Parameterized defuzzification with continuous weighted quasi-arithmetic means – An extension

Parameterized aggregation becomes an attractive idea in many applications. By applying the quasi-arithmetic mean-based defuzzification method and its orness measure, we extend the properties of discrete quasi-arithmetic mean with an orness measure to the case of continuous weighted quasi-arithmetic means, and apply them to the parameterized estimation of fuzzy or random variables. When facing the uncertainty of these variables, the decision maker can obtain the crisp value estimation which is always consistent with his/her preference information. Two families of continuous weighted quasi-arithmetic means with exponential and power function generators are discussed. Combining these conclusions with that of the discrete case, we can understand better the properties of quasi-arithmetic means and extend their possible applications.