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An interactive algorithm for multiobjective ranking for underlying linear and quasiconcave value functions
Author(s) -
Tezcaner Öztürk Diclehan,
Köksalan Murat
Publication year - 2021
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12704
Subject(s) - quasiconvex function , ranking (information retrieval) , preference , mathematical optimization , mathematics , convergence (economics) , linear programming , order (exchange) , set (abstract data type) , matrix (chemical analysis) , decision maker , value (mathematics) , computer science , preorder , algorithm , artificial intelligence , convex optimization , convex analysis , statistics , regular polygon , operations research , discrete mathematics , economics , geometry , materials science , finance , composite material , programming language , economic growth
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.