Abstract: This paper aimed to consider an extension of possibilistic Kripke structure,called possibilistic Kripke cost structure (PoKCS)．We focused on expected measures and multi-attribute decision making problem on PoKCS．A possibilistic Kripke cost structure is a possibilistic Kripke structure in which transitions (or states) are augmented with costs,natural numbers that can be interpreted as costs,or dually as bonuses．We only considered equipping transitions with costs．Finally,we described a case study about the management decision of project to illustrate application of the methods discussed in the paper．

Key words: Possibility measure,Possibilistic Kripke cost structure,Multi-attribute decision making,Expected measure