Eigenvectors and generators of fuzzy relations

Abstract

A new geometric approach to the study of the eigenvectors is provided. The T-eigenvectors of a T-indistinguishability operator are characterized as its generators in the sense of the representation theorem of L. Valverde (1985). This theorem states that every T-indistinguishability operator on a set X can be generated by a family of fuzzy subsets of X and, reciprocally, every family of fuzzy subsets of X generated a T-indistinguishability operator on X in a natural way. Some concepts related to T-eigenvectors and generators of T-indistinguishabilities are reviewed, and their relation is studied. Some examples are given.<>