Graded Aristotle's hexagon of opposition, Fuzzy intermediate quantifiers, Graded Peterson's hexagon of opposition, Fuzzy natural logic

In this publication we will first focus on the construction of the graded Aristotle's hexagon in fuzzy natural logic. The main goal will be to mathematically formulate a new definition of the contradictory property. In past publications this definition was based on delta operation, which gave very unnatural results. We will show that the contradictory property can behave more naturally. In the end, we will present another extension possibility in the form of a graded Peterson hexagon with fuzzy intermediate quantifiers.