A new map (¿E) between fuzzy subsets of a universe X endowed with a T-indistinguishability operator E is introduced. The main feature of ¿E is that it has the columns of E as fixed points, and thus it provides us with a new criterion to decide whether a generator is a column. Two well known maps (fE and ¿E) are also reviewed, in order to compare them with ¿E. Interesting properties of the fixed points of ¿E and ¿2 E are studied. Among others, the fixed points of ¿E (Fix(¿E)) are proved t...
A new map (¿E) between fuzzy subsets of a universe X endowed with a T-indistinguishability operator E is introduced. The main feature of ¿E is that it has the columns of E as fixed points, and thus it provides us with a new criterion to decide whether a generator is a column. Two well known maps (fE and ¿E) are also reviewed, in order to compare them with ¿E. Interesting properties of the fixed points of ¿E and ¿2 E are studied. Among others, the fixed points of ¿E (Fix(¿E)) are proved to be the maximal fuzzy points of (X,E) and the fixed points of ¿2 E coincide with the Image of ¿E. An isometric embedding of X into Fix(¿E) is established and studied.
A new map (ΛE) between fuzzy subsets of a universe X endowed with a T-indistinguishability operator E is introduced. The main feature of ΛE is that it has the columns of E as fixed points, and thus it provides us with a new criterion to decide whether a generator is a column. Two well known maps (φE and ψE) are also reviewed, in order to compare them with ΛE. Interesting properties of the fixed points of ΛE and Λ2
E are studied. Among others, the fixed points of ΛE (Fix(ΛE)) are proved to be the maximal fuzzy points of (X,E) and the fixed points of Λ2 E coincide with the Image of ΛE. An isometric embedding of X into Fix(ΛE) is established and studied.
Citation
Boixader Ibáñez, D.; Recasens Ferrés, J. A map characterizing the fuzzy points and columns of a T-indistinguishability operator. "International journal of uncertainty fuzziness and knowledge-based systems", Octubre 2005, vol. 16, núm. 2, p. 129-145.