Logarithmic aggregation operators and distance measures

Abstract

The Hamming distance is a well-known measure that isdesigned to provide insights into the similarity betweentwo strings of information. In this study, we use the Ham-ming distance, the optimal deviation model, and the gener-alized ordered weighted logarithmic averaging (GOWLA)operator to develop the ordered weighted logarithmicaveraging distance (OWLAD) operator and the gener-alized ordered weighted logarithmic averaging distance(GOWLAD) operator. The main advantage of these oper-ators is the possibility of modeling a wider range of com-plex representations of problems under the assumption ofan ideal possibility. We study the main properties, alterna-tive formulations, and families of the proposed operators.We analyze multiple classical measures to characterize theweighting vector and propose alternatives to deal with thelogarithmic properties of the operators. Furthermore, wepresent generalizations of the operators, which are obtainedby studying their weighting vectors and the lambda param-eter. Finally, an illustrative example regarding innovationproject management measurement is proposed, in which amulti-expert analysis and several of the newly introducedoperators are utilized.