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Value Functions When Decision Criteria Are Not Totally Substitutable

Author

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  • Jayavel Sounderpandian

    (University of Wisconsin–Parkside, Kenosha, Wisconsin)

Abstract

A necessary condition for the widely used additive value function is total preferential independence, or somewhat equivalently, total substitutability among the decision criteria. We consider cases where total substitutability is absent, and study the value functions that are applicable to such cases. First we take the case of total nonsubstitutability, and prove that the maximin value function is appropriate for it. This result easily extends to the closely related maximax value function. Next we consider the case where there is neither total substitutability nor total nonsubstitutability, and show how a minsum value function can be applicable. A minsum function is one that uses only addition and minimum extraction operations. We explain how the structure of a minsum function can be inferred from substitutability information. In the process, we encounter certain subsets of criteria which we call chains and cuts.

Suggested Citation

  • Jayavel Sounderpandian, 1991. "Value Functions When Decision Criteria Are Not Totally Substitutable," Operations Research, INFORMS, vol. 39(4), pages 592-600, August.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:4:p:592-600
    DOI: 10.1287/opre.39.4.592
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    Cited by:

    1. Beccacece, Francesca & Borgonovo, Emanuele & Buzzard, Greg & Cillo, Alessandra & Zionts, Stanley, 2015. "Elicitation of multiattribute value functions through high dimensional model representations: Monotonicity and interactions," European Journal of Operational Research, Elsevier, vol. 246(2), pages 517-527.
    2. Prinz, Aloys & Bünger, Björn, 2012. "Balancing ‘full life’: An economic approach to the route to happiness," Journal of Economic Psychology, Elsevier, vol. 33(1), pages 58-70.

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