Unidefiners

In this study, we examine the concept of a unidefiner, defined on the interval [0,∞], which provides a unified framework for both t-definer and t-codefiner structures. Similar to the approach of uninorms on [0,1], a unidefiner is a binary operation on [0,∞], with a neutral element e∈[0,∞],, which is associative, commutative, and monotonic. Consequently, when e = 0, it yields a t-definer, and when e =∞, it yields a t-codefiner. This paper discusses the theoretical properties of unidefiners and explores their relationship with t-definer and t-codefiner examples. In conclusion, it emphasizes that unidefiners can serve as a “generalized connective” analogous to uninorms for a “proper” identity value (i.e., e ≠ 0, e≠∞) in the [0,∞] range.