The concept of grade of membership
Fuzzy Sets and Systems - Interpretations of Grades on Membership
Consonant approximation of belief functions
International Journal of Approximate Reasoning
A generalization of the representation theorem
Fuzzy Sets and Systems
Graded sets and points: a stratified approach to fuzzy sets and points
Fuzzy Sets and Systems
Representations with fuzzy darts
Fuzzy Sets and Systems
The three semantics of fuzzy sets
Fuzzy Sets and Systems - Special issue: fuzzy sets: where do we stand? Where do we go?
A probabilistic definition of a nonconvex fuzzy cardinality
Fuzzy Sets and Systems
Quantifier guided aggregation of fuzzy criteria with associated importances
Aggregation operators
Modelling and Reasoning with Vague Concepts (Studies in Computational Intelligence)
Modelling and Reasoning with Vague Concepts (Studies in Computational Intelligence)
Fuzzy sets and sheaves. Part II
Fuzzy Sets and Systems
From fuzzy sets to the decompositions of non-rigid sets
Fuzzy Sets and Systems
Gradual elements in a fuzzy set
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Fuzzy Quantification Using Restriction Levels
WILF '09 Proceedings of the 8th International Workshop on Fuzzy Logic and Applications
Fuzzy Sets for Image Texture Modelling Based on Human Distinguishability of Coarseness
WILF '09 Proceedings of the 8th International Workshop on Fuzzy Logic and Applications
Possibilistic information fusion using maximal coherent subsets
IEEE Transactions on Fuzzy Systems
On existence of P-valued fuzzy sets with a given collection of cuts
Fuzzy Sets and Systems
Fuzzy Sets and Systems
A new fusion strategy for web metasearch
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special Issue on Soft Computing on Web; Guest Editors: A. G. López-Herrera, E. Herrera-Viedma
IEEE Transactions on Fuzzy Systems
Gradual Numbers and Their Application to Fuzzy Interval Analysis
IEEE Transactions on Fuzzy Systems
RL-bags: A conceptual, level-based approach to fuzzy bags
Fuzzy Sets and Systems
Comparing partitions by means of fuzzy data mining tools
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
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In this paper we describe a non-nested level-based representation of fuzziness, closely related to some existing models and concepts in the literature. Our objective is to motivate the use of this non-nested model by describing its theoretical possibilities, and illustrating them with some existing applications. From a theoretical point of view, we discuss the semantics of the representation, which goes beyond and has as a particular case fuzzy sets as represented by a collection of @a-cuts. In addition, the proposed operations on level-based representations, contrary to those of existing fuzzy set theories, satisfy all the properties of Boolean logic. We discuss the contributions of the representation and operation by levels to practical applications, in particular for extending crisp notions to the fuzzy case. In this respect, an important contribution of the proposal is that fuzzy mathematical objects (not only sets and the corresponding predicates) and operations are uniquely and easily defined as extensions of their crisp counterparts. In order to illustrate this claim, we recall level representations of quantities (gradual numbers) and their complementarity to fuzzy intervals (often inappropriately called fuzzy numbers).