Meryem Fakhraoui - LMACS, Laboratory of Applied Mathematics & Scientific Computing Sultan Moulay Slimane University, PO Box ۵۲۳, ۲۳۰۰۰ Beni Mellal Morocco.
Idris Bakhadach - LMACS, Laboratory of Applied Mathematics & Scientific Computing Sultan Moulay Slimane University, PO Box ۵۲۳, ۲۳۰۰۰ Beni Mellal Morocco.
Sofyane Achik - LMACS, Laboratory of Applied Mathematics & Scientific Computing Sultan Moulay Slimane University, PO Box ۵۲۳, ۲۳۰۰۰ Beni Mellal Morocco.
Hamid Sadiki - LMACS, Laboratory of Applied Mathematics & Scientific Computing Sultan Moulay Slimane University, PO Box ۵۲۳, ۲۳۰۰۰ Beni Mellal Morocco.

The Pythagorean fuzzy set is acknowledged for its proficiency in managing uncertainty across multifarious domains. In this investigation, we advance the Pythagorean fuzzy Artinian ring as an evolutionary progression from the conventional fuzzy ring, providing a comprehensive explication of its fundamental traits. Furthermore, this study introduces Pythagorean fuzzy Noetherian rings, delineating their intrinsic attributes, thereby enriching the comprehensive comprehension of these algebraic constructs.

Pythagorean fuzzy Artinian ring, Pythagorean fuzzy Noetherian ring, Pythagorean Fuzzy