Aggregation of Individual Rankings Through Fusion Functions: Criticism and Optimality Analysis

作     者：Bustince, Humberto Bedregal, Benjamin Jesus Campion, Maria da Silva, Ivanosca Fernandez, Javier Indurain, Esteban Raventos-Pujol, Armajac Santiago, Regivan H. N. 

作者机构：Univ Publ Navarra Dept Estad Informat & Matemat Pamplona 31006 Spain Univ Publ Navarra Inst Smart Cities Pamplona 31006 Spain Univ Fed Rio Grande Norte UFRN Dept Informat & Matemat Aplicada DIMAp BR-59078970 Natal RN Brazil Univ Publ Navarra Inst Adv Res Business & Econ Pamplona 31006 Spain Univ Fed Rio Grande Norte UFRN Diretoria Mat & Patrimonio DMP BR-59078970 Natal RN Brazil Univ Publ Navarra InaMat2 Inst Adv Mat & Math Pamplona 31006 Spain Univ Publ Navarra Inst Adv Res Business & Econ Pamplona 59078970 Spain 

出 版 物：《IEEE TRANSACTIONS ON FUZZY SYSTEMS》 (IEEE Trans Fuzzy Syst)

年 卷 期：2022年第30卷第3期

页      面：638-648页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：MINECO/AEIFEDER, UE [ECO2015-65031-R, MTM2015-63608-P] MINECO/AEI-FEDER, UE [TIN2016-77356-P] AEI [PID2019-108392GB-I00] Brazilian National Council for Scientific and Technological Development CNPq [307781/2016-0] 

主　　题：Decision making Proposals Mathematics Aggregates Smart cities Organizations Indexes Aggregation decision-making general means ranking ranking optimality score functions social choice 

摘      要：Throughout this article, our main idea is to analyze from a theoretical and normative point of view different methods to aggregate individual rankings. To do so, first, we introduce the concept of a general mean on an abstract set. This new concept conciliates the social choice-where well-known impossibility results as the Arrovian ones are encountered-and the decision-making approaches-where the necessity of fusing rankings is unavoidable. Moreover, it gives rise to a reasonable definition of the concept of a ranking fusion function that does indeed satisfy the axioms of a general mean. Then, we will introduce some methods to build ranking fusion functions, paying a special attention to the use of score functions, and pointing out the equivalence between ranking and scoring. To conclude, we prove that any ranking fusion function introduces a partial order on rankings implemented on a finite set of alternatives. Therefore, this allows us to compare rankings and different methods of aggregation, so that in practice, one should look for the maximal elements with respect to such orders defined on rankings.