PUBLIC GOOD INDEX FOR FUZZY SIMPLE GAMES IN MULTILINEAR EXTENSION FORM

Abstract: In this paper, I will mainly concerned on influence of a voter if he shift his rule from a winning situation to no participation (rights to reject) in a decision making situation. I will try to measure the power of voter mathematically using fuzzy approach while he shift his rule from a winning situation. I will propose public good index in fuzzy version as a method to measure power of voter. I propose the fuzzy versions of Public Good Index (PGI ) and corresponding characterizations for simple games with fuzzy coalition(fuzzy game). Finally in this paper Public Good Index is formulated for the class of simple games with fuzzy coalition in multilinear extension form.

Keywords: Decision making, Simple games, player, Fuzzy simple games, Public Good index, fuzzy coalition.