures produce identical ranking patterns and are capable of discerning differences between patterns. Furthermore, the findings demonstrate that the proposed measures are not restricted to a specific domain, but can be effectively utilized in a wide variety of applications.