Multiple-Criteria Fuzzy Evaluation in FuzzME - Transitions Between Different Aggregation Operators

The FuzzME is a software tool for multiple-criteria fuzzy evaluation. The type of evaluation employed in the fuzzy models fully agrees with the paradigm of the fuzzy set theory; the evaluations express the (fuzzy) degrees of fulfillment of the corresponding goals. The basic structure used for the evaluation is called a goals tree. Within the goals tree, the aggregation of partial fuzzy evaluations is done either by one of fuzzified aggregation operators or by a fuzzy expert system. In the FuzzME, the following aggregation methods are supported: fuzzy weighted average, fuzzy OWA operator, fuzzified WOWA operator, fuzzified discrete Choquet integral, and fuzzy expert system. The comprehensive description of the methods and their use in FuzzME has been published in [3]. The paper contains a brief description of the methods. The main part of the paper studies the situation when it turns out that the relationship among the criteria is more complex than it was expected. In this case, it would be favorable to replace the original aggregation operator with a more general one with a minimum effort. For this purpose, two algorithms will be presented. The first one allows to derive FNV-measure (fuzzy-number-valued fuzzy measure) for the fuzzy Choquet integral from the parameters of the original aggregation operator (any of the above mentioned aggregation operators can be used). The second algorithm can be used to derive a fuzzy rule base so that the result would be as similar as possible to the original aggregation method.