### Abstract

The classical problem of ranking alternatives when there exists partial information on the scaling constants for additive multi-attribute utility functions (MAUFs) is reexamined. Most approaches assume that the unknown scaling constants can be precisely known. In this paper, we argue that this assumption may not be realistic, and we develop a new approach based on an assumption that is less restrictive and does not require that the Decision Maker be "consistent" over the given partial information regarding the unknown scaling constants. Definitions and computationally efficient procedures are developed to identify nondominated alternatives with respect to partial information on the scaling constants, which is called "utility nondominancy." The concepts and procedures developed demonstrate, through two tests (solving two linear programming problems), whether or not the set of alternatives can be further screened. Finding the best alternative via an interactive method in which the proportion of alternatives screened may be changed is discussed. The approach is generalized and related to other MAUF structures such as multilinear, quasi-concave, and quasi-convex. It is demonstrated that linear programming is sufficient to solve all ensuing problems. Some examples are provided.

Original language | English (US) |
---|---|

Pages (from-to) | 69-87 |

Number of pages | 19 |

Journal | Applied Mathematics and Computation |

Volume | 60 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1994 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

### Cite this

*Applied Mathematics and Computation*,

*60*(1), 69-87. https://doi.org/10.1016/0096-3003(94)90207-0

}

*Applied Mathematics and Computation*, vol. 60, no. 1, pp. 69-87. https://doi.org/10.1016/0096-3003(94)90207-0

**Screening discrete alternatives with imprecisely assessed additive multi-attribute functions.** / Malakooti, B.; Duckstein, Lucien; Ravindran, Arunachalam.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Screening discrete alternatives with imprecisely assessed additive multi-attribute functions

AU - Malakooti, B.

AU - Duckstein, Lucien

AU - Ravindran, Arunachalam

PY - 1994/1/1

Y1 - 1994/1/1

N2 - The classical problem of ranking alternatives when there exists partial information on the scaling constants for additive multi-attribute utility functions (MAUFs) is reexamined. Most approaches assume that the unknown scaling constants can be precisely known. In this paper, we argue that this assumption may not be realistic, and we develop a new approach based on an assumption that is less restrictive and does not require that the Decision Maker be "consistent" over the given partial information regarding the unknown scaling constants. Definitions and computationally efficient procedures are developed to identify nondominated alternatives with respect to partial information on the scaling constants, which is called "utility nondominancy." The concepts and procedures developed demonstrate, through two tests (solving two linear programming problems), whether or not the set of alternatives can be further screened. Finding the best alternative via an interactive method in which the proportion of alternatives screened may be changed is discussed. The approach is generalized and related to other MAUF structures such as multilinear, quasi-concave, and quasi-convex. It is demonstrated that linear programming is sufficient to solve all ensuing problems. Some examples are provided.

AB - The classical problem of ranking alternatives when there exists partial information on the scaling constants for additive multi-attribute utility functions (MAUFs) is reexamined. Most approaches assume that the unknown scaling constants can be precisely known. In this paper, we argue that this assumption may not be realistic, and we develop a new approach based on an assumption that is less restrictive and does not require that the Decision Maker be "consistent" over the given partial information regarding the unknown scaling constants. Definitions and computationally efficient procedures are developed to identify nondominated alternatives with respect to partial information on the scaling constants, which is called "utility nondominancy." The concepts and procedures developed demonstrate, through two tests (solving two linear programming problems), whether or not the set of alternatives can be further screened. Finding the best alternative via an interactive method in which the proportion of alternatives screened may be changed is discussed. The approach is generalized and related to other MAUF structures such as multilinear, quasi-concave, and quasi-convex. It is demonstrated that linear programming is sufficient to solve all ensuing problems. Some examples are provided.

UR - http://www.scopus.com/inward/record.url?scp=38149144811&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38149144811&partnerID=8YFLogxK

U2 - 10.1016/0096-3003(94)90207-0

DO - 10.1016/0096-3003(94)90207-0

M3 - Article

AN - SCOPUS:38149144811

VL - 60

SP - 69

EP - 87

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 1

ER -