Binary convex fuzzy vector spaces over binary vector spaces and their applications

In this paper, we explore the concept of binary convex fuzzy vector spaces and binary convex fuzzy linear subspaces over binary vector spaces F2n by formalizing their definition, and we found interesting results on their properties. We also studied binary fuzzy vector spaces, and binary convex fuzzy sets by establishing relevant properties. We accomplish these by redefining fuzzy subsets over F2n in a new manner using the formula of the reliability of the channel to send messages correctly over noise channels to make the concepts applicable in natural and linguistic communication systems. We also defined binary convex fuzzy codes over binary convex fuzzy vector space and presented some properties. Furthermore, we realized that the properties discussed for binary fuzzy vector spaces are applied to binary convex fuzzy vector spaces. We used binary fuzzy vector spaces to formulate binary fuzzy codes and binary convex fuzzy vector spaces to define binary convex fuzzy codes. We also draw connections between binary fuzzy codes and binary convex fuzzy codes. The study of binary convex fuzzy vector spaces and binary fuzzy vector spaces is particularly relevant in the context of information transmission through noisy communication channels, where it allows for the exploration of fuzzy error-correcting/detecting codes and related properties to detect/correct errors that may occur during transmission.