Preference Graph of Potential Method as a Fuzzy Graph

Abstract

An autocatalytic set (ACS) is a graph. On the other hand, the Potential Method (PM) is an established graph based concept for optimization purpose. Firstly, a restricted form of ACS, namely, weak autocatalytic set (WACS), a derivation of transitive tournament, is introduced in this study. Then, a new mathematical concept, namely, fuzzy weak autocatalytic set (FWACS), is defined and its relations to transitive PM are established. Some theorems are proven to highlight their relations. Finally, this paper concludes that any preference graph is a fuzzy graph Type 5.