On rearrangement inequalities for triangular norms and co-norms in multi-valued logic

There is a variation of the rearrangement policy that involves examining two end numbers that are ordered in a certain way. In this variation, you attempt to determine whether the pairwise products of these numbers, when summed, will be maximized or minimized. For example, when dealing with the rearrangement inequality, you calculate the sums of pairwise products but select the numbers from the same two ends. There is a specific ordering method that allows for maximization in this case. By choosing adjacent pairs, the sum of pairwise products is maximized. On the other hand, if you select pairs that are opposite to each other, such as multiplying one number by another and then multiplying the second number by the first one, the sum is minimized. This concept can also be translated to a rearrangement equality that applies to real numbers, specifically when the operations of multiplication and addition are performed using T-norms and T Coors on the same table. Additionally, there is a dual version of this concept where the goal is to maximize the sum of pairwise products. Furthermore, there exists a circular rearrangement inequality that was studied by you a few years ago. In this inequality, you have N numbers and apply the rearrangement sequentially, starting with the first number and pairing it with the second, then pairing the second with the third, and so on, until the Nth number is paired with the first one.