Modeling Fuzzy and Interval Fuzzy Preferences Within a Graph Model Framework

Abstract

A methodology is developed to model a decision maker's (DM's) fuzzy and/or interval fuzzy preference over feasible scenarios or states within the framework of the graph model for conflict resolution. This technique uses the DM's fuzzy relative importance of its preference statements and their fuzzy truth values for the feasible states in a conflict under uncertain conditions. A preference statement of a DM is a preferable combination of DM's options or courses of action. The fuzzy importance for one preference statement over another, a value in the interval $[0, 1]$ , is interpreted as the degree to which the first preference statement is more important than the second to the DM. A fuzzy truth value of a preference statement at a feasible state is a number in the interval $[0, 1]$ that represents the degree to which the statement is true at the state. When the DM is confident in its pairwise fuzzy importance degrees over the preference statements and their fuzzy truth values at the feasible states, the methodology provides a fuzzy preference over the states. When there is an ordinary or crisp importance ordering of preference statements and when the truth values of preference statements are classical or crisp at the feasible states, the technique generates a crisp preference over the states. The methodology is illustrated using a case study.