Embedding problem of fuzzy number space: part II
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Analytical expressions for the addition of fuzzy intervals
Fuzzy Sets and Systems - Special issue: fuzzy arithmetic
Triangular-norm-based addition of fuzzy intervals
Fuzzy Sets and Systems - Special issue: fuzzy arithmetic
A generalization of the Minkowski embedding theorem and applications
Fuzzy Sets and Systems
On the associativity functional equation
Fuzzy Sets and Systems
Invex and generalized convex fuzzy mappings
Fuzzy Sets and Systems
Image Processing - Principles and Applications
Image Processing - Principles and Applications
A note on the sendograph metric of fuzzy numbers
Information Sciences: an International Journal
Bipolar Fuzzy Mathematical Morphology for Spatial Reasoning
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Preinvexity and Φ1-convexity of fuzzy mappings through a linear ordering
Computers & Mathematics with Applications
Sendograph metric and relatively compact sets of fuzzy sets
Fuzzy Sets and Systems
| Hi-index | 0.20 |
It is well-known that the class of upper semicontinuous normal convex fuzzy sets with compact supports can be embedded isometrically as a complete convex cone in a Banach space. We prove an analogous result for a subclass of fuzzy sets that is free from the normality limitation by exchanging the standard algebraic operations on fuzzy sets with operations based on strict t-norms. This allows us to investigate a new notion of fuzzy convexity that we call T-convexity. We show that the class of upper semicontinuous fuzzy T-convex sets with nonempty compact supports can be embedded as a closed convex cone in a Banach space. This implies that fuzzy T-convex sets satisfy the cancellation law. We discuss a possible application of the embedding theorem in mathematical morphology.