The minimal mathematical structure for a synchronic approach to fuzzy set theory

The paper gives a concrete presentation of the minimal structure on the monoid of an external subset classifier of a universe of usual sets with Zadeh-Goguen L-fuzzy subsets. The result was first investigated by the first author, with the aim of providing a new insight into the synchronic approach to fuzzy set theory. The extensive use of conceptual mathematics (i.e. category theory) in the original paper, restricts the audience of readers of this analysis to persons who are already acquainted with conceptual mathematics. The aim of this paper is to avoid as much as possible the use of functorial terminology in the presentation of the minimal mathematical structure on the set of truth values, for a synchronic approach to fuzzy sets. By doing so, we hope to widen the audience of scientists interested in the foundation of Zadeh-Goguen L-fuzzy sets and to provide a new way of looking at the synchronic approach to fuzziness.