Pythagorean fuzzy quasi coincidence: Analysis and applications

This article introduces an improved definition of Pythagorean fuzzy quasi-coincidence between the Pythagorean fuzzy sets enhancing the theoretical foundation of previous approaches. We investigate the theoretical aspects of the introduced Pythagorean fuzzy quasi-coincidence and corresponding Pythagorean fuzzy quasi-coincident set. The Pythagorean fuzzy quasi-coincident set is proven to be a Pythagorean fuzzy t-norm and the corresponding t-conorm with respect to the standard negation operator has been obtained. The introduced concept can reveal interrelationships among Pythagorean fuzzy sets, overcoming limitations of the fuzzy version of quasi-coincidence in scenarios involving uncertainty and hesitancy. Additionally, it enables range divisions, a feature previously unattainable in fuzzy quasi-coincidence methods. A significant novelty lies in the development of a Pythagorean fuzzy generator, the first of its kind, to generate Pythagorean fuzzy data from conventional fuzzy or Intuitionistic fuzzy information. This generator, accompanied by a generator sequence, allows customizable non-membership values based on user requirements. These advancements facilitate applications such as identifying high-risk zones during pandemics or natural disasters. Building on this foundation, we present practical applications to identify high-risk areas within regions affected by outbreaks of pandemics. We use he quasi-coincidence property, and group the affected area into distinct categories, such as red and yellow zones. Further, the application of the proposed theories is also depicted in medical diagnosis and we show that the method can also be used to re-frame traditional multi-criteria decision-making processes.