Abstract
It has been shown that the arrow category of type-2 fuzzy relations with respect to an arrow category \({\mathcal A}\) can be defined as the Kleisli category of \({\mathcal A}\) for a monad based on the concept of the extension of an object. In this paper we want to continue the study of higher-order arrow categories by showing two major results. First, we are going to remove the ad-hoc notion of an extension of an object completely from the construction of higher-order arrow categories. The second result establishes that the newly constructed higher-order arrow category has sufficient structure for constructing further higher-order arrow categories, i.e., that the process of moving from type-n to type-(n+1) arrow categories can always be iterated.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
