Fuzzy Generalized Aggregation Operators in a Unified Model between the Probability, the Weighted Average and the OWA Operator

We introduce a new model that unifies the probability, the weighted average and the ordered weighted average considering the degree of importance that each concept has in the aggregation. Moreover, this approach generalizes a wide range of aggregation operators by using generalized means. Furthermore, this approach is able to assess uncertain information that can be assessed with fuzzy numbers. We call it the fuzzy generalized probabilistic ordered weighted averaging weighted average (FGPOWAWA) operator. Its main advantage is that it includes a wide range of aggregation operators such as the FPOWAWA, the quadratic FPOWAWA, the arithmetic FOWAWA, the arithmetic FPOWA, the FPWA and the double FOWA operator. We further generalize this approach by using quasi-arithmetic means obtaining the Quasi-FPOWAWA operator. We also analyze the applicability of this new approach in decision making.