A multi-attribute ranking approach based on net inferiority and superiority indexes, two weight vectors, and generalized Heronian means

摘要

In this paper, we propose a three-phase multi-attribute ranking approach having as outcomes of the modeling phase what we refer to as net superiority and inferiority indexes. These are defined as bounded differences between the classical superiority and inferiority indexes. The suggested approach herein named MANISRA (Multi-Attribute Net Inferiority and Superiority based Ranking Approach) employs in the aggregation phase a bi-parameterized family of compound averaging operators (CAOPs) referred to as generalized Heronian OWAWA (GHROWAWA) operators having the usual OWAWA operators as special instances. Note that the new defined operators are built by using a composition of an arbitrary bi-parameterized binary Heronian mean with the weighted average (WA) and the ordered weighted averaging (OWA) operators. Also, note that the current developed MANISRA method generalizes the superiority and inferiority ranking (SIR-SAW) method which is known to coincide with the quite popular PROMETHEE II method when the net flow rule is used. With net superiority and inferiority indexes and GHROWAWA operators, we are better equipped to rank rationally prespecified alternatives. The basic formulations, notations, phases and interlocking tasks related to the proposed approach are presented herein and its feasibility and effectiveness are shown in a real problem.