Fuzzy Groups: some group-theoretic analogs
Information Sciences: an International Journal
Measurement of membership functions and their acquisition
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
Fuzzy Sets and Systems
Certain fuzzy ideals of rings redefined
Fuzzy Sets and Systems
A generalization of the representation theorem
Fuzzy Sets and Systems
On a representation of posets by fuzzy sets
Fuzzy Sets and Systems
On an equivalence of fuzzy subgroups I
Fuzzy Sets and Systems
Simulation, Knowledge-Based Computing, and Fuzzy Statistics
Simulation, Knowledge-Based Computing, and Fuzzy Statistics
Completion of ordered structures by cuts of fuzzy sets: an overview
Fuzzy Sets and Systems - Logic and algebra
Representing ordered structures by fuzzy sets: an overview
Fuzzy Sets and Systems - Logic and algebra
On an equivalence of fuzzy subgroups II
Fuzzy Sets and Systems - Logic and algebra
General form of lattice-valued fuzzy sets under the cutworthy approach
Fuzzy Sets and Systems
From fuzzy sets to the decompositions of non-rigid sets
Fuzzy Sets and Systems
Uniqueness results in the representation of families of sets by fuzzy sets
Fuzzy Sets and Systems
Some notes on equivalent fuzzy sets and fuzzy subgroups
Fuzzy Sets and Systems
On existence of P-valued fuzzy sets with a given collection of cuts
Fuzzy Sets and Systems
International Journal of Approximate Reasoning
Short communication: Lattice representations of interval-valued fuzzy sets
Fuzzy Sets and Systems
Hi-index | 0.20 |
The concept of representation of a given family of sets by a fuzzy set in such a way that the level sets of the fuzzy set are precisely the given sets is widely used in the literature for the classification and study of fuzzy algebraic structures on the same underlying set. The problem of existence of such fuzzy sets was investigated by various authors. As far as we know, the problem of uniqueness of such fuzzy sets was not studied before. We establish, among other things, necessary and sufficient conditions under which uniqueness is guaranteed in the cases of complete as well as partial representations of the level sets of the fuzzy set.