Basic intuitionistic principles in fuzzy set theories and its extensions (a terminological debate on Atanassov IFS) (Q869120)

A certain lattice-valued generalization of fuzzy sets was introduced in 1983 by \textit{K. T. Atanassov} [see, e.g., Intuitionistic fuzzy sets. Theory and applications. Heidelberg: Physica-Verlag (1999; Zbl 0939.03057)] and coined ``intuitionistic fuzzy sets'' (IFS). These objects have since been studied for diverse applications. From a formal point of view there is, however, neither a relationship to intuitionistic logic nor to intuitionistic mathematics. The growing misuse of the word ``intuitionistic'' in those studies caused a recent debate which became manifest in a paper by \textit{D. Dubois, S. Gottwald, P. Hájek, J. Kacprzyk} and \textit{H. Prade} [Fuzzy Sets Syst. 156, No. 3, 485--491 (2005; Zbl 1098.03061)]. The authors continue this debate from a more algebraic point of view and explain what are the main structural differences between the standard approach toward IFS and intuitionistic points of view.