Transitions Between Fuzzified Aggregation Operators
Pavel Holeček and Jana Talašová
An important problem in the multiple-criteria decision-making is how to combine multiple evaluations according to the individual criteria into the overall evaluation. Many aggregation methods have been developed for this task. When the evaluations are expressed by fuzzy numbers, fuzzified versions of these methods can be used. There is usually a trade-off between the versatility of the aggregation operator and the number of its parameters that have to be set. Setting correct parameters can pose a problem for the decision-maker in case of a more complex aggregation method. This paper proposes to overcome the problem in the following way – instead of creating a complex model directly, a simpler model, which represents only a rough approximation, is used first. In the next step, the model is refined and the original simple aggregation method is replaced by a more complex one. The parameters for the new aggregation method are derived automatically. Two algorithms are presented in the paper for this task – the first one derives a FNV-fuzzy measure (fuzzy-number-valued fuzzy measure) for the fuzzified Choquet integral, the latter one proposes a fuzzy rule base for the fuzzy expert system.
Keywords: Fuzzy; multiple-criteria decision-making; aggregation; Choquet integral; FNV-fuzzy measure, fuzzy expert system, fuzzy rule base