Publication Date



Technical Report: UTEP-CS-23-33

To appear in Proceedings of the 20th World Congress of the International Fuzzy Systems Association IFSA'2023, Daegu, South Korea, August 20-24, 2023.


Most formulas analyzed in fuzzy mathematics assume -- explicitly or implicitly -- that the corresponding "and"-operation (t-norm) is the simplest minimum operation. In this paper, we analyze what happens if instead, we use other "and"-operations. It turns out that for such operations, a fuzzification of a mathematical theory naturally leads to a more complex mathematical setting: fuzzification of equivalence relation leads to metric, fuzzification of order leads to kinematic metric, and fuzzification of topology leads to area or volume.