Abstract:
t-norms and t-conorms have many important applications in a wide scope of communities such as functional equation, ordered semigroup, many-valued logic, probabilistic metric space, fuzzy set theory and information aggregations.Constructions and characterizations of t-norms and conorms have been being one of research topics in related fields. Due to the well-known duality between t-norms and t-conorms, most researches focus on t-norms and then are transformed to t-conorms. However, not all properties or construction methods of t-norms can be translated by duality to t-conorms, and the construction of t-norms by means of pseudo-inverses of monotone functions is such a good counterexample. In this paper, construction methods of t-conorms in terms of right-continuous pseudo-inverses and quasi-inverses of monotone functions are proposed, which can be views as counterparts of the construction of t-norms based on left-continuous pseudo-inverses of monotone functions. Firstly, some basic properties of right-continuous pseudo-inverse of a monotone function on a closed interval are discussed, and then several methods for constructions of t-conorms conorms from given ones based on the right-continuous pseudo-inverse and quasi-inverse, respectively, of a non-decreasing function on the closed unit interval are obtained, with several supporting examples.
