Adding Compensatory Terms in the Fuzzy Integral for Synthetic Evaluation of Multi-attribute Alternatives

摘要

The fuzzy integral (FI) is an interesting and often advantageous method of obtaining synthetic evaluations of objects that possess several qualitative attributes. A synthetic evaluation of each prospect choice is represented by a single real number, which is convenient for establishing a ranking of preferences for a group of objects. The need of synthetic evaluations is particularly important in expert systems where an ordering of the feasible alternatives is expected. However, the traditional formulation of the FI lacks sensitivity to some changes that may occur in the scores that are assigned to particular characteristics of an object under appraisal. In this paper, a method to take into account the variations in the scores that are not captured by the max-min operations performed by the traditional FI is presented. For clarity, an example of application of the proposed process follows the theoretical considerations. Using the numerical data from the example, the results yielded by the approaches regarding the original FI and its modified version incorporating the compensatory terms are compared and briefly discussed.