An interactive algorithm for multiobjective ranking for underlying linear and quasiconcave value functions

TEZCANER ÖZTÜRK D., Koksalan M.

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, vol.28, no.6, pp.3513-3535, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 6
  • Publication Date: 2021
  • Doi Number: 10.1111/itor.12704
  • Journal Name: INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, ABI/INFORM, Aerospace Database, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, INSPEC, Metadex, vLex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.3513-3535
  • Keywords: interactive, strict total order, discrete alternative, convex cone, multiple criteria, transitivity, linear value function, quasiconcave value function, MULTIPLE CRITERIA, MAJORITY-RULE, ALTERNATIVES, PREFERENCES
  • Middle East Technical University Affiliated: Yes

Abstract

We develop interactive algorithms to find a strict total order for a set of discrete alternatives for two different value functions: linear and quasiconcave. The algorithms first construct a preference matrix and then find a strict total order. Based on the ordering, they select a meaningful pair of alternatives to present the decision maker (DM) for comparison. We employ methods to find all implied preferences of the DM, after he or she makes a preference. Considering all the preferences of the DM, the preference matrix is updated and a new strict total order is obtained until the termination conditions are met. We test the algorithms on several instances. The algorithms show fast convergence to the exact total order for both value functions, and eliciting preference information progressively proves to be efficient.