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Operations on inputs are partially or completely decisive for information aggregation, and parameterized operations are widely used due to their flexibility in practice. The Bonferroni mean is a typical mean operator taking into account interrelationships between any two input variables. In this paper, the Hamacher operations are considered in constructing q-rung orthopair fuzzy aggregation operators combined with the Bonferroni mean. First, explicit expressions of aggregated results by the q-rung orthopair fuzzy Hamacher Bonferroni mean operator are presented without intermediate variables, which would certainly improve the computational efficiency. Then, limits of these resulting aggregations are examined with respect to parameters within Hamacher operations and Bonferroni mean, respectively. The obtained conclusions reveal relations among the current mean operator and some existing ones, and some numerical examples are given to facilitate the conceptual arguments. Finally, the developed operator is employed to evaluate the service quality of passenger airlines in Taiwan, China, and a comparative analysis is presented in this study.

AbstractIn recent years, many methods have been proposed in order to deal with inconsistent information systems based on indiscernibility relations in rough set theory. However, a little attention has been paid to inconsistent ordered decision tables. In this paper, the concept of allocation reductions is proposed in inconsistent ordered decision tables. And an approach to computing this kind of reductions is then presented by introducing the discernibility matrix and discernibility function. Moreover, the relationship is investigated between the allocation reduction and the -upper (-lower) approximate distribution reduction in inconsistent ordered decision tables with a single decision attribute. A fictitious numerical example is employed to substantiate the conceptual argument throughout the paper.