Novel distance measure for q-rung orthopair fuzzy sets with application to transportation problem

The present study focuses on the development of a novel distance measure for q-rung orthopair fuzzy sets in cognitive decision-making problems. The q-rung orthopair fuzzy set is an extension of the intuitionistic fuzzy set that allows for precise manipulation of ambiguous environments. By combining the concept of distance measure with q-rung orthopair fuzzy sets, the study aims to address the shortcomings of previous distance measures and provide a more accurate evaluation of q-rung orthopair fuzzy inherent information. The new distance measure is designed to calculate the differences between different pairs of q-rung orthopair fuzzy sets. The study illustrates the advantages of the proposed distance measure through meticulous numerical examples and examines its general axioms. The comparative study reveals that many established distance measures yield identical values for different pairs of q-rung orthopair fuzzy sets, which makes them unsuitable for accurately representing q-rung orthopair fuzzy inherent information. Additionally, the study introduces a new algorithm for solving fuzzy transportation problem using the proposed distance measure. A numerical example is discussed to validate the feasibility and applicability of the algorithm in real-life scenarios. The significance of the proposed method is evaluated through a comparative study, degree of hesitancy analysis, statistical tests, result analysis, and computational complexity assessment. The study thoroughly discusses these aspects to demonstrate the effectiveness of the proposed method. Finally, the study concludes by summarizing the findings and discussing future research directions for further improvement in the field of fuzzy transportation problem. Overall, the present study contributes to the field of cognitive decision-making by introducing a novel distance measure for q-rung orthopair fuzzy sets and demonstrating its advantages through various analyses and examples.