A review on logical connectives defined on finite chains

Abstract

This paper aims to compile the main results published in the literature on the study of logical connectives defined on finite chains, as well as to establish relationships between different subfamilies and to set up a common notation for all of them. The operators defined on finite chains which are analyzed are conjunctions and disjunctions such as t-norms, t-conorms, copulas, uninorms, among others; also, results related to implications defined also on finite chains are additionally gathered. For all the theoretical properties, it is mentioned which have been completely or partially solved or, on the contrary, which remain as open problems.