Quantifiers in the formulation of multiple objective decision functions

Abstract

We discuss the interpretation of linguistically quantified statements using fuzzy sets. We indicate that there are two methods of interpreting these statements, the algebraic approach and the substitution approach. We then use quantified statements to express overall decision functions involving multiple objectives. These statements are of the type “A solution should satisfy many of the objectives”. Using the algebraic and substitution approach, we develop a whole family of forms for combining multiple objectives. We show that algebraic approach corresponds to situations in which we are unconcerned about the allocation of satisfaction amongst the objectives but just interested in getting much satisfaction. The substitution approach on the other hand leads to forms which are dependent upon the allocation of satisfaction between the objectives.