Properties on semi-ring of fuzzy matrices with compatible norm

Objectives: Using applying the concept of compatible norm, this study develops an entirely new type of fuzzy matrix semi-ring.Methods: The main goal of the current work is to present a novel fuzzy matrix idea on compatible norm SFMc.Findings: This study introduces fuzzy matrices and explains which ones multiply left and right over addition. Addition and multiplication are the two binary operations (+, ⨀) that occur in the semi-ring (S,+,⨀) of the set S.Novelty: The idea of generalized semi-ring of fuzzy matrix are studied. Using the fuzzy algebra & vector space over [0,1]. Forms a distributive law and comparable of semi-ring fuzzy matrices.