Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued ``intuitionistic'' sets, ``intuitionistic'' fuzzy sets and topologies
This is a category-theoretically based study of the appropriateness of different recent ``generalizations'' of the notion of fuzzy set. The authors prove that almost all of these generalizations of the standard notion of fuzzy set with the real unit interval as the membership degree structure become theoretically obsolete from the unifying point of view that the membership degree structures for fuzzy sets should be lattices, possibly enriched with additional operations like in the very popular case of residuated lattice-ordered semigroups. What remains, therefore, as motivations for such particular ``generalizations'' should be careful discussions what is needed for particular applications, a topic which quite often is extremely underrepresented in ``theoretical'' papers related to such ``generalizations''.
scientific article; zbMATH DE number 5001361
scientific article