Fuzzy Groups: some group-theoretic analogs
Information Sciences: an International Journal
Fuzzy Sets and Systems
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
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
From fuzzy sets to the decompositions of non-rigid sets
Fuzzy Sets and Systems
Alternative characterizations for the representation of families of sets by fuzzy sets
Information Sciences: an International Journal
Uniqueness in the generalized representation by fuzzy sets
Fuzzy Sets and Systems
On existence of P-valued fuzzy sets with a given collection of cuts
Fuzzy Sets and Systems
On lattice valued up-sets and down-sets
Fuzzy Sets and Systems
International Journal of Approximate Reasoning
A note on Nguyen--Fullér--Keresztfalvi theorem and Zadeh's extension principle
Fuzzy Sets and Systems
Short communication: Lattice representations of interval-valued fuzzy sets
Fuzzy Sets and Systems
Fuzzy identities with application to fuzzy semigroups
Information Sciences: an International Journal
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The important concept of identifying a fuzzy subset of a set R with its corresponding chain of level sets is widely used in the literature. We investigate in this paper the problem of characterization of all fuzzy subsets of R that can be identified with a given arbitrary family C of subsets of R together with a given arbitrary subset S of [0,1]. Although our main focus is on the problem of uniqueness, we start by giving necessary and sufficient conditions for both existence and uniqueness of such fuzzy subsets. We continue by obtaining several algebraic and topological properties under which uniqueness is guaranteed. To further support our results, we present some examples which we hope will shed more light on the above mentioned problem of identification. We finish by raising a few natural questions that are left as open problems for further investigation.