Modeling multi-criteria objective functions using fuzzy measures

• Use of measures to express decision maker’s objective function.
• Role of integral to evaluate an alternative’s overall satisfaction to objective function.
• Look at a number of special types of measure based decision objective functions.
• Measure representation of logically expressed combinations of criteria.
• Study quasi-additive and quasi-maxitive measures.

We introduce the idea of a measure. We describe several important finite integrals useful for obtaining an average value of a collection of argument values weighted by a measure. We particularly look at the case of binary measures and show that all integrals in this case evaluate to the same value. We describe the use of measures in multi-criteria decision making as a way of expressing a decision maker’s objective function in terms of collection of relevant criteria. We look at the role of an integral as a way to evaluate an alternative’s overall satisfaction to their objective function in terms of its satisfaction to the individual criteria. We look at a number of special types of measure based decision objective functions.