Journal paper accepted: Fuzzy Sets and Systems
02/11/23/10:36 Filed in: Journal paper
M. Ojeda-Aciego, N. Madrid. Approaching the square of opposition in terms of the f-indexes of inclusion and contradiction. Fuzzy Sets and Systems.
ABSTRACT We continue our research line on the analysis of the properties of the f-indexes of inclusion and contradiction; in this paper, specifically, we show that both notions can be related by means of the, conveniently reformulated, Aristotelian square of opposition. We firstly show that the extreme cases of the f-indexes of inclusion and contradiction coincide with the vertexes of the Aristotelian square of opposition in the crisp case; then, we allocate the rest of f-indexes in the diagonals of the extreme cases and we prove that the Contradiction, Contrariety, Subcontrariety, Subalternation and Superalternation relations also hold between the f-indexes of inclusion and contradiction.