The adequacy coefficient is a very useful technique that provides a more complete formulation than the Hamming distance in decision making problems. In this paper, we suggest a generalization by using generalized and quasi-arithmetic means. As a result, we will get the generalized ordered weighted averaging adequacy coefficient (GOWAAC) and the Quasi-OWAAC operator. These new aggregation operators generalize a wide range of particular cases such as the generalized adequacy coefficient (GAC), the weighted generalized adequacy coefficient (WGAC), the ordered weighted averaging adequacy coefficient (OWAAC), the ordered weighted quadratic averaging adequacy coefficient (OWQAAC), and others. We study different families and properties of these aggregation operators. We also analyze the unification point with distance measures and we find that in these situations, the GOWAAC and the Quasi-OWAAC become the Minkowski ordered weighted averaging distance (MOWAD) operator and the Quasi-OWAD operator, respectively. Finally, we also develop an application of the new approach in a strategic decision making problem about selection of strategies.
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