Abstract
The paper shows that a cube of opposition, a structure that generalizes the square of opposition invented in ancient logic, can be generated from the composition of a binary relation with a subset, by the effect of set complementation on the subset, on the relation, or on the result of the composition. Since the composition of relations is encountered in many areas, the structure of opposition exhibited by the cube of opposition has a universal flavor. In particular, it applies to information processing-oriented settings such as rough set theory, possibility theory, or formal concept analysis. We then discuss how this structure extends to a fuzzy relation and a fuzzy subset, and the graded cube of opposition thus obtained provides an organized view of the different existing compositions of fuzzy relations. The paper concludes by pointing out areas of research where the cube of opposition, or its graded version are of interest.
Sign-in/Register to access full text options 
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
