Operations on Finite Settings: from Triangular Norms to Copulas

Abstract

Operations defined on finite chains, usually known as discrete operations, have become a topic of increasing interest because of their applications in many fields. In this paper, we recall two of the main families of discrete operations: discrete t-norms with applications in fuzzy logic, approximate reasoning and computing with words, and discrete copulas with applications in probability, statistics and economy. For both kinds of operations, we emphasize their main properties, their structure and characterization. We also devote some part of the work to highlight the importance of these discrete operations and their impact in the mentioned fields.