Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a notion of dimension of max-min convex sets, following the approach of tropical convexity.  introduce a max-min analogue of the tropical rank of a matrix and show that it is equal to the dimension of the associated polytope.  describe the relation beten this rank and the notion of strong regularity in max-min algebra, which is traditionally defined in terms of unique solvability of linear systems and the trapezoidal property.
['Viorel Nitica', 'Sergeùõ Sergeev']
I am writing a research paper on a idea On the dimension of max-min convex sets
[{"from": "human", "value": "I am writing a research paper on a idea On the dimension of max-min convex sets"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a notion of dimension of max-min convex sets, following the approach of tropical convexity.  introduce a max-min analogue of the tropical rank of a matrix and show that it is equal to the dimension of the associated polytope.  describe the relation beten this rank and the notion of strong regularity in max-min algebra, which is traditionally defined in terms of unique solvability of linear systems and the trapezoidal property."}]