A Method Converting Multi-Properties Objective Reachability Problems to Multi-Objective Sets Reachability Problems over FKS

Abstract

In this paper, we focus on the symmetrical relationship between multi-properties objective reachability problems and multi-objective sets reachability problems over FKS based on Zadeh logic. First, we give the formal definitions of those two problems. Then, we study their relationships and find that a multi-properties objective reachability problem and a special case of multi-objective sets reachability problems have symmetry. Finally, we give a polynomial time algorithm based on this symmetry to convert a multi-properties objective reachability problem to a multi-objective sets reachability problem. In addition, an illustrative example is listed to express some possible application methods based on our work.

Keywords

• multi-properties objective reachability
• multi-objective sets reachability
• fuzzy kripke structure
• conversion algorithm