Space Of Fuzzy Sets Research Articles

Processing uncertain information in the linear space of fuzzy sets

The problem of processing uncertain information covering aspects of their repetitivity and negativity is studied. Both of these features are not handled within a lattic structure of fuzzy sets. It is pointed out how these issues can be addressed in a linear space of fuzzy sets. Quasi-ordering and ordering relations are also discussed.

Congruence classes of fuzzy sets form a Banach space

Asymmetry classes of normal, fuzzy convex fuzzy sets, on R n are defined. Unlike the linear structure of the space of fuzzy sets, which is only a real cone, the set of asymmetry classes can be given the structure of a linear space, which is complete with an appropriate metric.

Metric spaces of fuzzy sets

Two classes of metrics are introduced for spaces of fuzzy sets. Their equivalence is discussed and basic properties established. A characterisation of compact and locally compact subsets is given in terms of boundedness and p-mean equileft-continuity, and the spaces shown to be locally compact, complete and separable metric spaces.

On the convergence of fuzzy sets

Three kind of convergences are defined on a space of fuzzy sets. Relationships between these convergences are studied. Some comments on the fixed point property are represented.