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首页> 外文期刊>International Journal of Uncertainty, Fuzziness, and Knowledge-based Systems >MONOTONE APPROXIMATION OF AGGREGATION OPERATORS USING LEAST SQUARES SPLINES
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MONOTONE APPROXIMATION OF AGGREGATION OPERATORS USING LEAST SQUARES SPLINES

机译：用最小二乘样条逼近凝聚算子的单调逼近

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摘要

The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexibility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.
机译：当单调性在语义上很重要时，通常会在许多回归问题中出现对散乱数据进行单调近似的需求。一种这样的领域是模糊集理论，其中隶属函数和聚合算子是顺序保留的。最小二乘多项式样条曲线在为非线性函数建模时提供了很大的灵活性，但可能不能单调。样条系数的线性限制为样条单调性提供了必要和充分的条件。选择样条线的基础，使这些限制采用特别简单的形式。由此产生的非负最小二乘问题可以通过多种标准验证的技术来解决。也可以在同一框架中强加其他插值要求。该方法适用于模糊系统，其中从经验数据构造隶属函数和聚合算子。

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