三参数区间数调和平均算子及决策应用

针对决策信息以三参数区间数据形式给出的多属性决策问题，提出了一些新的三参数区间数据信息的集成算子和决策方法。基于连续区间数据有序加权调和平均(C OWHA)算子，定义了连续的三参数区间数据有序加权调和平均(CP OWHA)算子，并将该算子进行了拓展，提出了加权调和CP OWHA(WHCP OWHA)算子、有序加权调和CP OWHA(OWHCP OWHA)算子和组合的CP OWHA(CCP OWHA)算子。进一步证明了WHCP OWHA算子和OWHCP OWHA算子均为CCP OWHA算子的特例。CCP OWHA算子同时推广了WHCP OWHA算子和OWHCP OWHA算子，CCP OWHA算子不仅考虑了每个数据的自身重要性程度，而且还体现了该数据所在位置的重要性程度。基于WHCP OWHA算子和CCP OWHA算子，提出了一种属性权重和专家权重均为确定实数且属性值为三参数区间数的多属性群决策方法。最后给出了一个数值例子，结果表明该方法有效。

Some harmonic averaging operators over a continuous three parameters interval argument and application to decision making

With respect to the problem of multiple attribute decision making in which the decision making information values are three parameters interval argument,some information aggregation operators over a continuous three parameters interval argument and a new decision making method are proposed.Based on the continuous ordered weighted harmonic averaging (C-OWHA) operator,the continuous three parameters interval argument OWHA (CP-OWHA) operator is proposed.Further,some operators including weighted harmonic CP-OWHA (WHCP-OWHA) operator,ordered weighted harmonic CP-OWHA (OWHCP-OWHA) operator and combined CP-OWHA (CCP-OW HA) opera tor are proposed and an inference that is also proued.both WHCP-OWHA and OWHCP-OWHA operators are the special case of the CCP-OWHA operator the CCP-OWHA operator generalizes both the WHCP-OWHA and OWHCP-OWHA operators simultaneously,and reflects the importance degrees of both the given arguments and their ordered positions.A method based on the WHCP-OWHAand CCP-OWHA operators is developed for dealing with multiple attribute group decision making,in which the attribute weights and expert weights take the form of the real numbers,and the preference values take the form of the three parameters interval argument.Finally a numerical example is provided to illustrate the proposed method.The result shows the approach is simple,effective and easy to calculate.