Abstract
This paper introduced a novel concept of q‐rung orthopair fuzzy (q‐ROF) metric spaces, in connection with the idea of q‐ROF sets, which generalizes well‐known concepts of fuzzy metric spaces and intuitionistic fuzzy metric spaces. An elaborated example has been provided representing the increase in selection space due to the q‐ROF metric and limitations for the case of intuitionistic fuzzy metric space. We have presented the definitions of introduced concepts along with examples, so they are way more understandable for readers. Some basic topological results have been defined and proved for q‐ROF metric space. The concept of q‐ROF Menger boundedness is introduced, and its application in game theory is presented. Also we have presented the significance of introduced metric compared to existing versions of fuzzy metric in the consequent sections. Baire’s theorem and uniform limit theorem are also established in the perspective of q‐ROF metric spaces. An application of the obtained results in the field of game theory is also presented to draw the attention of investigators searching new fields of research.
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