h-type indices for multiple authorship papers based on “relative first author” principle

Recently, the number of multiple authorship and collaborative papers has been growing rapidly. This number differs significantly according to various scientific fields. Known that h-type indices (h-index, gindex, A-index, etc.) are used to evaluate the performance of researchers, which do not distinguish between single-author and multi-author papers in the evaluation process. In other words, a citation received from multi-authored papers is applied to all co-authors (as in the single-authored paper). To solve this problem, several weighted version of the h-index have been proposed. Most of these versions are indices and are based on the division principle of citations based on the co-author’s position in the authors’ order. In other words, according to the position of the co-authors order, the weight is assigned to the co-authors, and the citations are proportionally divided according to co-authors in these weights. Obviously, the calculation of weights is important in this case. h-type indices proposed in the paper are based on the “relative first author” (or “local first author”) principle. “Relative first author” means the co-authors being in the first position relative to the co-authors after him. Based on this principle, existing weighting schemes were modified, and then new weighted h-type indices were proposed for multiple authorship papers according to these weighting schemes. In other words, the “local first author” approach was proposed instead of the “global first author” approach in calculating the h-type indices for multiple authorship papers. The suggested indices were calculated for 30 researchers selected from the Google Scholar database and compared with other relevant h-type indices.