This paper studies a fuzzy graph rewriting with single pushout approach from a viewpoint of fuzzy relational calculus. Two possible kinds of matchings for fuzzy graph rewritings are given, namely, a rigorous matching which just generalizes matchings for crisp (or ordinary) graph rewritings, and an "-matching which represents rather ambiguous or fuzzy one. Finally the pullback structure of fuzzy...

uzzy graph theory is finding an increasing number of applications in modeling real time systems where the level of information inherent in the system varies with different levels of precision. In the applied field, the success of the use of fuzzy set theory depends on the choice of the membership function that we make. However, there are applications in which experts do not have precise knowled...

Mathematical morphology is based on the algebraic framework of complete lattices and adjunctions, which endows it with strong properties and allows for multiple extensions. In particular, extensions to fuzzy sets of the main morphological operators, such as dilation and erosion, can be done while preserving all properties of these operators. Another extension concerns bipolar fuzzy sets, where ...

Graph theory has numerous application to problems in systems analysis, operations research, economics, and transportation. However, in many cases, some aspects of a graph-theoretic problem may be uncertain. For example, the vehicle travel time or vehicle capacity on a road network may not be known exactly. In such cases, it is natural to deal with the uncertainty using the methods of fuzzy sets...

Problem statement: In this study researchers propose a new fuzzy graph theoretic construct called fuzzy metagraph and a new method of clustering finding the similar fuzzy nodes in a fuzzy metagraph. Approach: We adopted T-norms (Triangular Norms) functions and join two or more Tnorms to cluster the fuzzy nodes. Fuzzy metagraph is the fuzzyfication of the crisp Metagraphs using fuzzy Generating ...

V. Chv atal proved that no minimal imperfect graph has a small transversal, that is, a set of vertices of cardinality at most + ! 1 which meets every !-clique and every -stable set. In this paper we prove that a slight generalization of this notion of small transversal leads to a conjecture which is as strong as Berge's Strong Perfect Graph Conjecture for a very large class of graphs, although ...

In order to prove the Strong Perfect Graph Conjecture, the existence of a ”simple” property P holding for any minimal non-quasi-parity Berge graph G would really reduce the difficulty of the problem. We prove here that this property cannot be of type ”G is F-free”, where F is any fixed family of Berge graphs.