Szpilrajn's theorem on fuzzy orderings

Authors:
Hiroshi Hashimoto
Affiliations:
-
Venue:
Fuzzy Sets and Systems
Year:
1983

Citing 4
Cited 5

On the Consistency of Precedence Matrices

Journal of the ACM (JACM)
Fuzzy Sets and Systems: Theory and Applications

Fuzzy Sets and Systems: Theory and Applications
Graph Theory with Applications to Engineering and Computer Science (Prentice Hall Series in Automatic Computation)

Graph Theory with Applications to Engineering and Computer Science (Prentice Hall Series in Automatic Computation)
Similarity relations and fuzzy orderings

Information Sciences: an International Journal

Convergence of max-arithmetic mean powers of a fuzzy matrix

Fuzzy Sets and Systems
Convergence of powers for a fuzzy matrix with convex combination of max-min and max-arithmetic mean operations

Information Sciences: an International Journal
On the max-generalized mean powers of a fuzzy matrix

Fuzzy Sets and Systems
Canonical form of a transitive fuzzy matrix

Fuzzy Sets and Systems
Transitivity of generalized fuzzy matrices

Fuzzy Sets and Systems

Quantified Score

Hi-index	0.20

Visualization

Abstract

Fuzzy relation matrices are considered and the well-known Szpilrajn theorem on orderings is generalized to fuzzy orderings. Zadeh has already shown a generalized theorem, but another generalization is given in matrix form. Some interesting operations on fuzzy matrices are introduced, and their properties are mentioned briefly. The theorem is represented in terms of the matrix operations. The operations have many properties and are useful in the various applications of fuzzy matrices or fuzzy relations.