Generalized logarithmic proportional averaging operators and their applications to group decision making

In this paper, we present a new operator called the generalized ordered weighted logarithmic proportional averaging (GOWLPA) operator based on an optimal model, which is an extension of the generalized ordered weighted logarithm averaging (GOWLA) operator. The key advantage of the GOWLPA operator is not only that it is an aggregation operator with theoretic basis on aggregation, but also that the weighting vector of the GOWLPA operator depends on the input arguments. We analyze some properties and families of the GOWLPA operator and further develop generalizations of this operator including the generalized hybrid logarithmic proportional averaging (GHLPA) operator and the quasi ordered weighted logarithmic proportional averaging (QOWLPA) operator. To determine the GOWLPA operator weights, we propose the generalized logarithm chi-square method (GLCSM) which does not follow a regular distribution. Finally, we give a numerical example of an investment selection to illustrate the application of the GOWLPA operator to multiple attribute group decision making.

► Generalized ordered weighted logarithmic proportional averaging operator is developed.
► We study the properties and describe families of the new operator.
► We present generalizations of the new operator.
► We propose the generalized logarithm chi-square method to determine the new operator weights.
► The new operator is applied to group decision making.