Novel q-Rung Orthopair Fuzzy distance based similarity measure and score function in real life decision making

The distance and similarity measure are the most promising information measures to estimate the distance and similarity between two sets. In the present study, novel distance and similarity measure are introduced and affirmed their proficiencies by theoretical explications and numerical examples. To demonstrate the applicability of the proposed similarity measure (pSMr), medical diagnosis and pattern recognition problems have been solved. This study aims to develop a novel ranking method under q-Rung Orthopair Fuzzy Environment (q-ROFE) based on the proposed measure to solve multi-criteria group decision making (MCGDM) problem. This method aims to identify the most promising alternative based on similarity to positive ideal solution (PIS). The focus is to comprehend the closeness of performance of an alternative from desired performance relative to its distance from ideal solutions. Furthermore, an improved q-Rung orthopair fuzzy score function (SF) has also been proposed elaborating all the significant properties. Moreover, Full consistency method (FUCOM) has been reclaimed under q-ROFE with the aid of q-Rung orthopair fuzzy Weighted Averaging Operator (q-ROFWA). To validate the acceptability of the proposed ranking method, a problem of healthcare waste management (HCWM) has been structured and solved. The feasibility and effectiveness of integrated model have been encountered with comparative and sensitivity examinations. The proposed measures outperform over existing measures to discriminate two q-ROF numbers, which has been validated by comparison. Moreover, the novel $SF$ is competent enough to rank any type of q-ROF numbers regardless of their membership and non-membership grades and the dominance has been illustrated through comparisons.