Fuzzy Sets and Systems
Fuzzy matroids and a greedy algorithm
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Theory of topological molecular lattices
Fuzzy Sets and Systems
Fuzzy Sets and Systems
A comment on “Bases of fuzzy matroids” Fuzzy Sets and Systems 31 (1989) 253–261
Fuzzy Sets and Systems
On fuzzy independence set systems
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Gradual elements in a fuzzy set
Soft Computing - A Fusion of Foundations, Methodologies and Applications
L-fuzzy numbers and their properties
Information Sciences: an International Journal
A new approach to the fuzzification of matroids
Fuzzy Sets and Systems
The set of fuzzy rational numbers and flexible querying
Fuzzy Sets and Systems
A possibilistic approach to combinatorial optimization problems on fuzzy-valued matroids
WILF'05 Proceedings of the 6th international conference on Fuzzy Logic and Applications
Efficient methods for computing optimality degrees of elements in fuzzy weighted matroids
WILF'05 Proceedings of the 6th international conference on Fuzzy Logic and Applications
Categories of bi-fuzzy pre-matroids
Computers & Mathematics with Applications
Connectedness of refined Goetschel--Voxman fuzzy matroids
Fuzzy Sets and Systems
Characterizations and applications of M-fuzzifying matroids
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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In this paper, an extension of matroids is introduced in lattice-valued fuzzy set theory. Such a generalized matroid is a pair made of a finite set and a fuzzy subfamily of its lattice-valued fuzzy subsets satisfying three axioms. It uses two lattices: one for membership grades of elements to fuzzy sets, and another for membership degrees of fuzzy sets in a fuzzy family of fuzzy sets. It is a logical generalization of the notions of matroids and fuzzifying matroids. In our definition of generalized fuzzy matroids, each L-fuzzy subset can be regarded to be independent of other ones to some degree. The relevance of generalized fuzzy matroids is shown in the setting of fuzzy vector spaces and fuzzy graphs.