On a conjecture with implications for multicriteria decision making

TL;DR

This paper proves Soland's conjecture that an efficient solution in multicriteria optimization does not necessarily require a continuous, strictly increasing, and strictly concave criterion space function to attain its maximum, impacting decision-making approaches.

Contribution

It establishes a proof of Soland's conjecture, revealing that certain assumptions about criterion functions are not necessary for optimal solutions in multicriteria optimization.

Findings

Efficient solutions may exist without a strictly concave criterion function.

The result challenges common assumptions in multicriteria decision making.

Implications for designing decision-making models and criterion functions.

Abstract

I prove Richard Soland's conjecture that for an efficient solution to a multicriteria optimization problem, there need not exist a continuous, strictly increasing and strictly concave criterion space function that attains its maximum at the vector of criteria values achieved by that solution. I work out an important implication of this result for multicriteria decision making.