Fuzzy Mathematics under Non-Minimal "And"-Operations (t-Norms): Equivalence leads to Metric, Order Leads to Kinematic Metric, Topology Leads to Area or Volume

Authors

Purbita Jana, India Institute of Technology KanpurFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

7-1-2023

Comments

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.

Abstract

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.