Appendix A

Abstract

The first part of this appendix presents three approaches in defining the fuzzy version (generalization) of the mathematical graph structure: graphs with fuzzy vertices, graphs with fuzzy edges, and graphs with fuzzy vertices and edges. Their advantages and shortcomings are discussed briefly. Fuzzy graphs are observed in the light of fuzzy relations theory, and as a generalization of the notion of random graph. In the second part, we generalize some fuzzy algebraic structures towards not only [0, 1] valued, but lattice, poset, and relational structured valued structures. It is exciting to see how powerful a modeling tool they are, and also to see how classical results continue to hold as but a special case of the new results.