Fuzzy PTM subalgebra of PTM - algebra

Background This article introduces the concept of fuzzy pseudo-TM subalgebra (FPTMSA) of pseudo-TM algebra (PTMA). This study explores the relationship between FPTMSAs and their level sets within the context of PTMA. It further investigates the homomorphic behavior of FPTMSAs under various algebraic operations, thereby providing a foundation for further exploration of the algebraic structure of fuzzy pseudo-ideals within PTMAs. Methods The concept of level sets for FPTMSAs is defined and examined, highlighting their role in characterizing these subalgebras within a PTMA. This study explores the behavior of FPTMSAs under homomorphisms, considering both homomorphic images (HI) and inverse images (II) of FPTMSAs in PTMAs. In addition, the composition of epimorphic images and inverse images of FPTMSAs is discussed. The study also considers the properties of FPTMSAs under Cartesian products (CPs), demonstrating that the Cartesian product of two FPTMSAs remains an FPTMSA. Results This study establishes several key properties of FPTMSAs in PTMAs, particularly focusing on their behavior under homomorphisms, epimorphisms, and Cartesian products. Specifically, this study demonstrates that the Cartesian product of two FPTMSAs results in another FPTMSA. Additionally, this study examines the relationships between the homomorphic image and inverse image of FPTMSAs and presents further algebraic results related to these concepts. Conclusions The article concludes by highlighting the significant role of FPTMSAs in the structure of PTMAs, particularly in their interaction with homomorphisms, epimorphisms, and Cartesian products. The results suggest that the FPTMSAs are robust under various algebraic operations. Future work will extend these concepts to intuitionistic fuzzy pseudo-TM subalgebra within PTMAs with the goal of uncovering new algebraic insights and results.