Dual cone approach to convex-cone dominance in multiple criteria decision making

In a paper published in Management Science in 1984, Korhonen, Wallenius, and Zionts presented the idea and method based on convex-cone dominance in the discrete Multiple Criteria Decision Making framework. In our current paper, we revisit the old idea from a new standpoint and provide the mathematical theory leading to a dual-cone based approach to solving such problems. Our paper makes the old results computationally more tractable. The results provided in the present paper also help extend the theory.

[1]  Salvatore Greco,et al.  Rough sets theory for multicriteria decision analysis , 2001, Eur. J. Oper. Res..

[2]  S. Zionts,et al.  Theory of convex cones in multicriteria decision making , 1988 .

[3]  J. Wallenius,et al.  On value efficiency , 2014 .

[4]  Panu Korhonen,et al.  An algorithm for projecting a reference direction onto the nondominated set of given points , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[5]  S. Zionts,et al.  Solving the Discrete Multiple Criteria Problem using Convex Cones , 1984 .

[6]  Majid Soleimani-damaneh,et al.  Characterization of nonsmooth quasiconvex and pseudoconvex functions , 2007 .

[7]  Srinivas Y. Prasad,et al.  Use of Convex Cones in Interactive Multiple Objective Decision Making , 1997 .

[8]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  Hong Yan,et al.  A method of transferring cones of intersection form to cones of sum form and its applications in data envelopment analysis models , 2000, Int. J. Syst. Sci..

[10]  Murat Köksalan,et al.  Interactive Approaches for Discrete Alternative Multiple Criteria Decision Making with Monotone Utility Functions , 1995 .

[11]  Stanley Zionts,et al.  A multiple criteria method for choosing among discrete alternatives , 1981 .

[12]  Pekka Korhonen,et al.  A visual reference direction approach to solving discrete multiple criteria problems , 1988 .

[13]  Hanif D. Sherali,et al.  Linear Programming and Network Flows , 1977 .