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首页> 外文期刊>IEEE Transactions on Fuzzy Systems >A New Approach to Interval-Valued Choquet Integrals and the Problem of Ordering in Interval-Valued Fuzzy Set Applications
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A New Approach to Interval-Valued Choquet Integrals and the Problem of Ordering in Interval-Valued Fuzzy Set Applications

机译：区间值模糊集合的新方法和区间值模糊集应用中的有序问题

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摘要

We consider the problem of choosing a total order between intervals in multiexpert decision making problems. To do so, we first start researching the additivity of interval-valued aggregation functions. Next, we briefly treat the problem of preserving admissible orders by linear transformations. We study the construction of interval-valued ordered weighted aggregation operators by means of admissible orders and discuss their properties. In this setting, we present the definition of an interval-valued Choquet integral with respect to an admissible order based on an admissible pair of aggregation functions. The importance of the definition of the Choquet integral, which is introduced by us here, lies in the fact that if the considered data are pointwise (i.e., if they are not proper intervals), then it recovers the classical concept of this aggregation. Next, we show that if we make use of intervals in multiexpert decision making problems, then the solution at which we arrive may depend on the total order between intervals that has been chosen. For this reason, we conclude the paper by proposing two new algorithms such that the second one allows us, by means of the Shapley value, to pick up the best alternative from a set of winning alternatives provided by the first algorithm.
机译：在多专家决策问题中，我们考虑了在时间间隔之间选择总顺序的问题。为此，我们首先开始研究区间值聚合函数的可加性。接下来，我们简要地讨论通过线性变换保留可接纳订单的问题。我们研究了可容许阶数的区间值有序加权聚合算子的构造，并讨论了它们的性质。在这种情况下，我们基于可允许的聚集函数对，针对可允许的阶数给出了区间值Choquet积分的定义。我们在这里介绍的Choquet积分定义的重要性在于以下事实：如果考虑的数据是逐点的（即，如果它们不是适当的间隔），那么它将恢复这种聚合的经典概念。接下来，我们表明如果在多专家决策问题中使用间隔，那么我们得出的解决方案可能取决于所选间隔之间的总顺序。因此，我们通过提出两种新算法来结束本文，以便第二种算法通过Shapley值使我们能够从第一种算法提供的一组获胜替代方案中选择最佳替代方案。

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