Certainty aggregation and the certainty fuzzy measures. Issue 4 (6th February 2018) - Jin, LeSheng; Mesiar, Radko; Borkotokey, Surajit; Kalina, Martin
Abstract: Aggregation functions are mostly used in decision‐making situations that require information fusion in a meaningful manner. The main purpose of aggregation is to turn a group of input data into a single and comprehensive one. However, in real decision‐making and system evaluation problems, the decision maker may exhibit only some amount of certainty in her decision inputs. In this study, we show how to aggregate these certainty degrees assigned to a group of inputs in an intuitive and reasonable manner. One of the interesting aspects of the problem is that the value aggregation is independent of their certainty degrees while the certainty aggregation essentially depends on both the input values and the value aggregation function. The construction of the aggregation function gives rise to a fuzzy measure that satisfies some very interesting properties. The technique presented here has wide range of applications.